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Sample records for two-point boundary-value problem

  1. Solving fuzzy two-point boundary value problem using fuzzy Laplace transform

    OpenAIRE

    Ahmad, Latif; Farooq, Muhammad; Ullah, Saif; Abdullah, Saleem

    2014-01-01

    A natural way to model dynamic systems under uncertainty is to use fuzzy boundary value problems (FBVPs) and related uncertain systems. In this paper we use fuzzy Laplace transform to find the solution of two-point boundary value under generalized Hukuhara differentiability. We illustrate the method for the solution of the well known two-point boundary value problem Schrodinger equation, and homogeneous boundary value problem. Consequently, we investigate the solutions of FBVPs under as a ne...

  2. Solving inverse two-point boundary value problems using collage coding

    Science.gov (United States)

    Kunze, H.; Murdock, S.

    2006-08-01

    The method of collage coding, with its roots in fractal imaging, is the central tool in a recently established rigorous framework for solving inverse initial value problems for ordinary differential equations (Kunze and Vrscay 1999 Inverse Problems 15 745-70). We extend these ideas to solve the following inverse problem: given a function u(x) on [A, B] (which may be the interpolation of data points), determine a two-point boundary value problem on [A, B] which admits u(x) as a solution as closely as desired. The solution of such inverse problems may be useful in parameter estimation or determination of potential functional forms of the underlying differential equation. We discuss ways to improve results, including the development of a partitioning scheme. Several examples are considered.

  3. Existence and uniqueness for a two-point interface boundary value problem

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    Rakhim Aitbayev

    2013-10-01

    Full Text Available We obtain sufficient conditions, easily verifiable, for the existence and uniqueness of piecewise smooth solutions of a linear two-point boundary-value problem with general interface conditions. The coefficients of the differential equation may have jump discontinuities at the interface point. As an example, the conditions obtained are applied to a problem with typical interface such as perfect contact, non-perfect contact, and flux jump conditions.

  4. A New Numerical Algorithm for Two-Point Boundary Value Problems

    OpenAIRE

    Guo, Lihua; Wu, Boying; Zhang, Dazhi

    2014-01-01

    We present a new numerical algorithm for two-point boundary value problems. We first present the exact solution in the form of series and then prove that the n-term numerical solution converges uniformly to the exact solution. Furthermore, we establish the numerical stability and error analysis. The numerical results show the effectiveness of the proposed algorithm.

  5. Solving Singular Two-Point Boundary Value Problems Using Continuous Genetic Algorithm

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    Omar Abu Arqub

    2012-01-01

    Full Text Available In this paper, the continuous genetic algorithm is applied for the solution of singular two-point boundary value problems, where smooth solution curves are used throughout the evolution of the algorithm to obtain the required nodal values. The proposed technique might be considered as a variation of the finite difference method in the sense that each of the derivatives is replaced by an appropriate difference quotient approximation. This novel approach possesses main advantages; it can be applied without any limitation on the nature of the problem, the type of singularity, and the number of mesh points. Numerical examples are included to demonstrate the accuracy, applicability, and generality of the presented technique. The results reveal that the algorithm is very effective, straightforward, and simple.

  6. A priori bounds for solutions of two-point boundary value problems using differential inequalities

    International Nuclear Information System (INIS)

    Vidossich, G.

    1979-01-01

    Two point boundary value problems for systems of differential equations are studied with a new approach based on differential inequalities of first order. This leads to the following results: (i) one-sided conditions are enough, in the sense that the inner product is substituted to the norm; (ii) the upper bound exists for practically any kind of equations and boundary value problem if the interval is sufficiently small since it depends on the Peano existence theorem; (iii) the bound seems convenient when the equation has some singularity in t as well as when sigular problems are considered. (author)

  7. An analytical approximation scheme to two-point boundary value problems of ordinary differential equations

    International Nuclear Information System (INIS)

    Boisseau, Bruno; Forgacs, Peter; Giacomini, Hector

    2007-01-01

    A new (algebraic) approximation scheme to find global solutions of two-point boundary value problems of ordinary differential equations (ODEs) is presented. The method is applicable for both linear and nonlinear (coupled) ODEs whose solutions are analytic near one of the boundary points. It is based on replacing the original ODEs by a sequence of auxiliary first-order polynomial ODEs with constant coefficients. The coefficients in the auxiliary ODEs are uniquely determined from the local behaviour of the solution in the neighbourhood of one of the boundary points. The problem of obtaining the parameters of the global (connecting) solutions, analytic at one of the boundary points, reduces to find the appropriate zeros of algebraic equations. The power of the method is illustrated by computing the approximate values of the 'connecting parameters' for a number of nonlinear ODEs arising in various problems in field theory. We treat in particular the static and rotationally symmetric global vortex, the skyrmion, the Abrikosov-Nielsen-Olesen vortex, as well as the 't Hooft-Polyakov magnetic monopole. The total energy of the skyrmion and of the monopole is also computed by the new method. We also consider some ODEs coming from the exact renormalization group. The ground-state energy level of the anharmonic oscillator is also computed for arbitrary coupling strengths with good precision. (fast track communication)

  8. Use of Green's functions in the numerical solution of two-point boundary value problems

    Science.gov (United States)

    Gallaher, L. J.; Perlin, I. E.

    1974-01-01

    This study investigates the use of Green's functions in the numerical solution of the two-point boundary value problem. The first part deals with the role of the Green's function in solving both linear and nonlinear second order ordinary differential equations with boundary conditions and systems of such equations. The second part describes procedures for numerical construction of Green's functions and considers briefly the conditions for their existence. Finally, there is a description of some numerical experiments using nonlinear problems for which the known existence, uniqueness or convergence theorems do not apply. Examples here include some problems in finding rendezvous orbits of the restricted three body system.

  9. Modified Differential Transform Method for Two Singular Boundary Values Problems

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    Yinwei Lin

    2014-01-01

    Full Text Available This paper deals with the two singular boundary values problems of second order. Two singular points are both boundary values points of the differential equation. The numerical solutions are developed by modified differential transform method (DTM for expanded point. Linear and nonlinear models are solved by this method to get more reliable and efficient numerical results. It can also solve ordinary differential equations where the traditional one fails. Besides, we give the convergence of this new method.

  10. Two-point boundary value and Cauchy formulations in an axisymmetrical MHD equilibrium problem

    International Nuclear Information System (INIS)

    Atanasiu, C.V.; Subbotin, A.A.

    1999-01-01

    In this paper we present two equilibrium solvers for axisymmetrical toroidal configurations, both based on the expansion in poloidal angle method. The first one has been conceived as a two-point boundary value solver in a system of coordinates with straight field lines, while the second one uses a well-conditioned Cauchy formulation of the problem in a general curvilinear coordinate system. In order to check the capability of our moment methods to describe equilibrium accurately, a comparison of the moment solutions with analytical solutions obtained for a Solov'ev equilibrium has been performed. (author)

  11. METHOD OF GREEN FUNCTIONS IN MATHEMATICAL MODELLING FOR TWO-POINT BOUNDARY-VALUE PROBLEMS

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    E. V. Dikareva

    2015-01-01

    Full Text Available Summary. In many applied problems of control, optimization, system theory, theoretical and construction mechanics, for problems with strings and nods structures, oscillation theory, theory of elasticity and plasticity, mechanical problems connected with fracture dynamics and shock waves, the main instrument for study these problems is a theory of high order ordinary differential equations. This methodology is also applied for studying mathematical models in graph theory with different partitioning based on differential equations. Such equations are used for theoretical foundation of mathematical models but also for constructing numerical methods and computer algorithms. These models are studied with use of Green function method. In the paper first necessary theoretical information is included on Green function method for multi point boundary-value problems. The main equation is discussed, notions of multi-point boundary conditions, boundary functionals, degenerate and non-degenerate problems, fundamental matrix of solutions are introduced. In the main part the problem to study is formulated in terms of shocks and deformations in boundary conditions. After that the main results are formulated. In theorem 1 conditions for existence and uniqueness of solutions are proved. In theorem 2 conditions are proved for strict positivity and equal measureness for a pair of solutions. In theorem 3 existence and estimates are proved for the least eigenvalue, spectral properties and positivity of eigenfunctions. In theorem 4 the weighted positivity is proved for the Green function. Some possible applications are considered for a signal theory and transmutation operators.

  12. m-POINT BOUNDARY VALUE PROBLEM FOR SECOND ORDER IMPULSIVE DIFFERENTIAL EQUATION AT RESONANCE

    Institute of Scientific and Technical Information of China (English)

    2012-01-01

    In his paper,we obtain a general theorem concerning the existence of solutions to an m-point boundary value problem for the second-order differential equation with impulses.Moreover,the result can also be applied to study the usual m-point boundary value problem at resonance without impulses.

  13. Solution matching for a three-point boundary-value problem on atime scale

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    Martin Eggensperger

    2004-07-01

    Full Text Available Let $mathbb{T}$ be a time scale such that $t_1, t_2, t_3 in mathbb{T}$. We show the existence of a unique solution for the three-point boundary value problem $$displaylines{ y^{DeltaDeltaDelta}(t = f(t, y(t, y^Delta(t, y^{DeltaDelta}(t, quad t in [t_1, t_3] cap mathbb{T},cr y(t_1 = y_1, quad y(t_2 = y_2, quad y(t_3 = y_3,. }$$ We do this by matching a solution to the first equation satisfying a two-point boundary conditions on $[t_1, t_2] cap mathbb{T}$ with a solution satisfying a two-point boundary conditions on $[t_2, t_3] cap mathbb{T}$.

  14. EXISTENCE OF POSITIVE SOLUTION TO TWO-POINT BOUNDARY VALUE PROBLEM FOR A SYSTEM OF SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    2009-01-01

    In this paper, we consider a two-point boundary value problem for a system of second order ordinary differential equations. Under some conditions, we show the existence of positive solution to the system of second order ordinary differential equa-tions.

  15. Comments on the comparison of global methods for linear two-point boundary value problems

    International Nuclear Information System (INIS)

    de Boor, C.; Swartz, B.

    1977-01-01

    A more careful count of the operations involved in solving the linear system associated with collocation of a two-point boundary value problem using a rough splines reverses results recently reported by others in this journal. In addition, it is observed that the use of the technique of ''condensation of parameters'' can decrease the computer storage required. Furthermore, the use of a particular highly localized basis can also reduce the setup time when the mesh is irregular. Finally, operation counts are roughly estimated for the solution of certain linear system associated with two competing collocation methods; namely, collocation with smooth splines and collocation of the equivalent first order system with continuous piecewise polynomials

  16. Positive Solutions of Two-Point Boundary Value Problems for Monge-Ampère Equations

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    Baoqiang Yan

    2015-01-01

    Full Text Available This paper considers the following boundary value problem: ((-u'(tn'=ntn-1f(u(t,  01 is odd. We establish the method of lower and upper solutions for some boundary value problems which generalizes the above equations and using this method we present a necessary and sufficient condition for the existence of positive solutions to the above boundary value problem and some sufficient conditions for the existence of positive solutions.

  17. Numerical solutions of a three-point boundary value problem with an ...

    African Journals Online (AJOL)

    Numerical solutions of a three-point boundary value problem with an integral condition for a third-order partial differential equation by using Laplace transform method Solutions numeriques d'un probleme pour une classe d'equations differentielles d'ordr.

  18. Unique solvability of some two-point boundary value problems for linear functional differential equations with singularities

    Czech Academy of Sciences Publication Activity Database

    Rontó, András; Samoilenko, A. M.

    2007-01-01

    Roč. 41, - (2007), s. 115-136 ISSN 1512-0015 R&D Projects: GA ČR(CZ) GA201/06/0254 Institutional research plan: CEZ:AV0Z10190503 Keywords : two-point problem * functional differential equation * singular boundary problem Subject RIV: BA - General Mathematics

  19. On nonseparated three-point boundary value problems for linear functional differential equations

    Czech Academy of Sciences Publication Activity Database

    Rontó, András; Rontó, M.

    2011-01-01

    Roč. 2011, - (2011), s. 326052 ISSN 1085-3375 Institutional research plan: CEZ:AV0Z10190503 Keywords : functional-differential equation * three-point boundary value problem * nonseparated boundary condition Subject RIV: BA - General Mathematics Impact factor: 1.318, year: 2011 http://www.hindawi.com/journals/ aaa /2011/326052/

  20. Triple solutions for multi-point boundary-value problem with p-Laplace operator

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    Yansheng Liu

    2009-11-01

    Full Text Available Using a fixed point theorem due to Avery and Peterson, this article shows the existence of solutions for multi-point boundary-value problem with p-Laplace operator and parameters. Also, we present an example to illustrate the results obtained.

  1. Existence of positive solutions for a multi-point four-order boundary-value problem

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    Le Xuan Truong

    2011-10-01

    Full Text Available The article shows sufficient conditions for the existence of positive solutions to a multi-point boundary-value problem for a fourth-order differential equation. Our main tools are the Guo-Krasnoselskii fixed point theorem and the monotone iterative technique. We also show that the set of positive solutions is compact.

  2. On Existence of Solutions to the Caputo Type Fractional Order Three-Point Boundary Value Problems

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    B.M.B. Krushna

    2016-10-01

    Full Text Available In this paper, we establish the existence of solutions to the fractional order three-point boundary value problems by utilizing Banach contraction principle and Schaefer's fixed point theorem.

  3. Numerical solution of singularity-perturbed two-point boundary-value problems

    International Nuclear Information System (INIS)

    Masenge, R.W.P.

    1993-07-01

    Physical processes which involve transportation of slowly diffusing substances in a fast-flowing medium are mathematically modelled by so-called singularly-perturbed second order convection diffusion differential equations in which the convective first order terms dominate over the diffusive second order terms. In general, analytical solutions of such equations are characterized by having sharp solution fronts in some sections of the interior and/or the boundary of the domain of solution. The presence of these (usually very narrow) layer regions in the solution domain makes the task of globally approximating such solutions by standard numerical techniques very difficult. In this expository paper we use a simple one-dimensional prototype problem as a vehicle for analysing the nature of the numerical approximation difficulties involved. In the sequel we present, without detailed derivation, two practical numerical schemes which succeed in varying degrees in numerically resolving the layer of the solution to the prototype problem. (author). 3 refs, 1 fig., 1 tab

  4. A three-point Taylor algorithm for three-point boundary value problems

    NARCIS (Netherlands)

    J.L. López; E. Pérez Sinusía; N.M. Temme (Nico)

    2011-01-01

    textabstractWe consider second-order linear differential equations $\\varphi(x)y''+f(x)y'+g(x)y=h(x)$ in the interval $(-1,1)$ with Dirichlet, Neumann or mixed Dirichlet-Neumann boundary conditions given at three points of the interval: the two extreme points $x=\\pm 1$ and an interior point

  5. Positive solutions of three-point boundary-value problems for p-Laplacian singular differential equations

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    George N. Galanis

    2005-10-01

    Full Text Available In this paper we prove the existence of positive solutions for the three-point singular boundary-value problem$$ -[phi _{p}(u']'=q(tf(t,u(t,quad 0points and $g$ is a monotone continuous function defined on the real line $mathbb{R}$ with $g(0=0$ and $ug(ugeq 0$. Our approach is a combination of Nonlinear Alternative of Leray-Schauder with the properties of the associated vector field at the $(u,u'$ plane. More precisely, we show that the solutions of the above boundary-value problem remains away from the origin for the case where the nonlinearity is sublinear and so we avoid its singularity at $u=0$.

  6. Positive solutions of nonlinear fractional boundary value problems with Dirichlet boundary conditions

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    Qingkai Kong

    2012-02-01

    Full Text Available In this paper, we study the existence and multiplicity of positive solutions of a class of nonlinear fractional boundary value problems with  Dirichlet boundary conditions. By applying the fixed point theory on cones we establish a series of criteria for the existence of one, two, any arbitrary finite number, and an infinite number of positive solutions. A criterion for the nonexistence of positive solutions is also derived. Several examples are given for demonstration.

  7. On the Approximate Controllability of Some Semilinear Parabolic Boundary-Value Problems

    International Nuclear Information System (INIS)

    Diaz, J. I.; Henry, J.; Ramos, A. M.

    1998-01-01

    We prove the approximate controllability of several nonlinear parabolic boundary-value problems by means of two different methods: the first one can be called a Cancellation method and the second one uses the Kakutani fixed-point theorem

  8. Solvability of fractional multi-point boundary-value problems with p-Laplacian operator at resonance

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    Tengfei Shen

    2014-02-01

    Full Text Available In this article, we consider the multi-point boundary-value problem for nonlinear fractional differential equations with $p$-Laplacian operator: $$\\displaylines{ D_{0^+}^\\beta \\varphi_p (D_{0^+}^\\alpha u(t = f(t,u(t,D_{0^+}^{\\alpha - 2} u(t,D_{0^+}^{\\alpha - 1} u(t, D_{0^+}^\\alpha u(t,\\quad t \\in (0,1, \\cr u(0 = u'(0=D_{0^+}^\\alpha u(0 = 0,\\quad D_{0^+}^{\\alpha - 1} u(1 = \\sum_{i = 1}^m {\\sigma_i D_{0^+}^{\\alpha - 1} u(\\eta_i } , }$$ where $2 < \\alpha \\le 3$, $0 < \\beta \\le 1$, $3 < \\alpha + \\beta \\le 4$, $\\sum_{i = 1}^m {\\sigma_i } = 1$, $D_{0^+}^\\alpha$ is the standard Riemann-Liouville fractional derivative. $\\varphi_{p}(s=|s|^{p-2}s$ is p-Laplacians operator. The existence of solutions for above fractional boundary value problem is obtained by using the extension of Mawhin's continuation theorem due to Ge, which enrich konwn results. An example is given to illustrate the main result.

  9. Existence results for anisotropic discrete boundary value problems

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    Avci Avci

    2016-06-01

    Full Text Available In this article, we prove the existence of nontrivial weak solutions for a class of discrete boundary value problems. The main tools used here are the variational principle and critical point theory.

  10. Twin Positive Solutions of a Nonlinear m-Point Boundary Value Problem for Third-Order p-Laplacian Dynamic Equations on Time Scales

    Directory of Open Access Journals (Sweden)

    Wei Han

    2008-01-01

    Full Text Available Several existence theorems of twin positive solutions are established for a nonlinear m-point boundary value problem of third-order p-Laplacian dynamic equations on time scales by using a fixed point theorem. We present two theorems and four corollaries which generalize the results of related literature. As an application, an example to demonstrate our results is given. The obtained conditions are different from some known results.

  11. Bifurcation of solutions to Hamiltonian boundary value problems

    Science.gov (United States)

    McLachlan, R. I.; Offen, C.

    2018-06-01

    A bifurcation is a qualitative change in a family of solutions to an equation produced by varying parameters. In contrast to the local bifurcations of dynamical systems that are often related to a change in the number or stability of equilibria, bifurcations of boundary value problems are global in nature and may not be related to any obvious change in dynamical behaviour. Catastrophe theory is a well-developed framework which studies the bifurcations of critical points of functions. In this paper we study the bifurcations of solutions of boundary-value problems for symplectic maps, using the language of (finite-dimensional) singularity theory. We associate certain such problems with a geometric picture involving the intersection of Lagrangian submanifolds, and hence with the critical points of a suitable generating function. Within this framework, we then study the effect of three special cases: (i) some common boundary conditions, such as Dirichlet boundary conditions for second-order systems, restrict the possible types of bifurcations (for example, in generic planar systems only the A-series beginning with folds and cusps can occur); (ii) integrable systems, such as planar Hamiltonian systems, can exhibit a novel periodic pitchfork bifurcation; and (iii) systems with Hamiltonian symmetries or reversing symmetries can exhibit restricted bifurcations associated with the symmetry. This approach offers an alternative to the analysis of critical points in function spaces, typically used in the study of bifurcation of variational problems, and opens the way to the detection of more exotic bifurcations than the simple folds and cusps that are often found in examples.

  12. Boundary-value problems with free boundaries for elliptic systems of equations

    CERN Document Server

    Monakhov, V N

    1983-01-01

    This book is concerned with certain classes of nonlinear problems for elliptic systems of partial differential equations: boundary-value problems with free boundaries. The first part has to do with the general theory of boundary-value problems for analytic functions and its applications to hydrodynamics. The second presents the theory of quasiconformal mappings, along with the theory of boundary-value problems for elliptic systems of equations and applications of it to problems in the mechanics of continuous media with free boundaries: problems in subsonic gas dynamics, filtration theory, and problems in elastico-plasticity.

  13. Multi-point boundary value problems for linear functional-differential equations

    Czech Academy of Sciences Publication Activity Database

    Domoshnitsky, A.; Hakl, Robert; Půža, Bedřich

    2017-01-01

    Roč. 24, č. 2 (2017), s. 193-206 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : boundary value problems * linear functional-differential equations * functional-differential inequalities Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 0.290, year: 2016 https://www.degruyter.com/view/j/gmj.2017.24.issue-2/gmj-2016-0076/gmj-2016-0076. xml

  14. Multi-point boundary value problems for linear functional-differential equations

    Czech Academy of Sciences Publication Activity Database

    Domoshnitsky, A.; Hakl, Robert; Půža, Bedřich

    2017-01-01

    Roč. 24, č. 2 (2017), s. 193-206 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : boundary value problems * linear functional- differential equations * functional- differential inequalities Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 0.290, year: 2016 https://www.degruyter.com/view/j/gmj.2017.24.issue-2/gmj-2016-0076/gmj-2016-0076.xml

  15. Existence of solutions to boundary value problem of fractional differential equations with impulsive

    Directory of Open Access Journals (Sweden)

    Weihua JIANG

    2016-12-01

    Full Text Available In order to solve the boundary value problem of fractional impulsive differential equations with countable impulses and integral boundary conditions on the half line, the existence of solutions to the boundary problem is specifically studied. By defining suitable Banach spaces, norms and operators, using the properties of fractional calculus and applying the contraction mapping principle and Krasnoselskii's fixed point theorem, the existence of solutions for the boundary value problem of fractional impulsive differential equations with countable impulses and integral boundary conditions on the half line is proved, and examples are given to illustrate the existence of solutions to this kind of equation boundary value problems.

  16. Analytic Solution to Shell BoundaryValue Problems

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    Yu. I. Vinogradov

    2015-01-01

    Full Text Available Object of research is to find analytical solution to the shell boundaryvalue problems, i.e. to consider the solution for a class of problems concerning the mechanics of hoop closed shells strain.The objective of work is to create an analytical method to define a stress – strain state of shells under non-axisymmetric loading. Thus, a main goal is to derive the formulas – solutions of the linear ordinary differential equations with variable continuous coefficients.The partial derivative differential equations of mechanics of shells strain by Fourier's method of variables division are reduced to the system of the differential equations with ordinary derivatives. The paper presents the obtained formulas to define solutions of the uniform differential equations and received on their basis formulas to define a particular solution depending on a type of the right parts of the differential equations.The analytical algorithm of the solution of a boundary task uses an approach to transfer the boundary conditions to the randomly chosen point of an interval of changing independent variable through the solution of the canonical matrix ordinary differential equation with the subsequent solution of system of algebraic equations for compatibility of boundary conditions at this point. Efficiency of algorithm is based on the fact that the solution of the ordinary differential equations is defined as the values of Cauchy – Krylova functions, which meet initial arbitrary conditions.The results of researches presented in work are useful to experts in the field of calculus mathematics, dealing with solution of systems of linear ordinary differential equations and creation of effective analytical computing methods to solve shell boundaryvalue problems.

  17. Positive solutions of a three-point boundary-value problem for differential equations with damping and actively bounded delayed forcing term

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    George L. Karakostas

    2006-08-01

    Full Text Available We provide sufficient conditions for the existence of positive solutions of a three-point boundary value problem concerning a second order delay differential equation with damping and forcing term whose the delayed part is an actively bounded function, a meaning introduced in [19]. By writing the damping term as a difference of two factors one can extract more information on the solutions. (For instance, in an application, given in the last section, we can give the exact value of the norm of the solution.

  18. Boundary value problems and partial differential equations

    CERN Document Server

    Powers, David L

    2005-01-01

    Boundary Value Problems is the leading text on boundary value problems and Fourier series. The author, David Powers, (Clarkson) has written a thorough, theoretical overview of solving boundary value problems involving partial differential equations by the methods of separation of variables. Professors and students agree that the author is a master at creating linear problems that adroitly illustrate the techniques of separation of variables used to solve science and engineering.* CD with animations and graphics of solutions, additional exercises and chapter review questions* Nearly 900 exercises ranging in difficulty* Many fully worked examples

  19. Multiple Positive Solutions of a Nonlinear Four-Point Singular Boundary Value Problem with a p-Laplacian Operator on Time Scales

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    Shihuang Hong

    2009-01-01

    Full Text Available We present sufficient conditions for the existence of at least twin or triple positive solutions of a nonlinear four-point singular boundary value problem with a p-Laplacian dynamic equation on a time scale. Our results are obtained via some new multiple fixed point theorems.

  20. About potential of double layer and boundary value problems for Laplace equation

    International Nuclear Information System (INIS)

    Aleshin, M.V.

    1991-01-01

    An integral operator raisen by a kernel of the double layer's potential is investigated. The kernel is defined on S (S - two-digit variety of C 2 class presented by a boundary of the finite domain in R 3 ). The operator is considered on C(S). Following results are received: the operator's spectrum belongs to [-1,1]; it's eigenvalues and eigenfunctions may be found by Kellog's method; knowledge of the operator's spectrum is enough to construct it's resolvent. These properties permit to point out the determined interation processes, solving boundary value problems for Laplace equation. One of such processes - solving of Roben problem - is generalized on electrostatic problems. 6 refs

  1. POSITIVE SOLUTIONS OF A NONLINEAR THREE-POINT EIGENVALUE PROBLEM WITH INTEGRAL BOUNDARY CONDITIONS

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    FAOUZI HADDOUCHI

    2015-11-01

    Full Text Available In this paper, we study the existence of positive solutions of a three-point integral boundary value problem (BVP for the following second-order differential equation u''(t + \\lambda a(tf(u(t = 0; 0 0 is a parameter, 0 <\\eta < 1, 0 <\\alpha < 1/{\\eta}. . By using the properties of the Green's function and Krasnoselskii's fixed point theorem on cones, the eigenvalue intervals of the nonlinear boundary value problem are considered, some sufficient conditions for the existence of at least one positive solutions are established.

  2. Heat Kernel Asymptotics of Zaremba Boundary Value Problem

    Energy Technology Data Exchange (ETDEWEB)

    Avramidi, Ivan G. [Department of Mathematics, New Mexico Institute of Mining and Technology (United States)], E-mail: iavramid@nmt.edu

    2004-03-15

    The Zaremba boundary-value problem is a boundary value problem for Laplace-type second-order partial differential operators acting on smooth sections of a vector bundle over a smooth compact Riemannian manifold with smooth boundary but with discontinuous boundary conditions, which include Dirichlet boundary conditions on one part of the boundary and Neumann boundary conditions on another part of the boundary. We study the heat kernel asymptotics of Zaremba boundary value problem. The construction of the asymptotic solution of the heat equation is described in detail and the heat kernel is computed explicitly in the leading approximation. Some of the first nontrivial coefficients of the heat kernel asymptotic expansion are computed explicitly.

  3. Fourier analysis and boundary value problems

    CERN Document Server

    Gonzalez-Velasco, Enrique A

    1996-01-01

    Fourier Analysis and Boundary Value Problems provides a thorough examination of both the theory and applications of partial differential equations and the Fourier and Laplace methods for their solutions. Boundary value problems, including the heat and wave equations, are integrated throughout the book. Written from a historical perspective with extensive biographical coverage of pioneers in the field, the book emphasizes the important role played by partial differential equations in engineering and physics. In addition, the author demonstrates how efforts to deal with these problems have lead to wonderfully significant developments in mathematics.A clear and complete text with more than 500 exercises, Fourier Analysis and Boundary Value Problems is a good introduction and a valuable resource for those in the field.Key Features* Topics are covered from a historical perspective with biographical information on key contributors to the field* The text contains more than 500 exercises* Includes practical applicati...

  4. three solutions for a semilinear elliptic boundary value problem

    Indian Academy of Sciences (India)

    69

    Keywords: The Laplacian operator, elliptic problem, Nehari man- ifold, three critical points, weak solution. 1. Introduction. Let Ω be a smooth bounded domain in RN , N ≥ 3 . In this work, we show the existence of at least three solutions for the semilinear elliptic boundary- value problem: (Pλ).. −∆u = f(x)|u(x)|p−2u(x) + ...

  5. An inverse boundary value problem for the Schroedinger operator with vector potentials in two dimensions

    International Nuclear Information System (INIS)

    Ziqi Sun

    1993-01-01

    During the past few years a considerable interest has been focused on the inverse boundary value problem for the Schroedinger operator with a scalar (electric) potential. The popularity gained by this subject seems to be due to its connection with the inverse scattering problem at fixed energy, the inverse conductivity problem and other important inverse problems. This paper deals with an inverse boundary value problem for the Schroedinger operator with vector (electric and magnetic) potentials. As in the case of the scalar potential, results of this study would have immediate consequences in the inverse scattering problem for magnetic field at fixed energy. On the other hand, inverse boundary value problems for elliptic operators are of independent interest. The study is partly devoted to the understanding of the inverse boundary value problem for a class of general elliptic operator of second order. Note that a self-adjoint elliptic operator of second order with Δ as its principal symbol can always be written as a Schroedinger operator with vector potentials

  6. A Boundary Value Problem for Introductory Physics?

    Science.gov (United States)

    Grundberg, Johan

    2008-01-01

    The Laplace equation has applications in several fields of physics, and problems involving this equation serve as paradigms for boundary value problems. In the case of the Laplace equation in a disc there is a well-known explicit formula for the solution: Poisson's integral. We show how one can derive this formula, and in addition two equivalent…

  7. Mixed Boundary Value Problem on Hypersurfaces

    Directory of Open Access Journals (Sweden)

    R. DuDuchava

    2014-01-01

    Full Text Available The purpose of the present paper is to investigate the mixed Dirichlet-Neumann boundary value problems for the anisotropic Laplace-Beltrami equation divC(A∇Cφ=f on a smooth hypersurface C with the boundary Γ=∂C in Rn. A(x is an n×n bounded measurable positive definite matrix function. The boundary is decomposed into two nonintersecting connected parts Γ=ΓD∪ΓN and on ΓD the Dirichlet boundary conditions are prescribed, while on ΓN the Neumann conditions. The unique solvability of the mixed BVP is proved, based upon the Green formulae and Lax-Milgram Lemma. Further, the existence of the fundamental solution to divS(A∇S is proved, which is interpreted as the invertibility of this operator in the setting Hp,#s(S→Hp,#s-2(S, where Hp,#s(S is a subspace of the Bessel potential space and consists of functions with mean value zero.

  8. State-dependent impulses boundary value problems on compact interval

    CERN Document Server

    Rachůnková, Irena

    2015-01-01

    This book offers the reader a new approach to the solvability of boundary value problems with state-dependent impulses and provides recently obtained existence results for state dependent impulsive problems with general linear boundary conditions. It covers fixed-time impulsive boundary value problems both regular and singular and deals with higher order differential equations or with systems that are subject to general linear boundary conditions. We treat state-dependent impulsive boundary value problems, including a new approach giving effective conditions for the solvability of the Dirichlet problem with one state-dependent impulse condition and we show that the depicted approach can be extended to problems with a finite number of state-dependent impulses. We investigate the Sturm–Liouville boundary value problem for a more general right-hand side of a differential equation. Finally, we offer generalizations to higher order differential equations or differential systems subject to general linear boundary...

  9. Collisional plasma transport: two-dimensional scalar formulation of the initial boundary value problem and quasi one-dimensional models

    International Nuclear Information System (INIS)

    Mugge, J.W.

    1979-10-01

    The collisional plasma transport problem is formulated as an initial boundary value problem for general characteristic boundary conditions. Starting from the full set of hydrodynamic and electrodynamic equations an expansion in the electron-ion mass ratio together with a multiple timescale method yields simplified equations on each timescale. On timescales where many collisions have taken place for the simplified equations the initial boundary value problem is formulated. Through the introduction of potentials a two-dimensional scalar formulation in terms of quasi-linear integro-differential equations of second order for a domain consisting of plasma and vacuum sub-domains is obtained. (Auth.)

  10. Asymptotic behaviour of solutions of the first boundary-value problem for strongly hyperbolic systems near a conical point at the boundary of the domain

    International Nuclear Information System (INIS)

    Hung, Nguyen M

    1999-01-01

    An existence and uniqueness theorem for generalized solutions of the first initial-boundary-value problem for strongly hyperbolic systems in bounded domains is established. The question of estimates in Sobolev spaces of the derivatives with respect to time of the generalized solution is discussed. It is shown that the smoothness of generalized solutions with respect to time is independent of the structure of the boundary of the domain but depends on the coefficients of the right-hand side. Results on the smoothness of the generalized solution and its asymptotic behaviour in a neighbourhood of a conical boundary point are also obtained

  11. Positive solutions and eigenvalues of nonlocal boundary-value problems

    Directory of Open Access Journals (Sweden)

    Jifeng Chu

    2005-07-01

    Full Text Available We study the ordinary differential equation $x''+lambda a(tf(x=0$ with the boundary conditions $x(0=0$ and $x'(1=int_{eta}^{1}x'(sdg(s$. We characterize values of $lambda$ for which boundary-value problem has a positive solution. Also we find appropriate intervals for $lambda$ so that there are two positive solutions.

  12. Boundary-value problems for first and second order functional differential inclusions

    Directory of Open Access Journals (Sweden)

    Shihuang Hong

    2003-03-01

    Full Text Available This paper presents sufficient conditions for the existence of solutions to boundary-value problems of first and second order multi-valued differential equations in Banach spaces. Our results obtained using fixed point theorems, and lead to new existence principles.

  13. Analytic approximations to nonlinear boundary value problems modeling beam-type nano-electromechanical systems

    Energy Technology Data Exchange (ETDEWEB)

    Zou, Li [Dalian Univ. of Technology, Dalian City (China). State Key Lab. of Structural Analysis for Industrial Equipment; Liang, Songxin; Li, Yawei [Dalian Univ. of Technology, Dalian City (China). School of Mathematical Sciences; Jeffrey, David J. [Univ. of Western Ontario, London (Canada). Dept. of Applied Mathematics

    2017-06-01

    Nonlinear boundary value problems arise frequently in physical and mechanical sciences. An effective analytic approach with two parameters is first proposed for solving nonlinear boundary value problems. It is demonstrated that solutions given by the two-parameter method are more accurate than solutions given by the Adomian decomposition method (ADM). It is further demonstrated that solutions given by the ADM can also be recovered from the solutions given by the two-parameter method. The effectiveness of this method is demonstrated by solving some nonlinear boundary value problems modeling beam-type nano-electromechanical systems.

  14. Two-dimensional boundary-value problem for ion-ion diffusion

    International Nuclear Information System (INIS)

    Tuszewski, M.; Lichtenberg, A.J.

    1977-01-01

    Like-particle diffusion is usually negligible compared with unlike-particle diffusion because it is two orders higher in spatial derivatives. When the ratio of the ion gyroradius to the plasma transverse dimension is of the order of the fourth root of the mass ratio, previous one-dimensional analysis indicated that like-particle diffusion is significant. A two-dimensional boundary-value problem for ion-ion diffusion is investigated. Numerical solutions are found with models for which the nonlinear partial differential equation reduces to an ordinary fourth-order differential equation. These solutions indicate that the ion-ion losses are higher by a factor of six for a slab geometry, and by a factor of four for circular geometry, than estimated from dimensional analysis. The solutions are applied to a multiple mirror experiment stabilized with a quadrupole magnetic field which generates highly elliptical flux surfaces. It is found that the ion-ion losses dominate the electron-ion losses and that these classical radial losses contribute to a significant decrease of plasma lifetime, in qualitiative agreement with the experimental results

  15. Boundary Value Problems Arising in Kalman Filtering

    Directory of Open Access Journals (Sweden)

    Sinem Ertürk

    2009-01-01

    Full Text Available The classic Kalman filtering equations for independent and correlated white noises are ordinary differential equations (deterministic or stochastic with the respective initial conditions. Changing the noise processes by taking them to be more realistic wide band noises or delayed white noises creates challenging partial differential equations with initial and boundary conditions. In this paper, we are aimed to give a survey of this connection between Kalman filtering and boundary value problems, bringing them into the attention of mathematicians as well as engineers dealing with Kalman filtering and boundary value problems.

  16. Boundary Value Problems Arising in Kalman Filtering

    Directory of Open Access Journals (Sweden)

    Bashirov Agamirza

    2008-01-01

    Full Text Available The classic Kalman filtering equations for independent and correlated white noises are ordinary differential equations (deterministic or stochastic with the respective initial conditions. Changing the noise processes by taking them to be more realistic wide band noises or delayed white noises creates challenging partial differential equations with initial and boundary conditions. In this paper, we are aimed to give a survey of this connection between Kalman filtering and boundary value problems, bringing them into the attention of mathematicians as well as engineers dealing with Kalman filtering and boundary value problems.

  17. Positive solutions for a fourth order boundary value problem

    Directory of Open Access Journals (Sweden)

    Bo Yang

    2005-02-01

    Full Text Available We consider a boundary value problem for the beam equation, in which the boundary conditions mean that the beam is embedded at one end and free at the other end. Some new estimates to the positive solutions to the boundary value problem are obtained. Some sufficient conditions for the existence of at least one positive solution for the boundary value problem are established. An example is given at the end of the paper to illustrate the main results.

  18. Boundary value problem for Caputo-Hadamard fractional differential equations

    Directory of Open Access Journals (Sweden)

    Yacine Arioua

    2017-09-01

    Full Text Available The aim of this work is to study the existence and uniqueness solutions for boundary value problem of nonlinear fractional differential equations with Caputo-Hadamard derivative in bounded domain. We used the standard and Krasnoselskii's fixed point theorems. Some new results of existence and uniqueness solutions for Caputo-Hadamard fractional equations are obtained.

  19. Boundary value problems of holomorphic vector functions in 1D QCs

    International Nuclear Information System (INIS)

    Gao Yang; Zhao Yingtao; Zhao Baosheng

    2007-01-01

    By means of the generalized Stroh formalism, two-dimensional (2D) problems of one-dimensional (1D) quasicrystals (QCs) elasticity are turned into the boundary value problems of holomorphic vector functions in a given region. If the conformal mapping from an ellipse to a circle is known, a general method for solving the boundary value problems of holomorphic vector functions can be presented. To illustrate its utility, by using the necessary and sufficient condition of boundary value problems of holomorphic vector functions, we consider two basic 2D problems in 1D QCs, that is, an elliptic hole and a rigid line inclusion subjected to uniform loading at infinity. For the crack problem, the intensity factors of phonon and phason fields are determined, and the physical sense of the results relative to phason and the difference between mechanical behaviors of the crack problem in crystals and QCs are figured out. Moreover, the same procedure can be used to deal with the elastic problems for 2D and three-dimensional (3D) QCs

  20. Numerical solution of system of boundary value problems using B-spline with free parameter

    Science.gov (United States)

    Gupta, Yogesh

    2017-01-01

    This paper deals with method of B-spline solution for a system of boundary value problems. The differential equations are useful in various fields of science and engineering. Some interesting real life problems involve more than one unknown function. These result in system of simultaneous differential equations. Such systems have been applied to many problems in mathematics, physics, engineering etc. In present paper, B-spline and B-spline with free parameter methods for the solution of a linear system of second-order boundary value problems are presented. The methods utilize the values of cubic B-spline and its derivatives at nodal points together with the equations of the given system and boundary conditions, ensuing into the linear matrix equation.

  1. Numeric treatment of nonlinear second order multi-point boundary value problems using ANN, GAs and sequential quadratic programming technique

    Directory of Open Access Journals (Sweden)

    Zulqurnain Sabir

    2014-06-01

    Full Text Available In this paper, computational intelligence technique are presented for solving multi-point nonlinear boundary value problems based on artificial neural networks, evolutionary computing approach, and active-set technique. The neural network is to provide convenient methods for obtaining useful model based on unsupervised error for the differential equations. The motivation for presenting this work comes actually from the aim of introducing a reliable framework that combines the powerful features of ANN optimized with soft computing frameworks to cope with such challenging system. The applicability and reliability of such methods have been monitored thoroughly for various boundary value problems arises in science, engineering and biotechnology as well. Comprehensive numerical experimentations have been performed to validate the accuracy, convergence, and robustness of the designed scheme. Comparative studies have also been made with available standard solution to analyze the correctness of the proposed scheme.

  2. Positive Solutions of Three-Order Delayed Periodic Boundary Value Problems

    Directory of Open Access Journals (Sweden)

    Na Wang

    2017-01-01

    Full Text Available Our main purpose is to consider the existence of positive solutions for three-order two-point boundary value problem in the following form: u′′′(t+ρ3u(t=f(t,u(t-τ,  0≤t≤2π,  u(i(0=u(i(2π,  i=1,2,  u(t=σ,  -τ≤t≤0, where σ,ρ, and τ are given constants satisfying τ∈(0,π/2. Some inequality conditions on ρ3u-f(t,u guaranteeing the existence and nonexistence of positive solutions are presented. Our discussion is based on the fixed point theorem in cones.

  3. The focal boundary value problem for strongly singular higher-order nonlinear functional-differential equations

    Czech Academy of Sciences Publication Activity Database

    Mukhigulashvili, Sulkhan; Půža, B.

    2015-01-01

    Roč. 2015, January (2015), s. 17 ISSN 1687-2770 Institutional support: RVO:67985840 Keywords : higher order nonlinear functional-differential equations * two-point right-focal boundary value problem * strong singularity Subject RIV: BA - General Mathematics Impact factor: 0.642, year: 2015 http://link.springer.com/article/10.1186%2Fs13661-014-0277-1

  4. Fourth-order discrete anisotropic boundary-value problems

    Directory of Open Access Journals (Sweden)

    Maciej Leszczynski

    2015-09-01

    Full Text Available In this article we consider the fourth-order discrete anisotropic boundary value problem with both advance and retardation. We apply the direct method of the calculus of variations and the mountain pass technique to prove the existence of at least one and at least two solutions. Non-existence of non-trivial solutions is also undertaken.

  5. A numerical solution of a singular boundary value problem arising in boundary layer theory.

    Science.gov (United States)

    Hu, Jiancheng

    2016-01-01

    In this paper, a second-order nonlinear singular boundary value problem is presented, which is equivalent to the well-known Falkner-Skan equation. And the one-dimensional third-order boundary value problem on interval [Formula: see text] is equivalently transformed into a second-order boundary value problem on finite interval [Formula: see text]. The finite difference method is utilized to solve the singular boundary value problem, in which the amount of computational effort is significantly less than the other numerical methods. The numerical solutions obtained by the finite difference method are in agreement with those obtained by previous authors.

  6. Laplace boundary-value problem in paraboloidal coordinates

    International Nuclear Information System (INIS)

    Duggen, L; Willatzen, M; Voon, L C Lew Yan

    2012-01-01

    This paper illustrates both a problem in mathematical physics, whereby the method of separation of variables, while applicable, leads to three ordinary differential equations that remain fully coupled via two separation constants and a five-term recurrence relation for series solutions, and an exactly solvable problem in electrostatics, as a boundary-value problem on a paraboloidal surface. In spite of the complex nature of the former, it is shown that the latter solution can be quite simple. Results are provided for the equipotential surfaces and electric field lines are given near a paraboloidal conductor. (paper)

  7. On sign constant solutions of certain boundary value problems for second-order functional differential equations

    Czech Academy of Sciences Publication Activity Database

    Lomtatidze, Alexander; Vodstrčil, Petr

    2005-01-01

    Roč. 84, č. 2 (2005), s. 197-209 ISSN 0003-6811 Institutional research plan: CEZ:AV0Z10190503 Keywords : second order linear functional differential equations * nonnegative solution * two-point boundary value problem Subject RIV: BA - General Mathematics http://www.tandfonline.com/doi/full/10.1080/00036810410001724427

  8. Existence of Three Positive Solutions to Some p-Laplacian Boundary Value Problems

    Directory of Open Access Journals (Sweden)

    Moulay Rchid Sidi Ammi

    2013-01-01

    Full Text Available We obtain, by using the Leggett-Williams fixed point theorem, sufficient conditions that ensure the existence of at least three positive solutions to some p-Laplacian boundary value problems on time scales.

  9. The use of MACSYMA for solving elliptic boundary value problems

    Science.gov (United States)

    Thejll, Peter; Gilbert, Robert P.

    1990-01-01

    A boundary method is presented for the solution of elliptic boundary value problems. An approach based on the use of complete systems of solutions is emphasized. The discussion is limited to the Dirichlet problem, even though the present method can possibly be adapted to treat other boundary value problems.

  10. Existence of Positive Solutions for a Coupled System of (p, q-Laplacian Fractional Higher Order Boundary Value Problems

    Directory of Open Access Journals (Sweden)

    K.R. Prasad

    2015-11-01

    Full Text Available In this paper, we establish the existence of at least three positive solutions for a system of (p,q-Laplacian fractional order two-point boundary value problems by applying five functionals fixed point theorem under suitable conditions on a cone in a Banach space.

  11. On the solvability of initial boundary value problems for nonlinear ...

    African Journals Online (AJOL)

    In this paper, we study the initial boundary value problems for a non-linear time dependent Schrödinger equation with Dirichlet and Neumann boundary conditions, respectively. We prove the existence and uniqueness of solutions of the initial boundary value problems by using Galerkin's method. Keywords: Initial boundary ...

  12. Electromagnetic wave theory for boundary-value problems an advanced course on analytical methods

    CERN Document Server

    Eom, Hyo J

    2004-01-01

    Electromagnetic wave theory is based on Maxwell's equations, and electromagnetic boundary-value problems must be solved to understand electromagnetic scattering, propagation, and radiation. Electromagnetic theory finds practical applications in wireless telecommunications and microwave engineering. This book is written as a text for a two-semester graduate course on electromagnetic wave theory. As such, Electromagnetic Wave Theory for Boundary-Value Problems is intended to help students enhance analytic skills by solving pertinent boundary-value problems. In particular, the techniques of Fourier transform, mode matching, and residue calculus are utilized to solve some canonical scattering and radiation problems.

  13. A simple finite element method for boundary value problems with a Riemann–Liouville derivative

    KAUST Repository

    Jin, Bangti; Lazarov, Raytcho; Lu, Xiliang; Zhou, Zhi

    2016-01-01

    © 2015 Elsevier B.V. All rights reserved. We consider a boundary value problem involving a Riemann-Liouville fractional derivative of order α∈(3/2,2) on the unit interval (0,1). The standard Galerkin finite element approximation converges slowly due to the presence of singularity term xα-1 in the solution representation. In this work, we develop a simple technique, by transforming it into a second-order two-point boundary value problem with nonlocal low order terms, whose solution can reconstruct directly the solution to the original problem. The stability of the variational formulation, and the optimal regularity pickup of the solution are analyzed. A novel Galerkin finite element method with piecewise linear or quadratic finite elements is developed, and L2(D) error estimates are provided. The approach is then applied to the corresponding fractional Sturm-Liouville problem, and error estimates of the eigenvalue approximations are given. Extensive numerical results fully confirm our theoretical study.

  14. A simple finite element method for boundary value problems with a Riemann–Liouville derivative

    KAUST Repository

    Jin, Bangti

    2016-02-01

    © 2015 Elsevier B.V. All rights reserved. We consider a boundary value problem involving a Riemann-Liouville fractional derivative of order α∈(3/2,2) on the unit interval (0,1). The standard Galerkin finite element approximation converges slowly due to the presence of singularity term xα-1 in the solution representation. In this work, we develop a simple technique, by transforming it into a second-order two-point boundary value problem with nonlocal low order terms, whose solution can reconstruct directly the solution to the original problem. The stability of the variational formulation, and the optimal regularity pickup of the solution are analyzed. A novel Galerkin finite element method with piecewise linear or quadratic finite elements is developed, and L2(D) error estimates are provided. The approach is then applied to the corresponding fractional Sturm-Liouville problem, and error estimates of the eigenvalue approximations are given. Extensive numerical results fully confirm our theoretical study.

  15. Numerical solution of sixth-order boundary-value problems using Legendre wavelet collocation method

    Science.gov (United States)

    Sohaib, Muhammad; Haq, Sirajul; Mukhtar, Safyan; Khan, Imad

    2018-03-01

    An efficient method is proposed to approximate sixth order boundary value problems. The proposed method is based on Legendre wavelet in which Legendre polynomial is used. The mechanism of the method is to use collocation points that converts the differential equation into a system of algebraic equations. For validation two test problems are discussed. The results obtained from proposed method are quite accurate, also close to exact solution, and other different methods. The proposed method is computationally more effective and leads to more accurate results as compared to other methods from literature.

  16. State space approach to mixed boundary value problems.

    Science.gov (United States)

    Chen, C. F.; Chen, M. M.

    1973-01-01

    A state-space procedure for the formulation and solution of mixed boundary value problems is established. This procedure is a natural extension of the method used in initial value problems; however, certain special theorems and rules must be developed. The scope of the applications of the approach includes beam, arch, and axisymmetric shell problems in structural analysis, boundary layer problems in fluid mechanics, and eigenvalue problems for deformable bodies. Many classical methods in these fields developed by Holzer, Prohl, Myklestad, Thomson, Love-Meissner, and others can be either simplified or unified under new light shed by the state-variable approach. A beam problem is included as an illustration.

  17. Positive solutions of boundary value problem for singular positone and semi-positone third-order difference equations

    Directory of Open Access Journals (Sweden)

    Gai Gongqi

    2011-01-01

    Full Text Available Abstract This article studies the boundary value problems for the third-order nonlinear singular difference equations Δ 3 u ( i - 2 + λ a ( i f ( i , u ( i = 0 , i ∈ [ 2 , T + 2 ] , satisfying five kinds of different boundary value conditions. This article shows the existence of positive solutions for positone and semi-positone type. The nonlinear term may be singular. Two examples are also given to illustrate the main results. The arguments are based upon fixed point theorems in a cone. MSC [2008]: 34B15; 39A10.

  18. Infinitely many solutions for a fourth-order boundary-value problem

    Directory of Open Access Journals (Sweden)

    Seyyed Mohsen Khalkhali

    2012-09-01

    Full Text Available In this article we consider the existence of infinitely many solutions to the fourth-order boundary-value problem $$displaylines{ u^{iv}+alpha u''+eta(x u=lambda f(x,u+h(u,quad xin]0,1[cr u(0=u(1=0,cr u''(0=u''(1=0,. }$$ Our approach is based on variational methods and critical point theory.

  19. Multiple positive solutions for second order impulsive boundary value problems in Banach spaces

    Directory of Open Access Journals (Sweden)

    Zhi-Wei Lv

    2010-06-01

    Full Text Available By means of the fixed point index theory of strict set contraction operators, we establish new existence theorems on multiple positive solutions to a boundary value problem for second-order impulsive integro-differential equations with integral boundary conditions in a Banach space. Moreover, an application is given to illustrate the main result.

  20. On Riemann boundary value problems for null solutions of the two dimensional Helmholtz equation

    Science.gov (United States)

    Bory Reyes, Juan; Abreu Blaya, Ricardo; Rodríguez Dagnino, Ramón Martin; Kats, Boris Aleksandrovich

    2018-01-01

    The Riemann boundary value problem (RBVP to shorten notation) in the complex plane, for different classes of functions and curves, is still widely used in mathematical physics and engineering. For instance, in elasticity theory, hydro and aerodynamics, shell theory, quantum mechanics, theory of orthogonal polynomials, and so on. In this paper, we present an appropriate hyperholomorphic approach to the RBVP associated to the two dimensional Helmholtz equation in R^2 . Our analysis is based on a suitable operator calculus.

  1. Three symmetric positive solutions of fourth-order singular nonlocal boundary value problems

    Directory of Open Access Journals (Sweden)

    Fuyi Xu

    2011-12-01

    Full Text Available In this paper, we study the existence of three positive solutions of fourth-order singular nonlocal boundary value problems. We show that there exist triple symmetric positive solutions by using Leggett-Williams fixed-point theorem. The conclusions in this paper essentially extend and improve some known results.

  2. Boundary value problems and dichotomic stability

    NARCIS (Netherlands)

    England, R.; Mattheij, R.M.M.

    1988-01-01

    Since the conditioning of a boundary value problem (BVP) is closely related to the existence of a dichotomic fundamental solution (i.e., where one set of modes is increasing and a complementary set is decreasing), it is important to have discretization methods that conserve this dichotomy property.

  3. On a non-linear pseudodifferential boundary value problem

    International Nuclear Information System (INIS)

    Nguyen Minh Chuong.

    1989-12-01

    A pseudodifferential boundary value problem for operators with symbols taking values in Sobolev spaces and with non-linear right-hand side was studied. Existence and uniqueness theorems were proved. (author). 11 refs

  4. A combined analytic-numeric approach for some boundary-value problems

    Directory of Open Access Journals (Sweden)

    Mustafa Turkyilmazoglu

    2016-02-01

    Full Text Available A combined analytic-numeric approach is undertaken in the present work for the solution of boundary-value problems in the finite or semi-infinite domains. Equations to be treated arise specifically from the boundary layer analysis of some two and three-dimensional flows in fluid mechanics. The purpose is to find quick but accurate enough solutions. Taylor expansions at either boundary conditions are computed which are next matched to the other asymptotic or exact boundary conditions. The technique is applied to the well-known Blasius as well as Karman flows. Solutions obtained in terms of series compare favorably with the existing ones in the literature.

  5. Integral boundary-value problem for impulsive fractional functional differential equations with infinite delay

    Directory of Open Access Journals (Sweden)

    Archana Chauhan

    2012-12-01

    Full Text Available In this article, we establish a general framework for finding solutions for impulsive fractional integral boundary-value problems. Then, we prove the existence and uniqueness of solutions by applying well known fixed point theorems. The obtained results are illustrated with an example for their feasibility.

  6. Parallel algorithms for boundary value problems

    Science.gov (United States)

    Lin, Avi

    1991-01-01

    A general approach to solve boundary value problems numerically in a parallel environment is discussed. The basic algorithm consists of two steps: the local step where all the P available processors work in parallel, and the global step where one processor solves a tridiagonal linear system of the order P. The main advantages of this approach are twofold. First, this suggested approach is very flexible, especially in the local step and thus the algorithm can be used with any number of processors and with any of the SIMD or MIMD machines. Secondly, the communication complexity is very small and thus can be used as easily with shared memory machines. Several examples for using this strategy are discussed.

  7. Group invariance in engineering boundary value problems

    CERN Document Server

    Seshadri, R

    1985-01-01

    REFEREN CES . 156 9 Transforma.tion of a Boundary Value Problem to an Initial Value Problem . 157 9.0 Introduction . 157 9.1 Blasius Equation in Boundary Layer Flow . 157 9.2 Longitudinal Impact of Nonlinear Viscoplastic Rods . 163 9.3 Summary . 168 REFERENCES . . . . . . . . . . . . . . . . . . 168 . 10 From Nonlinear to Linear Differential Equa.tions Using Transformation Groups. . . . . . . . . . . . . . 169 . 10.1 From Nonlinear to Linear Differential Equations . 170 10.2 Application to Ordinary Differential Equations -Bernoulli's Equation . . . . . . . . . . . 173 10.3 Application to Partial Differential Equations -A Nonlinear Chemical Exchange Process . 178 10.4 Limitations of the Inspectional Group Method . 187 10.5 Summary . 188 REFERENCES . . . . 188 11 Miscellaneous Topics . 190 11.1 Reduction of Differential Equations to Algebraic Equations 190 11.2 Reduction of Order of an Ordinary Differential Equation . 191 11.3 Transformat.ion From Ordinary to Partial Differential Equations-Search for First Inte...

  8. Separable boundary-value problems in physics

    CERN Document Server

    Willatzen, Morten

    2011-01-01

    Innovative developments in science and technology require a thorough knowledge of applied mathematics, particularly in the field of differential equations and special functions. These are relevant in modeling and computing applications of electromagnetic theory and quantum theory, e.g. in photonics and nanotechnology. The problem of solving partial differential equations remains an important topic that is taught at both the undergraduate and graduate level. Separable Boundary-Value Problems in Physics is an accessible and comprehensive treatment of partial differential equations i

  9. The homogeneous boundary value problem of the thick spherical shell

    International Nuclear Information System (INIS)

    Linder, F.

    1975-01-01

    With the aim to solve boundary value problems in the same manner as it is attained at thin shell theory (Superposition of Membrane solution to solution of boundary values), one has to search solutions of the equations of equilibrium of the three dimensional thick shell which produce tensions at the cut edge and are zero on the whole shell surface inside and outside. This problem was solved with the premissions of the linear theory of Elasticity. The gained solution is exact and contains the symmetric and non-symmetric behaviour and is described in relatively short analytical expressions for the deformations and tensions, after the problem of the coupled system had been solved. The static condition of the two surfaces (zero tension) leads to a homogeneous system of complex equations with the index of the Legendre spherical function as Eigenvalue. One symmetrical case is calculated numerically and is compared with the method of finite elements. This comparison results in good accordance. (Auth.)

  10. Two-point functions and logarithmic boundary operators in boundary logarithmic conformal field theories

    International Nuclear Information System (INIS)

    Ishimoto, Yukitaka

    2004-01-01

    Amongst conformal field theories, there exist logarithmic conformal field theories such as c p,1 models. We have investigated c p,q models with a boundary in search of logarithmic theories and have found logarithmic solutions of two-point functions in the context of the Coulomb gas picture. We have also found the relations between coefficients in the two-point functions and correlation functions of logarithmic boundary operators, and have confirmed the solutions in [hep-th/0003184]. Other two-point functions and boundary operators have also been studied in the free boson construction of boundary CFT with SU(2) k symmetry in regard to logarithmic theories. This paper is based on a part of D. Phil. Thesis [hep-th/0312160]. (author)

  11. Positive solutions for a nonlocal boundary-value problem with vector-valued response

    Directory of Open Access Journals (Sweden)

    Andrzej Nowakowski

    2002-05-01

    Full Text Available Using variational methods, we study the existence of positive solutions for a nonlocal boundary-value problem with vector-valued response. We develop duality and variational principles for this problem and present a numerical version which enables the approximation of solutions and gives a measure of a duality gap between primal and dual functional for approximate solutions for this problem.

  12. Vragov’s boundary value problem for an implicit equation of mixed type

    Science.gov (United States)

    Egorov, I. E.

    2017-10-01

    We study a Vragov boundary value problem for a third-order implicit equation of mixed type with an arbitrary manifold of type switch. These Sobolev-type equations arise in many important applied problems. Given certain constraints on the coefficients and the right-hand side of the equation, we demonstrate, using nonstationary Galerkin method and regularization method, the unique regular solvability of the boundary value problem. We also obtain an error estimate for approximate solutions of the boundary value problem in terms of the regularization parameter and the eigenvalues of the Dirichlet spectral problem for the Laplace operator.

  13. Continuum and Discrete Initial-Boundary Value Problems and Einstein's Field Equations

    Directory of Open Access Journals (Sweden)

    Olivier Sarbach

    2012-08-01

    Full Text Available Many evolution problems in physics are described by partial differential equations on an infinite domain; therefore, one is interested in the solutions to such problems for a given initial dataset. A prominent example is the binary black-hole problem within Einstein's theory of gravitation, in which one computes the gravitational radiation emitted from the inspiral of the two black holes, merger and ringdown. Powerful mathematical tools can be used to establish qualitative statements about the solutions, such as their existence, uniqueness, continuous dependence on the initial data, or their asymptotic behavior over large time scales. However, one is often interested in computing the solution itself, and unless the partial differential equation is very simple, or the initial data possesses a high degree of symmetry, this computation requires approximation by numerical discretization. When solving such discrete problems on a machine, one is faced with a finite limit to computational resources, which leads to the replacement of the infinite continuum domain with a finite computer grid. This, in turn, leads to a discrete initial-boundary value problem. The hope is to recover, with high accuracy, the exact solution in the limit where the grid spacing converges to zero with the boundary being pushed to infinity. The goal of this article is to review some of the theory necessary to understand the continuum and discrete initial boundary-value problems arising from hyperbolic partial differential equations and to discuss its applications to numerical relativity; in particular, we present well-posed initial and initial-boundary value formulations of Einstein's equations, and we discuss multi-domain high-order finite difference and spectral methods to solve them.

  14. Continuum and Discrete Initial-Boundary Value Problems and Einstein's Field Equations.

    Science.gov (United States)

    Sarbach, Olivier; Tiglio, Manuel

    2012-01-01

    Many evolution problems in physics are described by partial differential equations on an infinite domain; therefore, one is interested in the solutions to such problems for a given initial dataset. A prominent example is the binary black-hole problem within Einstein's theory of gravitation, in which one computes the gravitational radiation emitted from the inspiral of the two black holes, merger and ringdown. Powerful mathematical tools can be used to establish qualitative statements about the solutions, such as their existence, uniqueness, continuous dependence on the initial data, or their asymptotic behavior over large time scales. However, one is often interested in computing the solution itself, and unless the partial differential equation is very simple, or the initial data possesses a high degree of symmetry, this computation requires approximation by numerical discretization. When solving such discrete problems on a machine, one is faced with a finite limit to computational resources, which leads to the replacement of the infinite continuum domain with a finite computer grid. This, in turn, leads to a discrete initial-boundary value problem. The hope is to recover, with high accuracy, the exact solution in the limit where the grid spacing converges to zero with the boundary being pushed to infinity. The goal of this article is to review some of the theory necessary to understand the continuum and discrete initial boundary-value problems arising from hyperbolic partial differential equations and to discuss its applications to numerical relativity; in particular, we present well-posed initial and initial-boundary value formulations of Einstein's equations, and we discuss multi-domain high-order finite difference and spectral methods to solve them.

  15. Numerical solution of large nonlinear boundary value problems by quadratic minimization techniques

    International Nuclear Information System (INIS)

    Glowinski, R.; Le Tallec, P.

    1984-01-01

    The objective of this paper is to describe the numerical treatment of large highly nonlinear two or three dimensional boundary value problems by quadratic minimization techniques. In all the different situations where these techniques were applied, the methodology remains the same and is organized as follows: 1) derive a variational formulation of the original boundary value problem, and approximate it by Galerkin methods; 2) transform this variational formulation into a quadratic minimization problem (least squares methods) or into a sequence of quadratic minimization problems (augmented lagrangian decomposition); 3) solve each quadratic minimization problem by a conjugate gradient method with preconditioning, the preconditioning matrix being sparse, positive definite, and fixed once for all in the iterative process. This paper will illustrate the methodology above on two different examples: the description of least squares solution methods and their application to the solution of the unsteady Navier-Stokes equations for incompressible viscous fluids; the description of augmented lagrangian decomposition techniques and their application to the solution of equilibrium problems in finite elasticity

  16. Nonlinear Elliptic Boundary Value Problems at Resonance with Nonlinear Wentzell Boundary Conditions

    Directory of Open Access Journals (Sweden)

    Ciprian G. Gal

    2017-01-01

    Full Text Available Given a bounded domain Ω⊂RN with a Lipschitz boundary ∂Ω and p,q∈(1,+∞, we consider the quasilinear elliptic equation -Δpu+α1u=f in Ω complemented with the generalized Wentzell-Robin type boundary conditions of the form bx∇up-2∂nu-ρbxΔq,Γu+α2u=g on ∂Ω. In the first part of the article, we give necessary and sufficient conditions in terms of the given functions f, g and the nonlinearities α1, α2, for the solvability of the above nonlinear elliptic boundary value problems with the nonlinear boundary conditions. In other words, we establish a sort of “nonlinear Fredholm alternative” for our problem which extends the corresponding Landesman and Lazer result for elliptic problems with linear homogeneous boundary conditions. In the second part, we give some additional results on existence and uniqueness and we study the regularity of the weak solutions for these classes of nonlinear problems. More precisely, we show some global a priori estimates for these weak solutions in an L∞-setting.

  17. Chebyshev Finite Difference Method for Fractional Boundary Value Problems

    Directory of Open Access Journals (Sweden)

    Boundary

    2015-09-01

    Full Text Available This paper presents a numerical method for fractional differential equations using Chebyshev finite difference method. The fractional derivatives are described in the Caputo sense. Numerical results show that this method is of high accuracy and is more convenient and efficient for solving boundary value problems involving fractional ordinary differential equations. AMS Subject Classification: 34A08 Keywords and Phrases: Chebyshev polynomials, Gauss-Lobatto points, fractional differential equation, finite difference 1. Introduction The idea of a derivative which interpolates between the familiar integer order derivatives was introduced many years ago and has gained increasing importance only in recent years due to the development of mathematical models of a certain situations in engineering, materials science, control theory, polymer modelling etc. For example see [20, 22, 25, 26]. Most fractional order differential equations describing real life situations, in general do not have exact analytical solutions. Several numerical and approximate analytical methods for ordinary differential equation Received: December 2014; Accepted: March 2015 57 Journal of Mathematical Extension Vol. 9, No. 3, (2015, 57-71 ISSN: 1735-8299 URL: http://www.ijmex.com Chebyshev Finite Difference Method for Fractional Boundary Value Problems H. Azizi Taft Branch, Islamic Azad University Abstract. This paper presents a numerical method for fractional differential equations using Chebyshev finite difference method. The fractional derivative

  18. Three-Field Modelling of Nonlinear Nonsmooth Boundary Value Problems and Stability of Differential Mixed Variational Inequalities

    Directory of Open Access Journals (Sweden)

    J. Gwinner

    2013-01-01

    Full Text Available The purpose of this paper is twofold. Firstly we consider nonlinear nonsmooth elliptic boundary value problems, and also related parabolic initial boundary value problems that model in a simplified way steady-state unilateral contact with Tresca friction in solid mechanics, respectively, stem from nonlinear transient heat conduction with unilateral boundary conditions. Here a recent duality approach, that augments the classical Babuška-Brezzi saddle point formulation for mixed variational problems to twofold saddle point formulations, is extended to the nonsmooth problems under consideration. This approach leads to variational inequalities of mixed form for three coupled fields as unknowns and to related differential mixed variational inequalities in the time-dependent case. Secondly we are concerned with the stability of the solution set of a general class of differential mixed variational inequalities. Here we present a novel upper set convergence result with respect to perturbations in the data, including perturbations of the associated nonlinear maps, the nonsmooth convex functionals, and the convex constraint set. We employ epiconvergence for the convergence of the functionals and Mosco convergence for set convergence. We impose weak convergence assumptions on the perturbed maps using the monotonicity method of Browder and Minty.

  19. Existence of solutions for a fourth-order boundary value problem on the half-line via critical point theory

    Directory of Open Access Journals (Sweden)

    Mabrouk Briki

    2016-05-01

    Full Text Available In this paper, a fourth-order boundary value problem on the half-line is considered and existence of solutions is proved using a minimization principle and the mountain pass theorem.

  20. Homology in Electromagnetic Boundary Value Problems

    Directory of Open Access Journals (Sweden)

    Pellikka Matti

    2010-01-01

    Full Text Available We discuss how homology computation can be exploited in computational electromagnetism. We represent various cellular mesh reduction techniques, which enable the computation of generators of homology spaces in an acceptable time. Furthermore, we show how the generators can be used for setting up and analysis of an electromagnetic boundary value problem. The aim is to provide a rationale for homology computation in electromagnetic modeling software.

  1. Two-point boundary correlation functions of dense loop models

    Directory of Open Access Journals (Sweden)

    Alexi Morin-Duchesne, Jesper Lykke Jacobsen

    2018-06-01

    Full Text Available We investigate six types of two-point boundary correlation functions in the dense loop model. These are defined as ratios $Z/Z^0$ of partition functions on the $m\\times n$ square lattice, with the boundary condition for $Z$ depending on two points $x$ and $y$. We consider: the insertion of an isolated defect (a and a pair of defects (b in a Dirichlet boundary condition, the transition (c between Dirichlet and Neumann boundary conditions, and the connectivity of clusters (d, loops (e and boundary segments (f in a Neumann boundary condition. For the model of critical dense polymers, corresponding to a vanishing loop weight ($\\beta = 0$, we find determinant and pfaffian expressions for these correlators. We extract the conformal weights of the underlying conformal fields and find $\\Delta = -\\frac18$, $0$, $-\\frac3{32}$, $\\frac38$, $1$, $\\tfrac \\theta \\pi (1+\\tfrac{2\\theta}\\pi$, where $\\theta$ encodes the weight of one class of loops for the correlator of type f. These results are obtained by analysing the asymptotics of the exact expressions, and by using the Cardy-Peschel formula in the case where $x$ and $y$ are set to the corners. For type b, we find a $\\log|x-y|$ dependence from the asymptotics, and a $\\ln (\\ln n$ term in the corner free energy. This is consistent with the interpretation of the boundary condition of type b as the insertion of a logarithmic field belonging to a rank two Jordan cell. For the other values of $\\beta = 2 \\cos \\lambda$, we use the hypothesis of conformal invariance to predict the conformal weights and find $\\Delta = \\Delta_{1,2}$, $\\Delta_{1,3}$, $\\Delta_{0,\\frac12}$, $\\Delta_{1,0}$, $\\Delta_{1,-1}$ and $\\Delta_{\\frac{2\\theta}\\lambda+1,\\frac{2\\theta}\\lambda+1}$, extending the results of critical dense polymers. With the results for type f, we reproduce a Coulomb gas prediction for the valence bond entanglement entropy of Jacobsen and Saleur.

  2. A new Ellipsoidal Gravimetric-Satellite Altimetry Boundary Value Problem; Case study: High Resolution Geoid of Iran

    Science.gov (United States)

    Ardalan, A.; Safari, A.; Grafarend, E.

    2003-04-01

    A new ellipsoidal gravimetric-satellite altimetry boundary value problem has been developed and successfully tested. This boundary value problem has been constructed for gravity observables of the type (i) gravity potential (ii) gravity intensity (iii) deflection of vertical and (iv) satellite altimetry data. The developed boundary value problem is enjoying the ellipsoidal nature and as such can take advantage of high precision GPS observations in the set-up of the problem. The highlights of the solution are as follows: begin{itemize} Application of ellipsoidal harmonic expansion up to degree/order and ellipsoidal centrifugal field for the reduction of global gravity and isostasy effects from the gravity observable at the surface of the Earth. Application of ellipsoidal Newton integral on the equal area map projection surface for the reduction of residual mass effects within a radius of 55 km around the computational point. Ellipsoidal harmonic downward continuation of the residual observables from the surface of the earth down to the surface of reference ellipsoid using the ellipsoidal height of the observation points derived from GPS. Restore of the removed effects at the application points on the surface of reference ellipsoid. Conversion of the satellite altimetry derived heights of the water bodies into potential. Combination of the downward continued gravity information with the potential equivalent of the satellite altimetry derived heights of the water bodies. Application of ellipsoidal Bruns formula for converting the potential values on the surface of the reference ellipsoid into the geoidal heights (i.e. ellipsoidal heights of the geoid) with respect to the reference ellipsoid. Computation of the high-resolution geoid of Iran has successfully tested this new methodology!

  3. On two-point boundary correlations in the six-vertex model with domain wall boundary conditions

    Science.gov (United States)

    Colomo, F.; Pronko, A. G.

    2005-05-01

    The six-vertex model with domain wall boundary conditions on an N × N square lattice is considered. The two-point correlation function describing the probability of having two vertices in a given state at opposite (top and bottom) boundaries of the lattice is calculated. It is shown that this two-point boundary correlator is expressible in a very simple way in terms of the one-point boundary correlators of the model on N × N and (N - 1) × (N - 1) lattices. In alternating sign matrix (ASM) language this result implies that the doubly refined x-enumerations of ASMs are just appropriate combinations of the singly refined ones.

  4. The vanishing discount problem and viscosity Mather measures. Part 2: boundary value problems

    OpenAIRE

    Ishii, Hitoshi; Mitake, Hiroyoshi; Tran, Hung V.

    2016-01-01

    In arXiv:1603.01051 (Part 1 of this series), we have introduced a variational approach to studying the vanishing discount problem for fully nonlinear, degenerate elliptic, partial differential equations in a torus. We develop this approach further here to handle boundary value problems. In particular, we establish new representation formulas for solutions of discount problems, critical values, and use them to prove convergence results for the vanishing discount problems.

  5. An initial boundary value problem for modeling a piezoelectric dipolar body

    Science.gov (United States)

    Marin, Marin; Öchsner, Andreas

    2018-03-01

    This study deals with the first initial boundary value problem in elasticity of piezoelectric dipolar bodies. We consider the most general case of an anisotropic and inhomogeneous elastic body having a dipolar structure. For two different types of restrictions imposed on the problem data, we prove two results regarding the uniqueness of solution, by using a different but accessible method. Then, the mixed problem is transformed in a temporally evolutionary equation on a Hilbert space, conveniently constructed based on the problem data. With the help of a known result from the theory of semigroups of operators, the existence and uniqueness of the weak solution for this equation are proved.

  6. Existence of solutions to fractional boundary-value problems with a parameter

    Directory of Open Access Journals (Sweden)

    Ya-Ning Li

    2013-06-01

    Full Text Available This article concerns the existence of solutions to the fractional boundary-value problem $$displaylines{ -frac{d}{dt} ig(frac{1}{2} {}_0D_t^{-eta}+ frac{1}{2}{}_tD_{T}^{-eta}igu'(t=lambda u(t+abla F(t,u(t,quad hbox{a.e. } tin[0,T], cr u(0=0,quad u(T=0. }$$ First for the eigenvalue problem associated with it, we prove that there is a sequence of positive and increasing real eigenvalues; a characterization of the first eigenvalue is also given. Then under different assumptions on the nonlinearity F(t,u, we show the existence of weak solutions of the problem when $lambda$ lies in various intervals. Our main tools are variational methods and critical point theorems.

  7. Initial-boundary value problems associated with the Ablowitz-Ladik system

    Science.gov (United States)

    Xia, Baoqiang; Fokas, A. S.

    2018-02-01

    We employ the Ablowitz-Ladik system as an illustrative example in order to demonstrate how to analyze initial-boundary value problems for integrable nonlinear differential-difference equations via the unified transform (Fokas method). In particular, we express the solutions of the integrable discrete nonlinear Schrödinger and integrable discrete modified Korteweg-de Vries equations in terms of the solutions of appropriate matrix Riemann-Hilbert problems. We also discuss in detail, for both the above discrete integrable equations, the associated global relations and the process of eliminating of the unknown boundary values.

  8. A fast direct solver for boundary value problems on locally perturbed geometries

    Science.gov (United States)

    Zhang, Yabin; Gillman, Adrianna

    2018-03-01

    Many applications including optimal design and adaptive discretization techniques involve solving several boundary value problems on geometries that are local perturbations of an original geometry. This manuscript presents a fast direct solver for boundary value problems that are recast as boundary integral equations. The idea is to write the discretized boundary integral equation on a new geometry as a low rank update to the discretized problem on the original geometry. Using the Sherman-Morrison formula, the inverse can be expressed in terms of the inverse of the original system applied to the low rank factors and the right hand side. Numerical results illustrate for problems where perturbation is localized the fast direct solver is three times faster than building a new solver from scratch.

  9. Inverse Boundary Value Problem for Non-linear Hyperbolic Partial Differential Equations

    OpenAIRE

    Nakamura, Gen; Vashisth, Manmohan

    2017-01-01

    In this article we are concerned with an inverse boundary value problem for a non-linear wave equation of divergence form with space dimension $n\\geq 3$. This non-linear wave equation has a trivial solution, i.e. zero solution. By linearizing this equation at the trivial solution, we have the usual linear isotropic wave equation with the speed $\\sqrt{\\gamma(x)}$ at each point $x$ in a given spacial domain. For any small solution $u=u(t,x)$ of this non-linear equation, we have the linear isotr...

  10. Existence and Uniqueness of Solutions for a Discrete Fractional Mixed Type Sum-Difference Equation Boundary Value Problem

    Directory of Open Access Journals (Sweden)

    Weidong Lv

    2015-01-01

    Full Text Available By means of Schauder’s fixed point theorem and contraction mapping principle, we establish the existence and uniqueness of solutions to a boundary value problem for a discrete fractional mixed type sum-difference equation with the nonlinear term dependent on a fractional difference of lower order. Moreover, a suitable choice of a Banach space allows the solutions to be unbounded and two representative examples are presented to illustrate the effectiveness of the main results.

  11. Solvability conditions for non-local boundary value problems for two-dimensional half-linear differential systems

    Czech Academy of Sciences Publication Activity Database

    Kiguradze, I.; Šremr, Jiří

    2011-01-01

    Roč. 74, č. 17 (2011), s. 6537-6552 ISSN 0362-546X Institutional research plan: CEZ:AV0Z10190503 Keywords : half-linear differential system * non-local boundary value problem * solvability Subject RIV: BA - General Mathematics Impact factor: 1.536, year: 2011 http://www.sciencedirect.com/science/article/pii/S0362546X11004573

  12. Existence of Positive Solutions to a Boundary Value Problem for a Delayed Nonlinear Fractional Differential System

    Directory of Open Access Journals (Sweden)

    Chen Yuming

    2011-01-01

    Full Text Available Though boundary value problems for fractional differential equations have been extensively studied, most of the studies focus on scalar equations and the fractional order between 1 and 2. On the other hand, delay is natural in practical systems. However, not much has been done for fractional differential equations with delays. Therefore, in this paper, we consider a boundary value problem of a general delayed nonlinear fractional system. With the help of some fixed point theorems and the properties of the Green function, we establish several sets of sufficient conditions on the existence of positive solutions. The obtained results extend and include some existing ones and are illustrated with some examples for their feasibility.

  13. Application of He's variational iteration method to the fifth-order boundary value problems

    International Nuclear Information System (INIS)

    Shen, S

    2008-01-01

    Variational iteration method is introduced to solve the fifth-order boundary value problems. This method provides an efficient approach to solve this type of problems without discretization and the computation of the Adomian polynomials. Numerical results demonstrate that this method is a promising and powerful tool for solving the fifth-order boundary value problems

  14. Appling Laplace Adomian decomposition method for delay differential equations with boundary value problems

    Science.gov (United States)

    Yousef, Hamood Mohammed; Ismail, Ahmad Izani

    2017-11-01

    In this paper, Laplace Adomian decomposition method (LADM) was applied to solve Delay differential equations with Boundary Value Problems. The solution is in the form of a convergent series which is easy to compute. This approach is tested on two test problem. The findings obtained exhibit the reliability and efficiency of the proposed method.

  15. Application of Monte Carlo method to solving boundary value problem of differential equations

    International Nuclear Information System (INIS)

    Zuo Yinghong; Wang Jianguo

    2012-01-01

    This paper introduces the foundation of the Monte Carlo method and the way how to generate the random numbers. Based on the basic thought of the Monte Carlo method and finite differential method, the stochastic model for solving the boundary value problem of differential equations is built. To investigate the application of the Monte Carlo method to solving the boundary value problem of differential equations, the model is used to solve Laplace's equations with the first boundary condition and the unsteady heat transfer equation with initial values and boundary conditions. The results show that the boundary value problem of differential equations can be effectively solved with the Monte Carlo method, and the differential equations with initial condition can also be calculated by using a stochastic probability model which is based on the time-domain finite differential equations. Both the simulation results and theoretical analyses show that the errors of numerical results are lowered as the number of simulation particles is increased. (authors)

  16. Numerical solution of fuzzy boundary value problems using Galerkin ...

    Indian Academy of Sciences (India)

    1 College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China. 2 Department of ... exact solution of fuzzy first-order boundary value problems. (BVPs). ...... edge partial financial support by the Ministerio de Economıa.

  17. An Adaptive Pseudospectral Method for Fractional Order Boundary Value Problems

    Directory of Open Access Journals (Sweden)

    Mohammad Maleki

    2012-01-01

    Full Text Available An adaptive pseudospectral method is presented for solving a class of multiterm fractional boundary value problems (FBVP which involve Caputo-type fractional derivatives. The multiterm FBVP is first converted into a singular Volterra integrodifferential equation (SVIDE. By dividing the interval of the problem to subintervals, the unknown function is approximated using a piecewise interpolation polynomial with unknown coefficients which is based on shifted Legendre-Gauss (ShLG collocation points. Then the problem is reduced to a system of algebraic equations, thus greatly simplifying the problem. Further, some additional conditions are considered to maintain the continuity of the approximate solution and its derivatives at the interface of subintervals. In order to convert the singular integrals of SVIDE into nonsingular ones, integration by parts is utilized. In the method developed in this paper, the accuracy can be improved either by increasing the number of subintervals or by increasing the degree of the polynomial on each subinterval. Using several examples including Bagley-Torvik equation the proposed method is shown to be efficient and accurate.

  18. Existence of positive solutions for boundary value problems of fractional functional differential equations

    Directory of Open Access Journals (Sweden)

    Chuanzhi Bai

    2010-06-01

    Full Text Available This paper deals with the existence of positive solutions for a boundary value problem involving a nonlinear functional differential equation of fractional order $\\alpha$ given by $ D^{\\alpha} u(t + f(t, u_t = 0$, $t \\in (0, 1$, $2 < \\alpha \\le 3$, $ u^{\\prime}(0 = 0$, $u^{\\prime}(1 = b u^{\\prime}(\\eta$, $u_0 = \\phi$. Our results are based on the nonlinear alternative of Leray-Schauder type and Krasnosel'skii fixed point theorem.

  19. A two-dimensional embedded-boundary method for convection problems with moving boundaries

    NARCIS (Netherlands)

    Y.J. Hassen (Yunus); B. Koren (Barry)

    2010-01-01

    htmlabstractIn this work, a two-dimensional embedded-boundary algorithm for convection problems is presented. A moving body of arbitrary boundary shape is immersed in a Cartesian finite-volume grid, which is fixed in space. The boundary surface is reconstructed in such a way that only certain fluxes

  20. Fermat collocation method for the solutions of nonlinear system of second order boundary value problems

    Directory of Open Access Journals (Sweden)

    Salih Yalcinbas

    2016-01-01

    Full Text Available In this study, a numerical approach is proposed to obtain approximate solutions of nonlinear system of second order boundary value problem. This technique is essentially based on the truncated Fermat series and its matrix representations with collocation points. Using the matrix method, we reduce the problem system of nonlinear algebraic equations. Numerical examples are also given to demonstrate the validity and applicability of the presented technique. The method is easy to implement and produces accurate results.

  1. Triple Positive Solutions of a Nonlocal Boundary Value Problem for Singular Differential Equations with p-Laplacian

    Directory of Open Access Journals (Sweden)

    Jufang Wang

    2013-01-01

    Full Text Available We establish the existence of triple positive solutions of an m-point boundary value problem for the nonlinear singular second-order differential equations of mixed type with a p-Laplacian operator by Leggett-William fixed point theorem. At last, we give an example to demonstrate the use of the main result of this paper. The conclusions in this paper essentially extend and improve the known results.

  2. Existence of positive solutions for nonlocal second-order boundary value problem with variable parameter in Banach spaces

    Directory of Open Access Journals (Sweden)

    Zhang Peiguo

    2011-01-01

    Full Text Available Abstract By obtaining intervals of the parameter λ, this article investigates the existence of a positive solution for a class of nonlinear boundary value problems of second-order differential equations with integral boundary conditions in abstract spaces. The arguments are based upon a specially constructed cone and the fixed point theory in cone for a strict set contraction operator. MSC: 34B15; 34B16.

  3. Solution of a Problem Linear Plane Elasticity with Mixed Boundary Conditions by the Method of Boundary Integrals

    Directory of Open Access Journals (Sweden)

    Nahed S. Hussein

    2014-01-01

    Full Text Available A numerical boundary integral scheme is proposed for the solution to the system of …eld equations of plane. The stresses are prescribed on one-half of the circle, while the displacements are given. The considered problem with mixed boundary conditions in the circle is replaced by two problems with homogeneous boundary conditions, one of each type, having a common solution. The equations are reduced to a system of boundary integral equations, which is then discretized in the usual way, and the problem at this stage is reduced to the solution to a rectangular linear system of algebraic equations. The unknowns in this system of equations are the boundary values of four harmonic functions which define the full elastic solution and the unknown boundary values of stresses or displacements on proper parts of the boundary. On the basis of the obtained results, it is inferred that a stress component has a singularity at each of the two separation points, thought to be of logarithmic type. The results are discussed and boundary plots are given. We have also calculated the unknown functions in the bulk directly from the given boundary conditions using the boundary collocation method. The obtained results in the bulk are discussed and three-dimensional plots are given. A tentative form for the singular solution is proposed and the corresponding singular stresses and displacements are plotted in the bulk. The form of the singular tangential stress is seen to be compatible with the boundary values obtained earlier. The efficiency of the used numerical schemes is discussed.

  4. Efficient algorithms for analyzing the singularly perturbed boundary value problems of fractional order

    Science.gov (United States)

    Sayevand, K.; Pichaghchi, K.

    2018-04-01

    In this paper, we were concerned with the description of the singularly perturbed boundary value problems in the scope of fractional calculus. We should mention that, one of the main methods used to solve these problems in classical calculus is the so-called matched asymptotic expansion method. However we shall note that, this was not achievable via the existing classical definitions of fractional derivative, because they do not obey the chain rule which one of the key elements of the matched asymptotic expansion method. In order to accommodate this method to fractional derivative, we employ a relatively new derivative so-called the local fractional derivative. Using the properties of local fractional derivative, we extend the matched asymptotic expansion method to the scope of fractional calculus and introduce a reliable new algorithm to develop approximate solutions of the singularly perturbed boundary value problems of fractional order. In the new method, the original problem is partitioned into inner and outer solution equations. The reduced equation is solved with suitable boundary conditions which provide the terminal boundary conditions for the boundary layer correction. The inner solution problem is next solved as a solvable boundary value problem. The width of the boundary layer is approximated using appropriate resemblance function. Some theoretical results are established and proved. Some illustrating examples are solved and the results are compared with those of matched asymptotic expansion method and homotopy analysis method to demonstrate the accuracy and efficiency of the method. It can be observed that, the proposed method approximates the exact solution very well not only in the boundary layer, but also away from the layer.

  5. Existence of Positive Solutions to a Singular Semipositone Boundary Value Problem of Nonlinear Fractional Differential Systems

    Directory of Open Access Journals (Sweden)

    Xiaofeng Zhang

    2017-12-01

    Full Text Available In this paper, we consider the existence of positive solutions to a singular semipositone boundary value problem of nonlinear fractional differential equations. By applying the fixed point index theorem, some new results for the existence of positive solutions are obtained. In addition, an example is presented to demonstrate the application of our main results.

  6. Adaptive wavelet collocation methods for initial value boundary problems of nonlinear PDE's

    Science.gov (United States)

    Cai, Wei; Wang, Jian-Zhong

    1993-01-01

    We have designed a cubic spline wavelet decomposition for the Sobolev space H(sup 2)(sub 0)(I) where I is a bounded interval. Based on a special 'point-wise orthogonality' of the wavelet basis functions, a fast Discrete Wavelet Transform (DWT) is constructed. This DWT transform will map discrete samples of a function to its wavelet expansion coefficients in O(N log N) operations. Using this transform, we propose a collocation method for the initial value boundary problem of nonlinear PDE's. Then, we test the efficiency of the DWT transform and apply the collocation method to solve linear and nonlinear PDE's.

  7. Asymptotic boundary value problems for evolution inclusions

    Directory of Open Access Journals (Sweden)

    Fürst Tomáš

    2006-01-01

    Full Text Available When solving boundary value problems on infinite intervals, it is possible to use continuation principles. Some of these principles take advantage of equipping the considered function spaces with topologies of uniform convergence on compact subintervals. This makes the representing solution operators compact (or condensing, but, on the other hand, spaces equipped with such topologies become more complicated. This paper shows interesting applications that use the strength of continuation principles and also presents a possible extension of such continuation principles to partial differential inclusions.

  8. Asymptotic boundary value problems for evolution inclusions

    Directory of Open Access Journals (Sweden)

    Tomáš Fürst

    2006-02-01

    Full Text Available When solving boundary value problems on infinite intervals, it is possible to use continuation principles. Some of these principles take advantage of equipping the considered function spaces with topologies of uniform convergence on compact subintervals. This makes the representing solution operators compact (or condensing, but, on the other hand, spaces equipped with such topologies become more complicated. This paper shows interesting applications that use the strength of continuation principles and also presents a possible extension of such continuation principles to partial differential inclusions.

  9. Algebraic structures in generalized Clifford analysis and applications to boundary value problems

    Directory of Open Access Journals (Sweden)

    José Játem

    2015-12-01

    Full Text Available The present article has a threefold purpose: First it is a survey of the algebraic structures of generalized Clifford-type algebras and shows the main results of the corresponding Clifford-type analysis and its application to boundary value problems known so far. Second it is aimed to implement algorithms to provide the fast and accurate computation of boundary value problems for inhomogeneous equations in the framework of the generalized Clifford analysis. Finally it is also aimed to encourage the development of a generalized discrete Clifford analysis.

  10. Positive solutions for second-order boundary-value problems with phi-Laplacian

    Directory of Open Access Journals (Sweden)

    Diana-Raluca Herlea

    2016-02-01

    Full Text Available This article concerns the existence, localization and multiplicity of positive solutions for the boundary-value problem $$\\displaylines{ \\big(\\phi(u' \\big '+f(t,u =0, \\cr u(0 - a u'(0 = u'(1= 0, }$$ where $f:[0,1]\\times \\mathbb{R}_{+}\\to \\mathbb{R}_{+}$ is a continuous function and $\\phi :\\mathbb{R}\\to (-b,b$ is an increasing homeomorphism with $\\phi (0=0$. We obtain existence, localization and multiplicity results of positive solutions using Krasnosel'skii fixed point theorem in cones, and a weak Harnack type inequality. Concerning systems, the localization is established by the vector version of Krasnosel'skii theorem, where the compression-expansion conditions are expressed on components.

  11. Boundary value problems on the half line in the theory of colloids

    Directory of Open Access Journals (Sweden)

    Ravi P. Agarwal

    2002-01-01

    Full Text Available We present existence results for some boundary value problems defined on infinite intervals. In particular our discussion includes a problem which arises in the theory of colloids.

  12. The boundary value problem for discrete analytic functions

    KAUST Repository

    Skopenkov, Mikhail

    2013-06-01

    This paper is on further development of discrete complex analysis introduced by R.Isaacs, J.Ferrand, R.Duffin, and C.Mercat. We consider a graph lying in the complex plane and having quadrilateral faces. A function on the vertices is called discrete analytic, if for each face the difference quotients along the two diagonals are equal.We prove that the Dirichlet boundary value problem for the real part of a discrete analytic function has a unique solution. In the case when each face has orthogonal diagonals we prove that this solution uniformly converges to a harmonic function in the scaling limit. This solves a problem of S.Smirnov from 2010. This was proved earlier by R.Courant-K.Friedrichs-H.Lewy and L.Lusternik for square lattices, by D.Chelkak-S.Smirnov and implicitly by P.G.Ciarlet-P.-A.Raviart for rhombic lattices.In particular, our result implies uniform convergence of the finite element method on Delaunay triangulations. This solves a problem of A.Bobenko from 2011. The methodology is based on energy estimates inspired by alternating-current network theory. © 2013 Elsevier Ltd.

  13. On a variational principle for shape optimization and elliptic free boundary problems

    Directory of Open Access Journals (Sweden)

    Raúl B. González De Paz

    2009-02-01

    Full Text Available A variational principle for several free boundary value problems using a relaxation approach is presented. The relaxed Energy functional is concave and it is defined on a convex set, so that the minimizing points are characteristic functions of sets. As a consequence of the first order optimality conditions, it is shown that the corresponding sets are domains bounded by free boundaries, so that the equivalence of the solution of the relaxed problem with the solution of several free boundary value problem is proved. Keywords: Calculus of variations, optimization, free boundary problems.

  14. Asymptotics for inhomogeneous Dirichlet initial-boundary value problem for the nonlinear Schrödinger equation

    Energy Technology Data Exchange (ETDEWEB)

    Kaikina, Elena I., E-mail: ekaikina@matmor.unam.mx [Centro de Ciencias Matemáticas, UNAM Campus Morelia, AP 61-3 (Xangari), Morelia CP 58089, Michoacán (Mexico)

    2013-11-15

    We consider the inhomogeneous Dirichlet initial-boundary value problem for the nonlinear Schrödinger equation, formulated on a half-line. We study traditionally important problems of the theory of nonlinear partial differential equations, such as global in time existence of solutions to the initial-boundary value problem and the asymptotic behavior of solutions for large time.

  15. Asymptotics for inhomogeneous Dirichlet initial-boundary value problem for the nonlinear Schrödinger equation

    International Nuclear Information System (INIS)

    Kaikina, Elena I.

    2013-01-01

    We consider the inhomogeneous Dirichlet initial-boundary value problem for the nonlinear Schrödinger equation, formulated on a half-line. We study traditionally important problems of the theory of nonlinear partial differential equations, such as global in time existence of solutions to the initial-boundary value problem and the asymptotic behavior of solutions for large time

  16. A Third-Order p-Laplacian Boundary Value Problem Solved by an SL(3,ℝ Lie-Group Shooting Method

    Directory of Open Access Journals (Sweden)

    Chein-Shan Liu

    2013-01-01

    Full Text Available The boundary layer problem for power-law fluid can be recast to a third-order p-Laplacian boundary value problem (BVP. In this paper, we transform the third-order p-Laplacian into a new system which exhibits a Lie-symmetry SL(3,ℝ. Then, the closure property of the Lie-group is used to derive a linear transformation between the boundary values at two ends of a spatial interval. Hence, we can iteratively solve the missing left boundary conditions, which are determined by matching the right boundary conditions through a finer tuning of r∈[0,1]. The present SL(3,ℝ Lie-group shooting method is easily implemented and is efficient to tackle the multiple solutions of the third-order p-Laplacian. When the missing left boundary values can be determined accurately, we can apply the fourth-order Runge-Kutta (RK4 method to obtain a quite accurate numerical solution of the p-Laplacian.

  17. On two special values of temperature factor in hypersonic flow stagnation point

    Science.gov (United States)

    Bilchenko, G. G.; Bilchenko, N. G.

    2018-03-01

    The hypersonic aircraft permeable cylindrical and spherical surfaces laminar boundary layer heat and mass transfer control mathematical model properties are investigated. The nonlinear algebraic equations systems are obtained for two special values of temperature factor in the hypersonic flow stagnation point. The mappings bijectivity between heat and mass transfer local parameters and controls is established. The computation experiments results are presented: the domains of allowed values “heat-friction” are obtained.

  18. Boundary Value Problems for a Super-Sublinear Asymmetric Oscillator: The Exact Number of Solutions

    Directory of Open Access Journals (Sweden)

    Armands Gritsans

    2013-01-01

    Full Text Available Properties of asymmetric oscillator described by the equation (i, where and , are studied. A set of such that the problem (i, (ii, and (iii have a nontrivial solution, is called α-spectrum. We give full description of α-spectra in terms of solution sets and solution surfaces. The exact number of nontrivial solutions of the two-parameter Dirichlet boundary value problem (i, and (ii is given.

  19. Variational methods for boundary value problems for systems of elliptic equations

    CERN Document Server

    Lavrent'ev, M A

    2012-01-01

    Famous monograph by a distinguished mathematician presents an innovative approach to classical boundary value problems. The treatment employs the basic scheme first suggested by Hilbert and developed by Tonnelli. 1963 edition.

  20. The boundary value problems of magnetotail equilibrium

    International Nuclear Information System (INIS)

    Birn, J.

    1991-01-01

    The equilibrium problem for the Earth's magnetotail is discussed under the assumption that the boundary of the tail can be prescribed or derived from the force balance with the solar wind. A general solution of this problem is presented for the two-dimensional case, where the dependence on the γ coordinate and the presence of Β gamma are neglected. These solutions are further generalized to include the γ dependence (but no Β gamma ) and an open magnetopause. In this formulation, a solution can be obtained by integration when the magnetopause boundary α(x,y), the total pressure function p(x), and the magnetic flux distribution A b (x,y) at the magnetopause are prescribed. Certain restrictions, however, may limit the free choice of these functions to yield physically reasonable, real solutions. When the interaction with the solar wind is included, the boundary location can no longer be chosen freely but follows from the force balance of the magnetotail with the solar wind. For a simplified description of this force balance a differential equation for the boundary location is derived, which generalizes an earlier result by Coroniti and Kennel (1972). It is shown that solutions of this differential equation are bounded by a maximum tail width if the plasma sheet thickness is limited. Several explicit solutions are presented, illustrating cases with and without tail flaring in the z direction, and including the restrictions of the force balance with the solar wind and of the conservation laws of adiabatic convection in a steady configuration

  1. Asymptotics of linear initial boundary value problems with periodic boundary data on the half-line and finite intervals

    KAUST Repository

    Dujardin, G. M.

    2009-01-01

    This paper deals with the asymptotic behaviour of the solutions of linear initial boundary value problems with constant coefficients on the half-line and on finite intervals. We assume that the boundary data are periodic in time and we investigate

  2. Searching spectrum points of difference initial-boundary value problems with using GAS

    International Nuclear Information System (INIS)

    Mazepa, N.E.

    1989-01-01

    A new algorithm for searching spectrum points is proposed. The difference schemes which approximate systems of linear differential equations of hyperbolic type with constant coefficients and in one space dimension are considered. For important class of practiclas problems this algorithm reduces the hard spectrum calculation problem to the polynomial equation solution. For complicated analytic manipulations connected with realization of this algorithm the computation algebraic system REDUCE is used. 28 refs

  3. The extended-domain-eigenfunction method for solving elliptic boundary value problems with annular domains

    Energy Technology Data Exchange (ETDEWEB)

    Aarao, J; Bradshaw-Hajek, B H; Miklavcic, S J; Ward, D A, E-mail: Stan.Miklavcic@unisa.edu.a [School of Mathematics and Statistics, University of South Australia, Mawson Lakes, SA 5095 (Australia)

    2010-05-07

    Standard analytical solutions to elliptic boundary value problems on asymmetric domains are rarely, if ever, obtainable. In this paper, we propose a solution technique wherein we embed the original domain into one with simple boundaries where the classical eigenfunction solution approach can be used. The solution in the larger domain, when restricted to the original domain, is then the solution of the original boundary value problem. We call this the extended-domain-eigenfunction method. To illustrate the method's strength and scope, we apply it to Laplace's equation on an annular-like domain.

  4. The numerical solution of boundary value problems over an infinite domain

    International Nuclear Information System (INIS)

    Shepherd, M.; Skinner, R.

    1976-01-01

    A method is presented for the numerical solution of boundary value problems over infinite domains. An example that illustrates also the strength and accuracy of a numerical procedure for calculating Green's functions is described in detail

  5. A free-boundary value problem related to auto ignition of ...

    African Journals Online (AJOL)

    We examine a free boundary value problem related to auto ignition of combustible fluid in insulation materials. The criteria for the existence of similarity solution of the model equations are established. The conditions for the existence of unique solution are also stated. The numerical results which show the influence of ...

  6. Modified quasi-boundary value method for Cauchy problems of elliptic equations with variable coefficients

    Directory of Open Access Journals (Sweden)

    Hongwu Zhang

    2011-08-01

    Full Text Available In this article, we study a Cauchy problem for an elliptic equation with variable coefficients. It is well-known that such a problem is severely ill-posed; i.e., the solution does not depend continuously on the Cauchy data. We propose a modified quasi-boundary value regularization method to solve it. Convergence estimates are established under two a priori assumptions on the exact solution. A numerical example is given to illustrate our proposed method.

  7. Boundary-value problems in ODE

    Science.gov (United States)

    Tanriverdi, Tanfer

    In this thesis we discuss two problems. The first problem is that of Fanno flow in a tube. In [10] the authors have discussed the mathematics of the Fanno model in much more detail than had been previously been done. The analysis in [10] indicates that the Fanno model becomes relevant, if t indicates the unscaled time and t=et , only when t is at least of order O(e- 1) . Indeed, two most important time scales are when t=O(e-1) and t=O(e- 2) . The authors, in the former case, set t=e- 1t1 (t1=t),x=e -11, and obtain the equation math> 62u6t 21- 62u 6x21=- 2u6 2u6t21 , ( 0.0.1) where u is the velocity of the gas, with p=1,6x1=0 (x1=0). One can follow the solution along the characteristic x1=t1 , and to match with the inviscid behaviour when t1-->0 , u=2+t1 (x1=t1). (0.0.2) In the region t=O(e2) , the authors set t=e2t2, x=e2x2,h= x2t2. For small e , the BC (0.0.02) now becomes u=t2 (x2=t 2), (0.0.3) so that (0.0.1) now has a similarity solution of the form u=t2g( h), u2=e- 1u, and (h2- 1)g'' +4hg'+2g=2g(g+hg' ),' =/ (0.0.4) with g(h)-->2 ash-->1- ,from(0.0.3) (0.0.5) g(h)-->∞ ash-->0- ,(fromthe pressure). ( 0.0.6) In a recent paper [11] the authors discuss the existence of a solution of (0.0.4)-(0.0.6) by using a two dimensional topological shooting method. We also discuss the existence of a solution of (0.0.4)-(0.0.6) by using a shooting method. We first turn the nonlinear ode (0.0.4) into an integral equation and then shoot from the singularity at ∞. The second problem arises when one considers eigenfunction expansions associated with second order ordinary differential equations, as Titchmarsh does in his book. One is concerned with the solutions of the equation - d2ydx2+ q(x)y=ly, (0.0.7) along with certain boundary conditions, where q(x)=-( n2- /)sech 2(x), n=n+/. The problem (0.0.7) has an application in the study of discrete reaction-diffusion equations. Our purpose in this problem is to look in some detail at the equation (0.0.7). We first use contour

  8. The polynomial property of self-adjoint elliptic boundary-value problems and an algebraic description of their attributes

    International Nuclear Information System (INIS)

    Nazarov, S A

    1999-01-01

    We describe a wide class of boundary-value problems for which the application of elliptic theory can be reduced to elementary algebraic operations and which is characterized by the following polynomial property: the sesquilinear form corresponding to the problem degenerates only on some finite-dimensional linear space P of vector polynomials. Under this condition the boundary-value problem is elliptic, and its kernel and cokernel can be expressed in terms of P. For domains with piecewise-smooth boundary or infinite ends (conic, cylindrical, or periodic), we also present fragments of asymptotic formulae for the solutions, give specific versions of general conditional theorems on the Fredholm property (in particular, by modifying the ordinary weighted norms), and compute the index of the operator corresponding to the boundary-value problem. The polynomial property is also helpful for asymptotic analysis of boundary-value problems in thin domains and junctions of such domains. Namely, simple manipulations with P permit one to find the size of the system obtained by dimension reduction as well as the orders of the differential operators occurring in that system and provide complete information on the boundary layer structure. The results are illustrated by examples from elasticity and hydromechanics

  9. Lower and Upper Solutions Method for Positive Solutions of Fractional Boundary Value Problems

    Directory of Open Access Journals (Sweden)

    R. Darzi

    2013-01-01

    Full Text Available We apply the lower and upper solutions method and fixed-point theorems to prove the existence of positive solution to fractional boundary value problem D0+αut+ft,ut=0, 0

  10. Analytic solutions to a family of boundary-value problems for Ginsburg-Landau type equations

    Science.gov (United States)

    Vassilev, V. M.; Dantchev, D. M.; Djondjorov, P. A.

    2017-10-01

    We consider a two-parameter family of nonlinear ordinary differential equations describing the behavior of a critical thermodynamic system, e.g., a binary liquid mixture, of film geometry within the framework of the Ginzburg-Landau theory by means of the order-parameter. We focus on the case in which the confining surfaces are strongly adsorbing but prefer different components of the mixture, i.e., the order-parameter tends to infinity at one of the boundaries and to minus infinity at the other one. We assume that the boundaries of the system are positioned at a finite distance from each other and give analytic solutions to the corresponding boundary-value problems in terms of Weierstrass and Jacobi elliptic functions.

  11. Order Reduction in High-Order Runge-Kutta Methods for Initial Boundary Value Problems

    OpenAIRE

    Rosales, Rodolfo Ruben; Seibold, Benjamin; Shirokoff, David; Zhou, Dong

    2017-01-01

    This paper studies the order reduction phenomenon for initial-boundary-value problems that occurs with many Runge-Kutta time-stepping schemes. First, a geometric explanation of the mechanics of the phenomenon is provided: the approximation error develops boundary layers, induced by a mismatch between the approximation error in the interior and at the boundaries. Second, an analysis of the modes of the numerical scheme is conducted, which explains under which circumstances boundary layers pers...

  12. BOUNDARY VALUE PROBLEM FOR A LOADED EQUATION ELLIPTIC-HYPERBOLIC TYPE IN A DOUBLY CONNECTED DOMAIN

    Directory of Open Access Journals (Sweden)

    O.Kh. Abdullaev

    2014-06-01

    Full Text Available We study the existence and uniqueness of the solution of one boundary value problem for the loaded elliptic-hyperbolic equation of the second order with two lines of change of type in double-connected domain. Similar results have been received by D.M.Kuryhazov, when investigated domain is one-connected.

  13. A boundary-value problem in weighted Hölder spaces for elliptic equations which degenerate at the boundary of the domain

    Energy Technology Data Exchange (ETDEWEB)

    Bazalii, B V; Degtyarev, S P [Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, Donetsk (Ukraine)

    2013-07-31

    An elliptic boundary-value problem for second-order equations with nonnegative characteristic form is investigated in the situation when there is a weak degeneracy on the boundary of the domain. A priori estimates are obtained for solutions and the problem is proved to be solvable in some weighted Hölder spaces. Bibliography: 18 titles.

  14. Student Solutions Manual to Boundary Value Problems and Partial Differential Equations

    CERN Document Server

    Powers, David L

    2005-01-01

    This student solutions manual accompanies the text, Boundary Value Problems and Partial Differential Equations, 5e. The SSM is available in print via PDF or electronically, and provides the student with the detailed solutions of the odd-numbered problems contained throughout the book.Provides students with exercises that skillfully illustrate the techniques used in the text to solve science and engineering problemsNearly 900 exercises ranging in difficulty from basic drills to advanced problem-solving exercisesMany exercises based on current engineering applications

  15. Boundary element methods applied to two-dimensional neutron diffusion problems

    International Nuclear Information System (INIS)

    Itagaki, Masafumi

    1985-01-01

    The Boundary element method (BEM) has been applied to two-dimensional neutron diffusion problems. The boundary integral equation and its discretized form have been derived. Some numerical techniques have been developed, which can be applied to critical and fixed-source problems including multi-region ones. Two types of test programs have been developed according to whether the 'zero-determinant search' or the 'source iteration' technique is adopted for criticality search. Both programs require only the fluxes and currents on boundaries as the unknown variables. The former allows a reduction in computing time and memory in comparison with the finite element method (FEM). The latter is not always efficient in terms of computing time due to the domain integral related to the inhomogeneous source term; however, this domain integral can be replaced by the equivalent boundary integral for a region with a non-multiplying medium or with a uniform source, resulting in a significant reduction in computing time. The BEM, as well as the FEM, is well suited for solving irregular geometrical problems for which the finite difference method (FDM) is unsuited. The BEM also solves problems with infinite domains, which cannot be solved by the ordinary FEM and FDM. Some simple test calculations are made to compare the BEM with the FEM and FDM, and discussions are made concerning the relative merits of the BEM and problems requiring future solution. (author)

  16. Discrete quintic spline for boundary value problem in plate deflation theory

    Science.gov (United States)

    Wong, Patricia J. Y.

    2017-07-01

    We propose a numerical scheme for a fourth-order boundary value problem arising from plate deflation theory. The scheme involves a discrete quintic spline, and it is of order 4 if a parameter takes a specific value, else it is of order 2. We also present a well known numerical example to illustrate the efficiency of our method as well as to compare with other numerical methods proposed in the literature.

  17. On Solutions of the Integrable Boundary Value Problem for KdV Equation on the Semi-Axis

    International Nuclear Information System (INIS)

    Ignatyev, M. Yu.

    2013-01-01

    This paper is concerned with the Korteweg–de Vries (KdV) equation on the semi-axis. The boundary value problem with inhomogeneous integrable boundary conditions is studied. We establish some characteristic properties of solutions of the problem. Also we construct a wide class of solutions of the problem using the inverse spectral method.

  18. Existence and uniqueness of entropy solution to initial boundary value problem for the inviscid Burgers equation

    CERN Document Server

    Zhu, C

    2003-01-01

    This paper is concerned with the existence and uniqueness of the entropy solution to the initial boundary value problem for the inviscid Burgers equation. To apply the method of vanishing viscosity to study the existence of the entropy solution, we first introduce the initial boundary value problem for the viscous Burgers equation, and as in Evans (1998 Partial Differential Equations (Providence, RI: American Mathematical Society) and Hopf (1950 Commun. Pure Appl. Math. 3 201-30), give the formula of the corresponding viscosity solutions by Hopf-Cole transformation. Secondly, we prove the convergence of the viscosity solution sequences and verify that the limiting function is an entropy solution. Finally, we give an example to show how our main result can be applied to solve the initial boundary value problem for the Burgers equation.

  19. Existence and uniqueness of entropy solution to initial boundary value problem for the inviscid Burgers equation

    International Nuclear Information System (INIS)

    Zhu, Changjiang; Duan, Renjun

    2003-01-01

    This paper is concerned with the existence and uniqueness of the entropy solution to the initial boundary value problem for the inviscid Burgers equation. To apply the method of vanishing viscosity to study the existence of the entropy solution, we first introduce the initial boundary value problem for the viscous Burgers equation, and as in Evans (1998 Partial Differential Equations (Providence, RI: American Mathematical Society) and Hopf (1950 Commun. Pure Appl. Math. 3 201-30), give the formula of the corresponding viscosity solutions by Hopf-Cole transformation. Secondly, we prove the convergence of the viscosity solution sequences and verify that the limiting function is an entropy solution. Finally, we give an example to show how our main result can be applied to solve the initial boundary value problem for the Burgers equation

  20. On a Mixed Nonlinear One Point Boundary Value Problem for an Integrodifferential Equation

    Directory of Open Access Journals (Sweden)

    Mesloub Said

    2008-01-01

    Full Text Available This paper is devoted to the study of a mixed problem for a nonlinear parabolic integro-differential equation which mainly arise from a one dimensional quasistatic contact problem. We prove the existence and uniqueness of solutions in a weighted Sobolev space. Proofs are based on some a priori estimates and on the Schauder fixed point theorem. we also give a result which helps to establish the regularity of a solution.

  1. Partial differential equations and boundary-value problems with applications

    CERN Document Server

    Pinsky, Mark A

    2011-01-01

    Building on the basic techniques of separation of variables and Fourier series, the book presents the solution of boundary-value problems for basic partial differential equations: the heat equation, wave equation, and Laplace equation, considered in various standard coordinate systems-rectangular, cylindrical, and spherical. Each of the equations is derived in the three-dimensional context; the solutions are organized according to the geometry of the coordinate system, which makes the mathematics especially transparent. Bessel and Legendre functions are studied and used whenever appropriate th

  2. Numerical Analysis of Forth-Order Boundary Value Problems in Fluid Mechanics and Mathematics

    DEFF Research Database (Denmark)

    Hosseinzadeh, E.; Barari, Amin; Fouladi, F.

    2011-01-01

    In this paper He's variational iteration method is used to solve some examples of linear and non-linear forth-order boundary value problems. The first problem compared with homotopy analysis method solution and the other ones with the exact solution. The results show the high accuracy and speed o...

  3. Numerical analysis of fourth-order boundary value problems in fluid mechanics and mathematics

    DEFF Research Database (Denmark)

    Hosseinzadeh, Elham; Barari, Amin; Fouladi, Fama

    2010-01-01

    In this paper He's variational iteration method is used to solve some examples of linear and non-linear forth-order boundary value problems. The first problem compared with homotopy analysis method solution and the other ones with the exact solution. The results show the high accuracy and speed o...

  4. On the asymptotic of solutions of elliptic boundary value problems in domains with edges

    International Nuclear Information System (INIS)

    Nkemzi, B.

    2005-10-01

    Solutions of elliptic boundary value problems in three-dimensional domains with edges may exhibit singularities. The usual procedure to study these singularities is by the application of the classical Mellin transformation or continuous Fourier transformation. In this paper, we show how the asymptotic behavior of solutions of elliptic boundary value problems in general three-dimensional domains with straight edges can be investigated by means of discrete Fourier transformation. We apply this approach to time-harmonic Maxwell's equations and prove that the singular solutions can fully be described in terms of Fourier series. The representation here can easily be used to approximate three-dimensional stress intensity factors associated with edge singularities. (author)

  5. Initial boundary value problems of nonlinear wave equations in an exterior domain

    International Nuclear Information System (INIS)

    Chen Yunmei.

    1987-06-01

    In this paper, we investigate the existence and uniqueness of the global solutions to the initial boundary value problems of nonlinear wave equations in an exterior domain. When the space dimension n >= 3, the unique global solution of the above problem is obtained for small initial data, even if the nonlinear term is fully nonlinear and contains the unknown function itself. (author). 10 refs

  6. Initial-boundary-value problem of the self-gravitating scalar field in the Bondi-Sachs gauge

    International Nuclear Information System (INIS)

    Frittelli, Simonetta; Gomez, Roberto

    2007-01-01

    It is shown that, in the Bondi-Sachs gauge that fixes the speed of incoming light rays to the value 1, the Einstein equations coupled to a scalar field in spherical symmetry are cast into a symmetric-hyperbolic system of equations for the scalar field, lapse and shift as fundamental variables. In this system of equations, the lapse and shift are incoming characteristic fields, and the scalar field has three components: incoming, outgoing and static. A constraint-preserving boundary condition is prescribed by imposing the projection of the Einstein equation normal to the boundary at the outer value of the radial coordinate. The boundary condition specifies one of the two incoming metric fields. The remaining incoming metric field and the incoming scalar field component need to be specified arbitrarily. Numerical simulations of the scattering of the scalar field by a black hole in the nonlinear regime are presented that illustrate interesting facts about black-hole physics and the behavior of the characteristic variables of the problem

  7. Necessary and Sufficient Conditions for the Existence of Positive Solution for Singular Boundary Value Problems on Time Scales

    Directory of Open Access Journals (Sweden)

    Zhang Xuemei

    2009-01-01

    Full Text Available By constructing available upper and lower solutions and combining the Schauder's fixed point theorem with maximum principle, this paper establishes sufficient and necessary conditions to guarantee the existence of as well as positive solutions for a class of singular boundary value problems on time scales. The results significantly extend and improve many known results for both the continuous case and more general time scales. We illustrate our results by one example.

  8. Response of Non-Linear Shock Absorbers-Boundary Value Problem Analysis

    Science.gov (United States)

    Rahman, M. A.; Ahmed, U.; Uddin, M. S.

    2013-08-01

    A nonlinear boundary value problem of two degrees-of-freedom (DOF) untuned vibration damper systems using nonlinear springs and dampers has been numerically studied. As far as untuned damper is concerned, sixteen different combinations of linear and nonlinear springs and dampers have been comprehensively analyzed taking into account transient terms. For different cases, a comparative study is made for response versus time for different spring and damper types at three important frequency ratios: one at r = 1, one at r > 1 and one at r <1. The response of the system is changed because of the spring and damper nonlinearities; the change is different for different cases. Accordingly, an initially stable absorber may become unstable with time and vice versa. The analysis also shows that higher nonlinearity terms make the system more unstable. Numerical simulation includes transient vibrations. Although problems are much more complicated compared to those for a tuned absorber, a comparison of the results generated by the present numerical scheme with the exact one shows quite a reasonable agreement

  9. Quasisolutions of Inverse Boundary-Value Problem of Aerodynamics for Dense Airfoil Grids

    Directory of Open Access Journals (Sweden)

    A.M. Elizarov

    2016-12-01

    Full Text Available In the process of turbomachinery development, it is of great importance to accurately design impellers and select their blade shape. One of the promising approaches to solving this problem is based on the theory of inverse boundary-value problems in aerodynamics. It helps to develop methods for profiling airfoil grids with predetermined properties in the same way as it is done for isolated airfoils. In this paper, methods have been worked out to find quasisolutions of the inverse boundary-value problem in aerodynamics for a plane airfoil grid. Two methods of quasisolution have been described. The first “`formal” method is similar, in its essence, to the method used for construction of quasisolution for an isolated airfoil. It has been shown that such quasisolutions provide satisfactory results for grids having a sufficiently large relative airfoil pitch. If pitch values are low, this method is unacceptable, because “modified” velocity distribution in some areas is significantly different from the original one in this case. For this reason, areas with significant changes in the angle of the tangent line appear in the airfoil contour and the flow region becomes multivalent. To satisfy the conditions of solvability in the case of grids having a small airfoil pitch, a new quasisolution construction method taking into account the specifics of the problem has been suggested. The desired effect has been achieved due to changes in the weighting function of the minimized functional. The comparison of the results of construction of the new quasisolution with the results obtained by the “formal” method has demonstrated that the constructed airfoils are very similar when the pitch is large. In the case of dense grids, it is clear that preference should be given to the second method, as it brings less distortion to the initial velocity distribution and, thus, allows to physically find an actual airfoil contour.

  10. IMPSOR, 3-D Boundary Problems Solution for Thermal Conductivity Calculation

    International Nuclear Information System (INIS)

    Wilson, D.G.; Williams, M.A.

    1994-01-01

    1 - Description of program or function: IMPSOR implements finite difference methods for multidimensional moving boundary problems with Dirichlet or Neumann boundary conditions. The geometry of the spatial domain is a rectangular parallelepiped with dimensions specified by the user. Dirichlet or Neumann boundary conditions may be specified on each face of the box independently. The user defines the initial and boundary conditions as well as the thermal and physical properties of the problem and several parameters for the numerical method, e.g. degree of implicitness, time-step size. 2 - Method of solution: The spatial domain is partitioned and the governing equation discretized, which yields a nonlinear system of equations at each time-step. This nonlinear system is solved using a successive over-relaxation (SOR) algorithm. For a given node, the previous iteration's temperature and thermal conductivity values are used for advanced points with current values at previous points. This constitutes a Gauss-Seidel iteration. Most of the computing time used by the numerical method is spent in the iterative solution of the nonlinear system. The SOR scheme employed is designed to accommodate vectorization on a Cray X-MP. 3 - Restrictions on the complexity of the problem: Maximum of 70,000 nodes

  11. Multiple positive solutions to nonlinear boundary value problems of a system for fractional differential equations.

    Science.gov (United States)

    Zhai, Chengbo; Hao, Mengru

    2014-01-01

    By using Krasnoselskii's fixed point theorem, we study the existence of at least one or two positive solutions to a system of fractional boundary value problems given by -D(0+)(ν1)y1(t) = λ1a1(t)f(y1(t), y2(t)), - D(0+)(ν2)y2(t) = λ2a2(t)g(y1(t), y2(t)), where D(0+)(ν) is the standard Riemann-Liouville fractional derivative, ν1, ν2 ∈ (n - 1, n] for n > 3 and n ∈ N, subject to the boundary conditions y1((i))(0) = 0 = y ((i))(0), for 0 ≤ i ≤ n - 2, and [D(0+)(α)y1(t)] t=1 = 0 = [D(0+ (α)y2(t)] t=1, for 1 ≤ α ≤ n - 2, or y1((i))(0) = 0 = y ((i))(0), for 0 ≤ i ≤ n - 2, and [D(0+)(α)y1(t)] t=1 = ϕ1(y1), [D(0+)(α)y2(t)] t=1 = ϕ2(y2), for 1 ≤ α ≤ n - 2, ϕ1, ϕ2 ∈ C([0,1], R). Our results are new and complement previously known results. As an application, we also give an example to demonstrate our result.

  12. Uniqueness Theorem for the Inverse Aftereffect Problem and Representation the Nodal Points Form

    OpenAIRE

    A. Neamaty; Sh. Akbarpoor; A. Dabbaghian

    2015-01-01

    In this paper, we consider a boundary value problem with aftereffect on a finite interval. Then, the asymptotic behavior of the solutions, eigenvalues, the nodal points and the associated nodal length are studied. We also calculate the numerical values of the nodal points and the nodal length. Finally, we prove the uniqueness theorem for the inverse aftereffect problem by applying any dense subset of the nodal points.

  13. B-spline solution of a singularly perturbed boundary value problem arising in biology

    International Nuclear Information System (INIS)

    Lin Bin; Li Kaitai; Cheng Zhengxing

    2009-01-01

    We use B-spline functions to develop a numerical method for solving a singularly perturbed boundary value problem associated with biology science. We use B-spline collocation method, which leads to a tridiagonal linear system. The accuracy of the proposed method is demonstrated by test problems. The numerical result is found in good agreement with exact solution.

  14. Classical boundary-value problem in Riemannian quantum gravity and self-dual Taub-NUT-(anti)de Sitter geometries

    International Nuclear Information System (INIS)

    Akbar, M.M.; D'Eath, P.D.

    2003-01-01

    The classical boundary-value problem of the Einstein field equations is studied with an arbitrary cosmological constant, in the case of a compact (S 3 ) boundary given a biaxial Bianchi-IX positive-definite three-metric, specified by two radii (a,b). For the simplest, four-ball, topology of the manifold with this boundary, the regular classical solutions are found within the family of Taub-NUT-(anti)de Sitter metrics with self-dual Weyl curvature. For arbitrary choice of positive radii (a,b), we find that there are three solutions for the infilling geometry of this type. We obtain exact solutions for them and for their Euclidean actions. The case of negative cosmological constant is investigated further. For reasonable squashing of the three-sphere, all three infilling solutions have real-valued actions which possess a 'cusp catastrophe' structure with a non-self-intersecting 'catastrophe manifold' implying that the dominant contribution comes from the unique real positive-definite solution on the ball. The positive-definite solution exists even for larger deformations of the three-sphere, as long as a certain inequality between a and b holds. The action of this solution is proportional to -a 3 for large a (∼b) and hence larger radii are favoured. The same boundary-value problem with more complicated interior topology containing a 'bolt' is investigated in a forthcoming paper

  15. Nonlinear second-order multivalued boundary value problems

    Indian Academy of Sciences (India)

    R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22

    Department of Mathematics, National Technical University, Zografou Campus,. Athens 15780 ... incorporates gradient systems, evolutionary variational inequalities and the classical boundary value ... We are led to an eventual application.

  16. Uniqueness Theorem for the Inverse Aftereffect Problem and Representation the Nodal Points Form

    Directory of Open Access Journals (Sweden)

    A. Neamaty

    2015-03-01

    Full Text Available In this paper, we consider a boundary value problem with aftereffect on a finite interval. Then, the asymptotic behavior of the solutions, eigenvalues, the nodal points and the associated nodal length are studied. We also calculate the numerical values of the nodal points and the nodal length. Finally, we prove the uniqueness theorem for the inverse aftereffect problem by applying any dense subset of the nodal points.

  17. On some boundary value problems in quantum statistical mechanics

    International Nuclear Information System (INIS)

    Angelescu, N.

    1978-01-01

    The following two topics of equilibrium quantum statistical mechanics are discussed in this thesis: (i) the independence of the thermodynamic limit of grand-canonical pressure on the boundary conditions; (ii) the magnetic properties of free quantum gases. Problem (i) is handled with a functional integration technique. Wiener-type conditional measures are constructed for a given domain and a general class of mixed conditions on its boundary, these measures are used to write down Feynman-Kac formulae for the kernels of exp(-βH), where H is the Hamiltonian of N interacting particles in the given domain. These measures share the property that they assign the same mass as the usual Wiener measure to any set of trajectories not intersecting the boundary. Local estimates on the kernels of exp(-βH) are derived, which imply independence of the pressure on the boundary conditions in the thermodynamic limit. Problem (ii) has a historical development: since Landau's work (1930), much discussion has been devoted to the influence of the finite size on the susceptibility. In finite volume, Dirichlet boundary conditions are imposed, on the ground that they ensure gauge invariance. The thermodynamic limit of the pressure is proved, using again functional integration. The functional measure is now complex but absolutely continuous with respect to Wiener measure, so the usual local estimates hold true. The controversy in the literature was concentrated on the commutativity of the operations of H-derivation and thermodynamic limit, so the existence of this limit for the zero-field susceptibility and its surface term are proved separately, demonstrating this commutativity. The proof relies on the following result of independent interest: the perturbation theory of self-adjoint trace-class semigroups is trace-class convergent and analytic. (author)

  18. A uniformly valid approximation algorithm for nonlinear ordinary singular perturbation problems with boundary layer solutions.

    Science.gov (United States)

    Cengizci, Süleyman; Atay, Mehmet Tarık; Eryılmaz, Aytekin

    2016-01-01

    This paper is concerned with two-point boundary value problems for singularly perturbed nonlinear ordinary differential equations. The case when the solution only has one boundary layer is examined. An efficient method so called Successive Complementary Expansion Method (SCEM) is used to obtain uniformly valid approximations to this kind of solutions. Four test problems are considered to check the efficiency and accuracy of the proposed method. The numerical results are found in good agreement with exact and existing solutions in literature. The results confirm that SCEM has a superiority over other existing methods in terms of easy-applicability and effectiveness.

  19. The Laplace equation boundary value problems on bounded and unbounded Lipschitz domains

    CERN Document Server

    Medková, Dagmar

    2018-01-01

    This book is devoted to boundary value problems of the Laplace equation on bounded and unbounded Lipschitz domains. It studies the Dirichlet problem, the Neumann problem, the Robin problem, the derivative oblique problem, the transmission problem, the skip problem and mixed problems. It also examines different solutions - classical, in Sobolev spaces, in Besov spaces, in homogeneous Sobolev spaces and in the sense of non-tangential limit. It also explains relations between different solutions. The book has been written in a way that makes it as readable as possible for a wide mathematical audience, and includes all the fundamental definitions and propositions from other fields of mathematics. This book is of interest to research students, as well as experts in partial differential equations and numerical analysis.

  20. Nature Inspired Computational Technique for the Numerical Solution of Nonlinear Singular Boundary Value Problems Arising in Physiology

    Directory of Open Access Journals (Sweden)

    Suheel Abdullah Malik

    2014-01-01

    Full Text Available We present a hybrid heuristic computing method for the numerical solution of nonlinear singular boundary value problems arising in physiology. The approximate solution is deduced as a linear combination of some log sigmoid basis functions. A fitness function representing the sum of the mean square error of the given nonlinear ordinary differential equation (ODE and its boundary conditions is formulated. The optimization of the unknown adjustable parameters contained in the fitness function is performed by the hybrid heuristic computation algorithm based on genetic algorithm (GA, interior point algorithm (IPA, and active set algorithm (ASA. The efficiency and the viability of the proposed method are confirmed by solving three examples from physiology. The obtained approximate solutions are found in excellent agreement with the exact solutions as well as some conventional numerical solutions.

  1. Numerical continuation methods for dynamical systems path following and boundary value problems

    CERN Document Server

    Krauskopf, Bernd; Galan-Vioque, Jorge

    2007-01-01

    Path following in combination with boundary value problem solvers has emerged as a continuing and strong influence in the development of dynamical systems theory and its application. It is widely acknowledged that the software package AUTO - developed by Eusebius J. Doedel about thirty years ago and further expanded and developed ever since - plays a central role in the brief history of numerical continuation. This book has been compiled on the occasion of Sebius Doedel''s 60th birthday. Bringing together for the first time a large amount of material in a single, accessible source, it is hoped that the book will become the natural entry point for researchers in diverse disciplines who wish to learn what numerical continuation techniques can achieve. The book opens with a foreword by Herbert B. Keller and lecture notes by Sebius Doedel himself that introduce the basic concepts of numerical bifurcation analysis. The other chapters by leading experts discuss continuation for various types of systems and objects ...

  2. Analytic solution of boundary-value problems for nonstationary model kinetic equations

    International Nuclear Information System (INIS)

    Latyshev, A.V.; Yushkanov, A.A.

    1993-01-01

    A theory for constructing the solutions of boundary-value problems for non-stationary model kinetic equations is constructed. This theory was incorrectly presented equation, separation of the variables is used, this leading to a characteristic equation. Eigenfunctions are found in the space of generalized functions, and the eigenvalue spectrum is investigated. An existence and uniqueness theorem for the expansion of the Laplace transform of the solution with respect to the eigenfunctions is proved. The proof is constructive and gives explicit expressions for the expansion coefficients. An application to the Rayleigh problem is obtained, and the corresponding result of Cercignani is corrected

  3. Symmetry analysis and exact solutions of one class of (1+3)-dimensional boundary-value problems of the Stefan type

    OpenAIRE

    Kovalenko, S. S.

    2014-01-01

    We present the group classification of one class of (1+3)-dimensional nonlinear boundary-value problems of the Stefan type that simulate the processes of melting and evaporation of metals. The results obtained are used for the construction of the exact solution of one boundary-value problem from the class under study.

  4. Investigation of solutions of state-dependent multi-impulsive boundary value problems

    Czech Academy of Sciences Publication Activity Database

    Rontó, András; Rachůnková, I.; Rontó, M.; Rachůnek, L.

    2017-01-01

    Roč. 24, č. 2 (2017), s. 287-312 ISSN 1072-947X R&D Projects: GA ČR(CZ) GA14-06958S Institutional support: RVO:67985840 Keywords : state-dependent multi-impulsive systems * non-linear boundary value problem * parametrization technique Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 0.290, year: 2016 https://www.degruyter.com/view/j/gmj.2017.24.issue-2/gmj-2016-0084/gmj-2016-0084. xml

  5. Investigation of solutions of state-dependent multi-impulsive boundary value problems

    Czech Academy of Sciences Publication Activity Database

    Rontó, András; Rachůnková, I.; Rontó, M.; Rachůnek, L.

    2017-01-01

    Roč. 24, č. 2 (2017), s. 287-312 ISSN 1072-947X R&D Projects: GA ČR(CZ) GA14-06958S Institutional support: RVO:67985840 Keywords : state-dependent multi-impulsive systems * non-linear boundary value problem * parametrization technique Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 0.290, year: 2016 https://www.degruyter.com/view/j/gmj.2017.24.issue-2/gmj-2016-0084/gmj-2016-0084.xml

  6. Existence of 2m-1 Positive Solutions for Sturm-Liouville Boundary Value Problems with Linear Functional Boundary Conditions on the Half-Line

    Directory of Open Access Journals (Sweden)

    Yanmei Sun

    2012-01-01

    Full Text Available By using the Leggett-Williams fixed theorem, we establish the existence of multiple positive solutions for second-order nonhomogeneous Sturm-Liouville boundary value problems with linear functional boundary conditions. One explicit example with singularity is presented to demonstrate the application of our main results.

  7. Generalised functions method in the boundary value problems of elastodynamics by stationary running loads

    International Nuclear Information System (INIS)

    Alexeyeva, L.A.

    2001-01-01

    Investigation of diffraction processes of seismic waves on underground tunnels and pipelines with use of mathematical methods is related to solving boundary value problems (BVP) for hyperbolic system of differential equations in domains with cylindrical cavities when seismic disturbances propagate along boundaries with subsonic or transonic speeds. Also such classes of problems appear when it's necessary to study the behavior of underground constructions and Stress-strain State of environment. But in this case the velocities of running loads are less than velocities of wave propagation in surrounding medium. At present similar problems were solved only for constructions of circular cylindrical form with use of methods of full and not full dividing of variables. For cylindrical constructions of complex cross section strong mathematical theories for solving these problems were absent.(author)

  8. Geopotential coefficient determination and the gravimetric boundary value problem: A new approach

    Science.gov (United States)

    Sjoeberg, Lars E.

    1989-01-01

    New integral formulas to determine geopotential coefficients from terrestrial gravity and satellite altimetry data are given. The formulas are based on the integration of data over the non-spherical surface of the Earth. The effect of the topography to low degrees and orders of coefficients is estimated numerically. Formulas for the solution of the gravimetric boundary value problem are derived.

  9. Necessary and Sufficient Conditions for the Existence of Positive Solution for Singular Boundary Value Problems on Time Scales

    Directory of Open Access Journals (Sweden)

    Meiqiang Feng

    2009-01-01

    Full Text Available By constructing available upper and lower solutions and combining the Schauder's fixed point theorem with maximum principle, this paper establishes sufficient and necessary conditions to guarantee the existence of Cld[0,1]𝕋 as well as CldΔ[0,1]𝕋 positive solutions for a class of singular boundary value problems on time scales. The results significantly extend and improve many known results for both the continuous case and more general time scales. We illustrate our results by one example.

  10. Layer potentials and boundary-value problems for second order elliptic operators with data in Besov spaces

    CERN Document Server

    Barton, Ariel

    2016-01-01

    This monograph presents a comprehensive treatment of second order divergence form elliptic operators with bounded measurable t-independent coefficients in spaces of fractional smoothness, in Besov and weighted L^p classes. The authors establish: (1) Mapping properties for the double and single layer potentials, as well as the Newton potential; (2) Extrapolation-type solvability results: the fact that solvability of the Dirichlet or Neumann boundary value problem at any given L^p space automatically assures their solvability in an extended range of Besov spaces; (3) Well-posedness for the non-homogeneous boundary value problems. In particular, the authors prove well-posedness of the non-homogeneous Dirichlet problem with data in Besov spaces for operators with real, not necessarily symmetric, coefficients.

  11. Variational Homotopy Perturbation Method for Solving Higher Dimensional Initial Boundary Value Problems

    Directory of Open Access Journals (Sweden)

    Muhammad Aslam Noor

    2008-01-01

    Full Text Available We suggest and analyze a technique by combining the variational iteration method and the homotopy perturbation method. This method is called the variational homotopy perturbation method (VHPM. We use this method for solving higher dimensional initial boundary value problems with variable coefficients. The developed algorithm is quite efficient and is practically well suited for use in these problems. The proposed scheme finds the solution without any discritization, transformation, or restrictive assumptions and avoids the round-off errors. Several examples are given to check the reliability and efficiency of the proposed technique.

  12. Elliptic boundary value problems with fractional regularity data the first order approach

    CERN Document Server

    Amenta, Alex

    2018-01-01

    In this monograph the authors study the well-posedness of boundary value problems of Dirichlet and Neumann type for elliptic systems on the upper half-space with coefficients independent of the transversal variable and with boundary data in fractional Hardy-Sobolev and Besov spaces. The authors use the so-called "first order approach" which uses minimal assumptions on the coefficients and thus allows for complex coefficients and for systems of equations. This self-contained exposition of the first order approach offers new results with detailed proofs in a clear and accessible way and will become a valuable reference for graduate students and researchers working in partial differential equations and harmonic analysis.

  13. The nonlocal boundary value problems for strongly singular higher-order nonlinear functional-differential equations

    Czech Academy of Sciences Publication Activity Database

    Mukhigulashvili, Sulkhan

    -, č. 35 (2015), s. 23-50 ISSN 1126-8042 Institutional support: RVO:67985840 Keywords : higher order functional differential equations * Dirichlet boundary value problem * strong singularity Subject RIV: BA - General Mathematics http://ijpam.uniud.it/online_issue/201535/03-Mukhigulashvili.pdf

  14. An Existence Principle for Nonlocal Difference Boundary Value Problems with φ-Laplacian and Its Application to Singular Problems

    Directory of Open Access Journals (Sweden)

    Svatoslav Stanêk

    2008-03-01

    Full Text Available The paper presents an existence principle for solving a large class of nonlocal regular discrete boundary value problems with the φ-Laplacian. Applications of the existence principle to singular discrete problems are given.

  15. Remark on periodic boundary-value problem for second-order linear ordinary differential equations

    Czech Academy of Sciences Publication Activity Database

    Dosoudilová, M.; Lomtatidze, Alexander

    2018-01-01

    Roč. 2018, č. 13 (2018), s. 1-7 ISSN 1072-6691 Institutional support: RVO:67985840 Keywords : second-order linear equation * periodic boundary value problem * unique solvability Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 0.954, year: 2016 https://ejde.math.txstate.edu/Volumes/2018/13/abstr.html

  16. Singular boundary value problem for the integrodifferential equation in an insurance model with stochastic premiums: Analysis and numerical solution

    Science.gov (United States)

    Belkina, T. A.; Konyukhova, N. B.; Kurochkin, S. V.

    2012-10-01

    A singular boundary value problem for a second-order linear integrodifferential equation with Volterra and non-Volterra integral operators is formulated and analyzed. The equation is defined on ℝ+, has a weak singularity at zero and a strong singularity at infinity, and depends on several positive parameters. Under natural constraints on the coefficients of the equation, existence and uniqueness theorems for this problem with given limit boundary conditions at singular points are proved, asymptotic representations of the solution are given, and an algorithm for its numerical determination is described. Numerical computations are performed and their interpretation is given. The problem arises in the study of the survival probability of an insurance company over infinite time (as a function of its initial surplus) in a dynamic insurance model that is a modification of the classical Cramer-Lundberg model with a stochastic process rate of premium under a certain investment strategy in the financial market. A comparative analysis of the results with those produced by the model with deterministic premiums is given.

  17. Random walks in the quarter plane algebraic methods, boundary value problems, applications to queueing systems and analytic combinatorics

    CERN Document Server

    Fayolle, Guy; Malyshev, Vadim

    2017-01-01

    This monograph aims to promote original mathematical methods to determine the invariant measure of two-dimensional random walks in domains with boundaries. Such processes arise in numerous applications and are of interest in several areas of mathematical research, such as Stochastic Networks, Analytic Combinatorics, and Quantum Physics. This second edition consists of two parts. Part I is a revised upgrade of the first edition (1999), with additional recent results on the group of a random walk. The theoretical approach given therein has been developed by the authors since the early 1970s. By using Complex Function Theory, Boundary Value Problems, Riemann Surfaces, and Galois Theory, completely new methods are proposed for solving functional equations of two complex variables, which can also be applied to characterize the Transient Behavior of the walks, as well as to find explicit solutions to the one-dimensional Quantum Three-Body Problem, or to tackle a new class of Integrable Systems. Part II borrows spec...

  18. Positive solutions for a nonlinear periodic boundary-value problem with a parameter

    Directory of Open Access Journals (Sweden)

    Jingliang Qiu

    2012-08-01

    Full Text Available Using topological degree theory with a partially ordered structure of space, sufficient conditions for the existence and multiplicity of positive solutions for a second-order nonlinear periodic boundary-value problem are established. Inspired by ideas in Guo and Lakshmikantham [6], we study the dependence of positive periodic solutions as a parameter approaches infinity, $$ lim_{lambdao +infty}|x_{lambda}|=+infty,quadhbox{or}quad lim_{lambdao+infty}|x_{lambda}|=0. $$

  19. The Method of Subsuper Solutions for Weighted p(r-Laplacian Equation Boundary Value Problems

    Directory of Open Access Journals (Sweden)

    Zhimei Qiu

    2008-10-01

    Full Text Available This paper investigates the existence of solutions for weighted p(r-Laplacian ordinary boundary value problems. Our method is based on Leray-Schauder degree. As an application, we give the existence of weak solutions for p(x-Laplacian partial differential equations.

  20. Uniqueness in some higher order elliptic boundary value problems in n dimensional domains

    Directory of Open Access Journals (Sweden)

    C.-P. Danet

    2011-07-01

    Full Text Available We develop maximum principles for several P functions which are defined on solutions to equations of fourth and sixth order (including a equation which arises in plate theory and bending of cylindrical shells. As a consequence, we obtain uniqueness results for fourth and sixth order boundary value problems in arbitrary n dimensional domains.

  1. Homotopy Analysis Method for Boundary-Value Problem of Turbo Warrant Pricing under Stochastic Volatility

    Directory of Open Access Journals (Sweden)

    Hoi Ying Wong

    2013-01-01

    Full Text Available Turbo warrants are liquidly traded financial derivative securities in over-the-counter and exchange markets in Asia and Europe. The structure of turbo warrants is similar to barrier options, but a lookback rebate will be paid if the barrier is crossed by the underlying asset price. Therefore, the turbo warrant price satisfies a partial differential equation (PDE with a boundary condition that depends on another boundary-value problem (BVP of PDE. Due to the highly complicated structure of turbo warrants, their valuation presents a challenging problem in the field of financial mathematics. This paper applies the homotopy analysis method to construct an analytic pricing formula for turbo warrants under stochastic volatility in a PDE framework.

  2. Variational Iteration Method for Fifth-Order Boundary Value Problems Using He's Polynomials

    Directory of Open Access Journals (Sweden)

    Muhammad Aslam Noor

    2008-01-01

    Full Text Available We apply the variational iteration method using He's polynomials (VIMHP for solving the fifth-order boundary value problems. The proposed method is an elegant combination of variational iteration and the homotopy perturbation methods and is mainly due to Ghorbani (2007. The suggested algorithm is quite efficient and is practically well suited for use in these problems. The proposed iterative scheme finds the solution without any discritization, linearization, or restrictive assumptions. Several examples are given to verify the reliability and efficiency of the method. The fact that the proposed technique solves nonlinear problems without using Adomian's polynomials can be considered as a clear advantage of this algorithm over the decomposition method.

  3. Recursive recovery of Markov transition probabilities from boundary value data

    Energy Technology Data Exchange (ETDEWEB)

    Patch, Sarah Kathyrn [Univ. of California, Berkeley, CA (United States)

    1994-04-01

    In an effort to mathematically describe the anisotropic diffusion of infrared radiation in biological tissue Gruenbaum posed an anisotropic diffusion boundary value problem in 1989. In order to accommodate anisotropy, he discretized the temporal as well as the spatial domain. The probabilistic interpretation of the diffusion equation is retained; radiation is assumed to travel according to a random walk (of sorts). In this random walk the probabilities with which photons change direction depend upon their previous as well as present location. The forward problem gives boundary value data as a function of the Markov transition probabilities. The inverse problem requires finding the transition probabilities from boundary value data. Problems in the plane are studied carefully in this thesis. Consistency conditions amongst the data are derived. These conditions have two effects: they prohibit inversion of the forward map but permit smoothing of noisy data. Next, a recursive algorithm which yields a family of solutions to the inverse problem is detailed. This algorithm takes advantage of all independent data and generates a system of highly nonlinear algebraic equations. Pluecker-Grassmann relations are instrumental in simplifying the equations. The algorithm is used to solve the 4 x 4 problem. Finally, the smallest nontrivial problem in three dimensions, the 2 x 2 x 2 problem, is solved.

  4. Partial differential equations & boundary value problems with Maple

    CERN Document Server

    Articolo, George A

    2009-01-01

    Partial Differential Equations and Boundary Value Problems with Maple presents all of the material normally covered in a standard course on partial differential equations, while focusing on the natural union between this material and the powerful computational software, Maple. The Maple commands are so intuitive and easy to learn, students can learn what they need to know about the software in a matter of hours- an investment that provides substantial returns. Maple''s animation capabilities allow students and practitioners to see real-time displays of the solutions of partial differential equations.  Maple files can be found on the books website. Ancillary list: Maple files- http://www.elsevierdirect.com/companion.jsp?ISBN=9780123747327  Provides a quick overview of the software w/simple commands needed to get startedIncludes review material on linear algebra and Ordinary Differential equations, and their contribution in solving partial differential equationsIncorporates an early introduction to Sturm-L...

  5. Uniqueness in the inverse boundary value problem for piecewise homogeneous anisotropic elasticity

    OpenAIRE

    Cârstea, Cătălin I.; Honda, Naofumi; Nakamura, Gen

    2016-01-01

    Consider a three dimensional piecewise homogeneous anisotropic elastic medium $\\Omega$ which is a bounded domain consisting of a finite number of bounded subdomains $D_\\alpha$, with each $D_\\alpha$ a homogeneous elastic medium. One typical example is a finite element model with elements with curvilinear interfaces for an ansiotropic elastic medium. Assuming the $D_\\alpha$ are known and Lipschitz, we are concerned with the uniqueness in the inverse boundary value problem of identifying the ani...

  6. A classical Perron method for existence of smooth solutions to boundary value and obstacle problems for degenerate-elliptic operators via holomorphic maps

    Science.gov (United States)

    Feehan, Paul M. N.

    2017-09-01

    We prove existence of solutions to boundary value problems and obstacle problems for degenerate-elliptic, linear, second-order partial differential operators with partial Dirichlet boundary conditions using a new version of the Perron method. The elliptic operators considered have a degeneracy along a portion of the domain boundary which is similar to the degeneracy of a model linear operator identified by Daskalopoulos and Hamilton [9] in their study of the porous medium equation or the degeneracy of the Heston operator [21] in mathematical finance. Existence of a solution to the partial Dirichlet problem on a half-ball, where the operator becomes degenerate on the flat boundary and a Dirichlet condition is only imposed on the spherical boundary, provides the key additional ingredient required for our Perron method. Surprisingly, proving existence of a solution to this partial Dirichlet problem with ;mixed; boundary conditions on a half-ball is more challenging than one might expect. Due to the difficulty in developing a global Schauder estimate and due to compatibility conditions arising where the ;degenerate; and ;non-degenerate boundaries; touch, one cannot directly apply the continuity or approximate solution methods. However, in dimension two, there is a holomorphic map from the half-disk onto the infinite strip in the complex plane and one can extend this definition to higher dimensions to give a diffeomorphism from the half-ball onto the infinite ;slab;. The solution to the partial Dirichlet problem on the half-ball can thus be converted to a partial Dirichlet problem on the slab, albeit for an operator which now has exponentially growing coefficients. The required Schauder regularity theory and existence of a solution to the partial Dirichlet problem on the slab can nevertheless be obtained using previous work of the author and C. Pop [16]. Our Perron method relies on weak and strong maximum principles for degenerate-elliptic operators, concepts of

  7. On one two-point BVP for the fourth order linear ordinary differential equation

    Czech Academy of Sciences Publication Activity Database

    Mukhigulashvili, Sulkhan; Manjikashvili, M.

    2017-01-01

    Roč. 24, č. 2 (2017), s. 265-275 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : fourth order linear ordinary differential equations * two-point boundary value problems Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 0.290, year: 2016 https://www.degruyter.com/view/j/gmj.2017.24.issue-2/gmj-2016-0077/gmj-2016-0077. xml

  8. On one two-point BVP for the fourth order linear ordinary differential equation

    Czech Academy of Sciences Publication Activity Database

    Mukhigulashvili, Sulkhan; Manjikashvili, M.

    2017-01-01

    Roč. 24, č. 2 (2017), s. 265-275 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : fourth order linear ordinary differential equations * two-point boundary value problems Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 0.290, year: 2016 https://www.degruyter.com/view/j/gmj.2017.24.issue-2/gmj-2016-0077/gmj-2016-0077.xml

  9. The shooting method and multiple solutions of two/multi-point BVPs of second-order ODE

    Directory of Open Access Journals (Sweden)

    Man Kam Kwong

    2006-06-01

    Full Text Available Within the last decade, there has been growing interest in the study of multiple solutions of two- and multi-point boundary value problems of nonlinear ordinary differential equations as fixed points of a cone mapping. Undeniably many good results have emerged. The purpose of this paper is to point out that, in the special case of second-order equations, the shooting method can be an effective tool, sometimes yielding better results than those obtainable via fixed point techniques.

  10. Adaptive boundary conditions for exterior flow problems

    CERN Document Server

    Boenisch, V; Wittwer, S

    2003-01-01

    We consider the problem of solving numerically the stationary incompressible Navier-Stokes equations in an exterior domain in two dimensions. This corresponds to studying the stationary fluid flow past a body. The necessity to truncate for numerical purposes the infinite exterior domain to a finite domain leads to the problem of finding appropriate boundary conditions on the surface of the truncated domain. We solve this problem by providing a vector field describing the leading asymptotic behavior of the solution. This vector field is given in the form of an explicit expression depending on a real parameter. We show that this parameter can be determined from the total drag exerted on the body. Using this fact we set up a self-consistent numerical scheme that determines the parameter, and hence the boundary conditions and the drag, as part of the solution process. We compare the values of the drag obtained with our adaptive scheme with the results from using traditional constant boundary conditions. Computati...

  11. Theorems on differential inequalities and periodic boundary value problem for second-order ordinary differential equations

    Czech Academy of Sciences Publication Activity Database

    Lomtatidze, Alexander

    2016-01-01

    Roč. 67, č. 1 (2016), s. 1-129 ISSN 1512-0015 Institutional support: RVO:67985840 Keywords : periodic boundary value problem * positive solution * singular equation Subject RIV: BA - General Mathematics http://rmi.tsu.ge/jeomj/memoirs/vol67/abs67-1.htm

  12. On Impulsive Boundary Value Problems of Fractional Differential Equations with Irregular Boundary Conditions

    Directory of Open Access Journals (Sweden)

    Guotao Wang

    2012-01-01

    Full Text Available We study nonlinear impulsive differential equations of fractional order with irregular boundary conditions. Some existence and uniqueness results are obtained by applying standard fixed-point theorems. For illustration of the results, some examples are discussed.

  13. Initial-Boundary Value Problem Solution of the Nonlinear Shallow-water Wave Equations

    Science.gov (United States)

    Kanoglu, U.; Aydin, B.

    2014-12-01

    The hodograph transformation solutions of the one-dimensional nonlinear shallow-water wave (NSW) equations are usually obtained through integral transform techniques such as Fourier-Bessel transforms. However, the original formulation of Carrier and Greenspan (1958 J Fluid Mech) and its variant Carrier et al. (2003 J Fluid Mech) involve evaluation integrals. Since elliptic integrals are highly singular as discussed in Carrier et al. (2003), this solution methodology requires either approximation of the associated integrands by smooth functions or selection of regular initial/boundary data. It should be noted that Kanoglu (2004 J Fluid Mech) partly resolves this issue by simplifying the resulting integrals in closed form. Here, the hodograph transform approach is coupled with the classical eigenfunction expansion method rather than integral transform techniques and a new analytical model for nonlinear long wave propagation over a plane beach is derived. This approach is based on the solution methodology used in Aydın & Kanoglu (2007 CMES-Comp Model Eng) for wind set-down relaxation problem. In contrast to classical initial- or boundary-value problem solutions, here, the NSW equations are formulated to yield an initial-boundary value problem (IBVP) solution. In general, initial wave profile with nonzero initial velocity distribution is assumed and the flow variables are given in the form of Fourier-Bessel series. The results reveal that the developed method allows accurate estimation of the spatial and temporal variation of the flow quantities, i.e., free-surface height and depth-averaged velocity, with much less computational effort compared to the integral transform techniques such as Carrier et al. (2003), Kanoglu (2004), Tinti & Tonini (2005 J Fluid Mech), and Kanoglu & Synolakis (2006 Phys Rev Lett). Acknowledgments: This work is funded by project ASTARTE- Assessment, STrategy And Risk Reduction for Tsunamis in Europe. Grant 603839, 7th FP (ENV.2013.6.4-3 ENV

  14. A Hartman–Nagumo inequality for the vector ordinary -Laplacian and applications to nonlinear boundary value problems

    Directory of Open Access Journals (Sweden)

    Ureña Antonio J

    2002-01-01

    Full Text Available A generalization of the well-known Hartman–Nagumo inequality to the case of the vector ordinary -Laplacian and classical degree theory provide existence results for some associated nonlinear boundary value problems.

  15. Asymptotics of linear initial boundary value problems with periodic boundary data on the half-line and finite intervals

    KAUST Repository

    Dujardin, G. M.

    2009-08-12

    This paper deals with the asymptotic behaviour of the solutions of linear initial boundary value problems with constant coefficients on the half-line and on finite intervals. We assume that the boundary data are periodic in time and we investigate whether the solution becomes time-periodic after sufficiently long time. Using Fokas\\' transformation method, we show that, for the linear Schrödinger equation, the linear heat equation and the linearized KdV equation on the half-line, the solutions indeed become periodic for large time. However, for the same linear Schrödinger equation on a finite interval, we show that the solution, in general, is not asymptotically periodic; actually, the asymptotic behaviour of the solution depends on the commensurability of the time period T of the boundary data with the square of the length of the interval over. © 2009 The Royal Society.

  16. Monotone methods for solving a boundary value problem of second order discrete system

    Directory of Open Access Journals (Sweden)

    Wang Yuan-Ming

    1999-01-01

    Full Text Available A new concept of a pair of upper and lower solutions is introduced for a boundary value problem of second order discrete system. A comparison result is given. An existence theorem for a solution is established in terms of upper and lower solutions. A monotone iterative scheme is proposed, and the monotone convergence rate of the iteration is compared and analyzed. The numerical results are given.

  17. Existence and Estimates of Positive Solutions for Some Singular Fractional Boundary Value Problems

    Directory of Open Access Journals (Sweden)

    Habib Mâagli

    2014-01-01

    fractional boundary value problem:Dαu(x=−a(xuσ(x, x∈(0,1 with the conditions limx→0+⁡x2−αu(x=0, u(1=0, where 1<α≤2, σ∈(−1,1, and a is a nonnegative continuous function on (0,1 that may be singular at x=0 or x=1. We also give the global behavior of such a solution.

  18. On some examples of pollutant transport problems solved numerically using the boundary element method

    Science.gov (United States)

    Azis, Moh. Ivan; Kasbawati; Haddade, Amiruddin; Astuti Thamrin, Sri

    2018-03-01

    A boundary element method (BEM) is obtained for solving a boundary value problem of homogeneous anisotropic media governed by diffusion-convection equation. The application of the BEM is shown for two particular pollutant transport problems of Tello river and Unhas lake in Makassar Indonesia. For the two particular problems a variety of the coefficients of diffusion and the velocity components are taken. The results show that the solutions vary as the parameters change. And this suggests that one has to be careful in measuring or determining the values of the parameters.

  19. Closed form solution to a second order boundary value problem and its application in fluid mechanics

    International Nuclear Information System (INIS)

    Eldabe, N.T.; Elghazy, E.M.; Ebaid, A.

    2007-01-01

    The Adomian decomposition method is used by many researchers to investigate several scientific models. In this Letter, the modified Adomian decomposition method is applied to construct a closed form solution for a second order boundary value problem with singularity

  20. Extension Theory and Krein-type Resolvent Formulas for Nonsmooth Boundary Value Problems

    DEFF Research Database (Denmark)

    Abels, Helmut; Grubb, Gerd; Wood, Ian Geoffrey

    2014-01-01

    The theory of selfadjoint extensions of symmetric operators, and more generally the theory of extensions of dual pairs, was implemented some years ago for boundary value problems for elliptic operators on smooth bounded domains. Recently, the questions have been taken up again for nonsmooth domains....... In the present work we show that pseudodifferential methods can be used to obtain a full characterization, including Kreĭn resolvent formulas, of the realizations of nonselfadjoint second-order operators on View the MathML source

  1. Nonlinear triple-point problems on time scales

    Directory of Open Access Journals (Sweden)

    Douglas R. Anderson

    2004-04-01

    Full Text Available We establish the existence of multiple positive solutions to the nonlinear second-order triple-point boundary-value problem on time scales, $$displaylines{ u^{Delta abla}(t+h(tf(t,u(t=0, cr u(a=alpha u(b+delta u^Delta(a,quad eta u(c+gamma u^Delta(c=0 }$$ for $tin[a,c]subsetmathbb{T}$, where $mathbb{T}$ is a time scale, $eta, gamma, deltage 0$ with $Beta+gamma>0$, $0

  2. Non-equilibrium scalar two point functions in AdS/CFT

    Energy Technology Data Exchange (ETDEWEB)

    Keränen, Ville [Rudolf Peierls Centre for Theoretical Physics, University of Oxford,1 Keble Road, Oxford OX1 3NP (United Kingdom); Kleinert, Philipp [Rudolf Peierls Centre for Theoretical Physics, University of Oxford,1 Keble Road, Oxford OX1 3NP (United Kingdom); Merton College, University of Oxford,Merton Street, Oxford OX1 4JD (United Kingdom)

    2015-04-22

    In the first part of the paper, we discuss different versions of the AdS/CFT dictionary out of equilibrium. We show that the Skenderis-van Rees prescription and the “extrapolate” dictionary are equivalent at the level of “in-in” two point functions of free scalar fields in arbitrary asymptotically AdS spacetimes. In the second part of the paper, we calculate two point correlation functions in dynamical spacetimes using the “extrapolate” dictionary. These calculations are performed for conformally coupled scalar fields in examples of spacetimes undergoing gravitational collapse, the AdS{sub 2}-Vaidya spacetime and the AdS{sub 3}-Vaidya spacetime, which allow us to address the problem of thermalization following a quench in the boundary field theory. The computation of the correlators is formulated as an initial value problem in the bulk spacetime. Finally, we compare our results for AdS{sub 3}-Vaidya to results in the previous literature obtained using the geodesic approximation and we find qualitative agreement.

  3. Non-equilibrium scalar two point functions in AdS/CFT

    International Nuclear Information System (INIS)

    Keränen, Ville; Kleinert, Philipp

    2015-01-01

    In the first part of the paper, we discuss different versions of the AdS/CFT dictionary out of equilibrium. We show that the Skenderis-van Rees prescription and the “extrapolate” dictionary are equivalent at the level of “in-in” two point functions of free scalar fields in arbitrary asymptotically AdS spacetimes. In the second part of the paper, we calculate two point correlation functions in dynamical spacetimes using the “extrapolate” dictionary. These calculations are performed for conformally coupled scalar fields in examples of spacetimes undergoing gravitational collapse, the AdS 2 -Vaidya spacetime and the AdS 3 -Vaidya spacetime, which allow us to address the problem of thermalization following a quench in the boundary field theory. The computation of the correlators is formulated as an initial value problem in the bulk spacetime. Finally, we compare our results for AdS 3 -Vaidya to results in the previous literature obtained using the geodesic approximation and we find qualitative agreement.

  4. Maximum Principles and Boundary Value Problems for First-Order Neutral Functional Differential Equations

    Directory of Open Access Journals (Sweden)

    Domoshnitsky Alexander

    2009-01-01

    Full Text Available We obtain the maximum principles for the first-order neutral functional differential equation where , and are linear continuous operators, and are positive operators, is the space of continuous functions, and is the space of essentially bounded functions defined on . New tests on positivity of the Cauchy function and its derivative are proposed. Results on existence and uniqueness of solutions for various boundary value problems are obtained on the basis of the maximum principles.

  5. Stabilizing local boundary conditions for two-dimensional shallow water equations

    KAUST Repository

    Dia, Ben Mansour

    2018-03-27

    In this article, we present a sub-critical two-dimensional shallow water flow regulation. From the energy estimate of a set of one-dimensional boundary stabilization problems, we obtain a set of polynomial equations with respect to the boundary values as a requirement for the energy decrease. Using the Riemann invariant analysis, we build stabilizing local boundary conditions that guarantee the stability of the hydrodynamical state around a given steady state. Numerical results for the controller applied to the nonlinear problem demonstrate the performance of the method.

  6. Multiple and sign-changing solutions for discrete Robin boundary value problem with parameter dependence

    Directory of Open Access Journals (Sweden)

    Long Yuhua

    2017-12-01

    Full Text Available In this paper, we study second-order nonlinear discrete Robin boundary value problem with parameter dependence. Applying invariant sets of descending flow and variational methods, we establish some new sufficient conditions on the existence of sign-changing solutions, positive solutions and negative solutions of the system when the parameter belongs to appropriate intervals. In addition, an example is given to illustrate our results.

  7. A symmetric solution of a multipoint boundary value problem at resonance

    Directory of Open Access Journals (Sweden)

    2006-01-01

    Full Text Available We apply a coincidence degree theorem of Mawhin to show the existence of at least one symmetric solution of the nonlinear second-order multipoint boundary value problem u ″ ( t = f ( t , u ( t , | u ′ ( t | , t ∈ ( 0 , 1 , u ( 0 = ∑ i = 1 n μ i u ( ξ i , u ( 1 − t = u ( t , t ∈ ( 0 , 1 ] , where 0 < ξ 1 < ξ 2 < … ≤ ξ n 1 / 2 , ∑ i = 1 n μ i = 1 , f : [ 0 , 1 ] × ℝ 2 → ℝ with f ( t , x , y = f ( 1 − t , x , y , ( t , x , y ∈ [ 0 , 1 ] × ℝ 2 , satisfying the Carathéodory conditions.

  8. Uniqueness and Asymptotic Behavior of Positive Solutions for a Fractional-Order Integral Boundary Value Problem

    Directory of Open Access Journals (Sweden)

    Min Jia

    2012-01-01

    Full Text Available We study a model arising from porous media, electromagnetic, and signal processing of wireless communication system -tαx(t=f(t,x(t,x'(t,x”(t,…,x(n-2(t,  0boundary value problem for fractional differential equation are obtained. Our analysis relies on Schauder's fixed-point theorem and upper and lower solution method.

  9. Polyharmonic boundary value problems positivity preserving and nonlinear higher order elliptic equations in bounded domains

    CERN Document Server

    Gazzola, Filippo; Sweers, Guido

    2010-01-01

    This monograph covers higher order linear and nonlinear elliptic boundary value problems in bounded domains, mainly with the biharmonic or poly-harmonic operator as leading principal part. Underlying models and, in particular, the role of different boundary conditions are explained in detail. As for linear problems, after a brief summary of the existence theory and Lp and Schauder estimates, the focus is on positivity or - since, in contrast to second order equations, a general form of a comparison principle does not exist - on “near positivity.” The required kernel estimates are also presented in detail. As for nonlinear problems, several techniques well-known from second order equations cannot be utilized and have to be replaced by new and different methods. Subcritical, critical and supercritical nonlinearities are discussed and various existence and nonexistence results are proved. The interplay with the positivity topic from the first part is emphasized and, moreover, a far-reaching Gidas-Ni-Nirenbe...

  10. Sufficient condition for existence of solutions for higher-order resonance boundary value problem with one-dimensional p-Laplacian

    Directory of Open Access Journals (Sweden)

    Liu Yang

    2007-10-01

    Full Text Available By using coincidence degree theory of Mawhin, existence results for some higher order resonance multipoint boundary value problems with one dimensional p-Laplacian operator are obtained.

  11. Application of power series to the solution of the boundary value problem for a second order nonlinear differential equation

    International Nuclear Information System (INIS)

    Semenova, V.N.

    2016-01-01

    A boundary value problem for a nonlinear second order differential equation has been considered. A numerical method has been proposed to solve this problem using power series. Results of numerical experiments have been presented in the paper [ru

  12. The Initial and Neumann Boundary Value Problem for a Class Parabolic Monge-Ampère Equation

    Directory of Open Access Journals (Sweden)

    Juan Wang

    2013-01-01

    Full Text Available We consider the existence, uniqueness, and asymptotic behavior of a classical solution to the initial and Neumann boundary value problem for a class nonlinear parabolic equation of Monge-Ampère type. We show that such solution exists for all times and is unique. It converges eventually to a solution that satisfies a Neumann type problem for nonlinear elliptic equation of Monge-Ampère type.

  13. Existence of Triple Positive Solutions for Second-Order Discrete Boundary Value Problems

    Directory of Open Access Journals (Sweden)

    Yanping Guo

    2007-01-01

    Full Text Available By using a new fixed-point theorem introduced by Avery and Peterson (2001, we obtain sufficient conditions for the existence of at least three positive solutions for the equation Δ2x(k−1+q(kf(k,x(k,Δx(k=0, for k∈{1,2,…,n−1}, subject to the following two boundary conditions: x(0=x(n=0 or x(0=Δx(n−1=0, where n≥3.

  14. Existence of global solutions to free boundary value problems for bipolar Navier-Stokes-Possion systems

    Directory of Open Access Journals (Sweden)

    Jian Liu

    2013-09-01

    Full Text Available In this article, we consider the free boundary value problem for one-dimensional compressible bipolar Navier-Stokes-Possion (BNSP equations with density-dependent viscosities. For general initial data with finite energy and the density connecting with vacuum continuously, we prove the global existence of the weak solution. This extends the previous results for compressible NS [27] to NSP.

  15. Integral methods of solving boundary-value problems of nonstationary heat conduction and their comparative analysis

    Science.gov (United States)

    Kot, V. A.

    2017-11-01

    The modern state of approximate integral methods used in applications, where the processes of heat conduction and heat and mass transfer are of first importance, is considered. Integral methods have found a wide utility in different fields of knowledge: problems of heat conduction with different heat-exchange conditions, simulation of thermal protection, Stefantype problems, microwave heating of a substance, problems on a boundary layer, simulation of a fluid flow in a channel, thermal explosion, laser and plasma treatment of materials, simulation of the formation and melting of ice, inverse heat problems, temperature and thermal definition of nanoparticles and nanoliquids, and others. Moreover, polynomial solutions are of interest because the determination of a temperature (concentration) field is an intermediate stage in the mathematical description of any other process. The following main methods were investigated on the basis of the error norms: the Tsoi and Postol’nik methods, the method of integral relations, the Gudman integral method of heat balance, the improved Volkov integral method, the matched integral method, the modified Hristov method, the Mayer integral method, the Kudinov method of additional boundary conditions, the Fedorov boundary method, the method of weighted temperature function, the integral method of boundary characteristics. It was established that the two last-mentioned methods are characterized by high convergence and frequently give solutions whose accuracy is not worse that the accuracy of numerical solutions.

  16. Multiple Solutions of Nonlinear Boundary Value Problems of Fractional Order: A New Analytic Iterative Technique

    Directory of Open Access Journals (Sweden)

    Omar Abu Arqub

    2014-01-01

    Full Text Available The purpose of this paper is to present a new kind of analytical method, the so-called residual power series, to predict and represent the multiplicity of solutions to nonlinear boundary value problems of fractional order. The present method is capable of calculating all branches of solutions simultaneously, even if these multiple solutions are very close and thus rather difficult to distinguish even by numerical techniques. To verify the computational efficiency of the designed proposed technique, two nonlinear models are performed, one of them arises in mixed convection flows and the other one arises in heat transfer, which both admit multiple solutions. The results reveal that the method is very effective, straightforward, and powerful for formulating these multiple solutions.

  17. Antiperiodic Boundary Value Problems for Second-Order Impulsive Ordinary Differential Equations

    Directory of Open Access Journals (Sweden)

    2009-02-01

    Full Text Available We consider a second-order ordinary differential equation with antiperiodic boundary conditions and impulses. By using Schaefer's fixed-point theorem, some existence results are obtained.

  18. A boundary value problem for a third order hyperbolic equation with degeneration of order inside the domain

    Directory of Open Access Journals (Sweden)

    Ruzanna Kh. Makaova

    2017-12-01

    Full Text Available In this paper we study the boundary value problem for a degenerating third order equation of hyperbolic type in a mixed domain. The equation under consideration in the positive part of the domain coincides with the Hallaire equation, which is a pseudoparabolic type equation. Moreover, in the negative part of the domain it coincides with a degenerating hyperbolic equation of the first kind, the particular case of the Bitsadze–Lykov equation. The existence and uniqueness theorem for the solution is proved. The uniqueness of the solution to the problem is proved with the Tricomi method. Using the functional relationships of the positive and negative parts of the domain on the degeneration line, we arrive at the convolution type Volterra integral equation of the 2nd kind with respect to the desired solution by a derivative trace. With the Laplace transform method, we obtain the solution of the integral equation in its explicit form. At last, the solution to the problem under study is written out explicitly as the solution of the second boundary-value problem in the positive part of the domain for the Hallaire equation and as the solution to the Cauchy problem in the negative part of the domain for a degenerate hyperbolic equation of the first kind.

  19. Asymptotic behaviour around a boundary point of the q-Painlevé VI equation and its connection problem

    International Nuclear Information System (INIS)

    Mano, Toshiyuki

    2010-01-01

    We study analytic properties of solutions to the q-Painlevé VI equation (q-P VI ), which was derived by Jimbo and Sakai as the compatibility condition for a connection preserving deformation (CPD) of a linear q-difference equation. We investigate local behaviours of solutions to q-P VI around a boundary point making use of the structure of the CPD. We also give a formula connecting the local behaviours of a solution around two boundary points. The results in this paper should be useful in future for studying more detailed global properties of solutions to q-P VI or exploring new special solutions with remarkable analytic properties

  20. Existence and nonexistence results for a singular boundary value problem arising in the theory of epitaxial growth

    Czech Academy of Sciences Publication Activity Database

    Escudero, C.; Hakl, Robert; Peral, I.; Torres, P.J.

    2014-01-01

    Roč. 37, č. 6 (2014), s. 793-807 ISSN 0170-4214 Institutional support: RVO:67985840 Keywords : singular boundary value problem * epitaxial growth * radial solution Subject RIV: BA - General Mathematics Impact factor: 0.918, year: 2014 http://onlinelibrary.wiley.com/doi/10.1002/mma.2836/full

  1. Solvability of a (p, n-p-type multi-point boundary-value problem for higher-order differential equations

    Directory of Open Access Journals (Sweden)

    Yuji Liu

    2003-12-01

    Full Text Available In this article, we study the differential equation $$ (-1^{n-p} x^{(n}(t=f(t,x(t,x'(t,dots,x^{(n-1}(t, $$ subject to the multi-point boundary conditions $$displaylines{ x^{(i}(0=0 quad hbox{for }i=0,1,dots,p-1,cr x^{(i}(1=0 quad hbox{for }i=p+1,dots,n-1,cr sum_{i=1}^malpha_ix^{(p}(xi_i=0, }$$ where $1le ple n-1$. We establish sufficient conditions for the existence of at least one solution at resonance and another at non-resonance. The emphasis in this paper is that $f$ depends on all higher-order derivatives. Examples are given to illustrate the main results of this article.

  2. Boundary layer flow of an oldroyd-b fluid in the region of stagnation point over a stretching sheet

    International Nuclear Information System (INIS)

    Sajid, M.

    2012-01-01

    The mathematical modeling for the two-dimensional boundary layer flow of an Oldroyd-B fluid is presented. The developed equations are used to discuss the problem of two-dimensional flow in the region of a stagnation point over a stretching sheet. The obtained partial differential equations are reduced to an ordinary differential equation by a suitable transformation. The obtained equation is then solved using a finite difference method. The influence of the pertinent fluid parameters on the velocity is discussed through graphs. The behavior of f (0) is also investigated for the change in parameter values. Our main focus is to discuss the effects of relaxation and retardation time parameters on the velocity components in the x and y directions. In addition to it the skin friction coefficient is evaluated which is a measure of frictional drag at the surface illustrates that the boundary layer thickness decreases due to an increase in the relaxation time constant. The reason is that a higher relaxation time constant give rise to a slower recovery process and as a result the boundary layer thickness grows at a slower rate for a higher value of the relaxation time constant when compared with its lower value. (orig./A.B.)

  3. On solution of the integral equations for the potential problems of two circular-strips

    Directory of Open Access Journals (Sweden)

    C. Sampath

    1988-01-01

    Dirichlet and Newmann boundary value problems of two equal infinite coaxial circular strips in various branches of potential theory. For illustration, these solutions are applied to solve some boundary value problems in electrostatics, hydrodynamics, and expressions for the physical quantities of interest are derived.

  4. Optimal boundary control and boundary stabilization of hyperbolic systems

    CERN Document Server

    Gugat, Martin

    2015-01-01

    This brief considers recent results on optimal control and stabilization of systems governed by hyperbolic partial differential equations, specifically those in which the control action takes place at the boundary.  The wave equation is used as a typical example of a linear system, through which the author explores initial boundary value problems, concepts of exact controllability, optimal exact control, and boundary stabilization.  Nonlinear systems are also covered, with the Korteweg-de Vries and Burgers Equations serving as standard examples.  To keep the presentation as accessible as possible, the author uses the case of a system with a state that is defined on a finite space interval, so that there are only two boundary points where the system can be controlled.  Graduate and post-graduate students as well as researchers in the field will find this to be an accessible introduction to problems of optimal control and stabilization.

  5. Direct approach for solving nonlinear evolution and two-point

    Indian Academy of Sciences (India)

    Time-delayed nonlinear evolution equations and boundary value problems have a wide range of applications in science and engineering. In this paper, we implement the differential transform method to solve the nonlinear delay differential equation and boundary value problems. Also, we present some numerical examples ...

  6. Global solutions to the initial-boundary value problem for the quasilinear viscoelastic equation with a derivative nonlinearity

    Directory of Open Access Journals (Sweden)

    Mitsuhiro Nakao

    2014-01-01

    Full Text Available We prove the existence and uniqueness of a global decaying solution to the initial boundary value problem for the quasilinear wave equation with Kelvin-Voigt dissipation and a derivative nonlinearity. To derive the required estimates of the solutions we employ a 'loan' method and use a difference inequality on the energy.

  7. Natural convection flow between moving boundaries | Chepkwony ...

    African Journals Online (AJOL)

    The two-point boundary value problem governing the flow is characterized by a non-dimensional parameter K. It is solved numerically using shooting method and the Newton-Raphson method to locate the missing initial conditions. The numerical results reveal that no solution exists beyond a critical value of K and that dual ...

  8. Initial-boundary value problems for multi-term time-fractional diffusion equations with x-dependent coefficients

    OpenAIRE

    Li, Zhiyuan; Huang, Xinchi; Yamamoto, Masahiro

    2018-01-01

    In this paper, we discuss an initial-boundary value problem (IBVP) for the multi-term time-fractional diffusion equation with x-dependent coefficients. By means of the Mittag-Leffler functions and the eigenfunction expansion, we reduce the IBVP to an equivalent integral equation to show the unique existence and the analyticity of the solution for the equation. Especially, in the case where all the coefficients of the time-fractional derivatives are non-negative, by the Laplace and inversion L...

  9. The Boundary Element Method Applied to the Two Dimensional Stefan Moving Boundary Problem

    Science.gov (United States)

    1991-03-15

    Unc), - ( UGt )t - (UG,,),,] - (UG), If we integrate this equation with respect to r from 0 to t - c and with respect to and ij on the region 11(r...and others. "Moving Boundary Problems in Phase Change Mod- els," SIGNUM Newsletter, 20: 8-12 (1985). 21. Stefan, J. "Ober einige Probleme der Theorie ...ier Wirmelcitung," S.-B. \\Vein. Akad. Mat. Natur., 98: 173-484 (1889). 22.-. "flber (lie Theorie der Eisbildung insbesondere fiber die lisbildung im

  10. New formulations on the finite element method for boundary value problems with internal/external boundary layers

    International Nuclear Information System (INIS)

    Pereira, Luis Carlos Martins

    1998-06-01

    New Petrov-Galerkin formulations on the finite element methods for convection-diffusion problems with boundary layers are presented. Such formulations are based on a consistent new theory on discontinuous finite element methods. Existence and uniqueness of solutions for these problems in the new finite element spaces are demonstrated. Some numerical experiments shows how the new formulation operate and also their efficacy. (author)

  11. The Boundary Function Method. Fundamentals

    Science.gov (United States)

    Kot, V. A.

    2017-03-01

    The boundary function method is proposed for solving applied problems of mathematical physics in the region defined by a partial differential equation of the general form involving constant or variable coefficients with a Dirichlet, Neumann, or Robin boundary condition. In this method, the desired function is defined by a power polynomial, and a boundary function represented in the form of the desired function or its derivative at one of the boundary points is introduced. Different sequences of boundary equations have been set up with the use of differential operators. Systems of linear algebraic equations constructed on the basis of these sequences allow one to determine the coefficients of a power polynomial. Constitutive equations have been derived for initial boundary-value problems of all the main types. With these equations, an initial boundary-value problem is transformed into the Cauchy problem for the boundary function. The determination of the boundary function by its derivative with respect to the time coordinate completes the solution of the problem.

  12. Description of internal flow problems by a boundary integral method with dipole panels

    International Nuclear Information System (INIS)

    Krieg, R.; Hailfinger, G.

    1979-01-01

    In reactor safety studies the failure of single components is postulated or sudden accident loadings are assumed and the consequences are investigated. Often as a first consequence highly transient three dimensional flow problems occur. In contrast to classical flow problems, in most of the above cases the fluid velocities are relatively small whereas the accelerations assume high values. As a consequence both, viscosity effects and dynamic pressures which are proportional to the square of the fluid velocities are usually negligible. For cases, where the excitation times are considerably longer than the times necessary for a wave to traverse characteristic regions of the fluid field, also the fluid compressibility is negligible. Under these conditions boundary integral methods are an appropriate tool to deal with the problem. Flow singularities are distributed over the fluid boundaries in such a way that pressure and velocity fields are obtained which satisfy the boundary conditions. In order to facilitate the numerical treatment the fluid boundaries are approximated by a finite number of panels with uniform singularity distributions on each of them. Consequently the pressure and velocity field of the given problem may be obtained by superposition of the corresponding fields due to these panels with their singularity intensities as unknown factors. Then satisfying the boundary conditions in so many boundary points as panels have been introduced, yields a system of linear equations which in general allows for a unique determination of the unknown intensities. (orig./RW)

  13. EXTRACTION OF BUILDING BOUNDARY LINES FROM AIRBORNE LIDAR POINT CLOUDS

    Directory of Open Access Journals (Sweden)

    Y.-H. Tseng

    2016-10-01

    Full Text Available Building boundary lines are important spatial features that characterize the topographic maps and three-dimensional (3D city models. Airborne LiDAR Point clouds provide adequate 3D spatial information for building boundary mapping. However, information of boundary features contained in point clouds is implicit. This study focuses on developing an automatic algorithm of building boundary line extraction from airborne LiDAR data. In an airborne LiDAR dataset, top surfaces of buildings, such as roofs, tend to have densely distributed points, but vertical surfaces, such as walls, usually have sparsely distributed points or even no points. The intersection lines of roof and wall planes are, therefore, not clearly defined in point clouds. This paper proposes a novel method to extract those boundary lines of building edges. The extracted line features can be used as fundamental data to generate topographic maps of 3D city model for an urban area. The proposed method includes two major process steps. The first step is to extract building boundary points from point clouds. Then the second step is followed to form building boundary line features based on the extracted boundary points. In this step, a line fitting algorithm is developed to improve the edge extraction from LiDAR data. Eight test objects, including 4 simple low buildings and 4 complicated tall buildings, were selected from the buildings in NCKU campus. The test results demonstrate the feasibility of the proposed method in extracting complicate building boundary lines. Some results which are not as good as expected suggest the need of further improvement of the method.

  14. Existence and smoothness of solutions to second initial boundary value problems for Schrodinger systems in cylinders with non-smooth bases

    Directory of Open Access Journals (Sweden)

    Nguyen Manh Hung

    2008-03-01

    Full Text Available In this paper, we consider the second initial boundary value problem for strongly general Schrodinger systems in both the finite and the infinite cylinders $Q_T, 0problem are given.

  15. Nonlinear radiative heat transfer in magnetohydrodynamic (MHD stagnation point flow of nanofluid past a stretching sheet with convective boundary condition

    Directory of Open Access Journals (Sweden)

    Wubshet Ibrahim

    2015-12-01

    Full Text Available Two-dimensional boundary layer flow of nanofluid fluid past a stretching sheet is examined. The paper reveals the effect of non-linear radiative heat transfer on magnetohydrodynamic (MHD stagnation point flow past a stretching sheet with convective heating. Condition of zero normal flux of nanoparticles at the wall for the stretched flow is considered. The nanoparticle fractions on the boundary are considered to be passively controlled. The solution for the velocity, temperature and nanoparticle concentration depends on parameters viz. Prandtl number Pr, velocity ratio parameter A, magnetic parameter M, Lewis number Le, Brownian motion Nb, and the thermophoresis parameter Nt. Moreover, the problem is governed by temperature ratio parameter (Nr=TfT∞ and radiation parameter Rd. Similarity transformation is used to reduce the governing non-linear boundary-value problems into coupled higher order non-linear ordinary differential equation. These equations were numerically solved using the function bvp4c from the matlab software for different values of governing parameters. Numerical results are obtained for velocity, temperature and concentration, as well as the skin friction coefficient and local Nusselt number. The results indicate that the skin friction coefficient Cf increases as the values of magnetic parameter M increase and decreases as the values of velocity ratio parameter A increase. The local Nusselt number −θ′(0 decreases as the values of thermophoresis parameter Nt and radiation parameter Nr increase and it increases as the values of both Biot number Bi and Prandtl number Pr increase. Furthermore, radiation has a positive effect on temperature and concentration profiles.

  16. Two-phase semilinear free boundary problem with a degenerate phase

    KAUST Repository

    Matevosyan, Norayr

    2010-10-16

    We study minimizers of the energy functional ∫D[{pipe}∇u{pipe}2 + λ(u+)p]dx for p ∈ (0, 1) without any sign restriction on the function u. The distinguished feature of the problem is the lack of nondegeneracy in the negative phase. The main result states that in dimension two the free boundaries Γ+ = ∂{u > 0} ∩ D andΓ- = ∂{u < 0} ∩ D are C1,α-regular, provided 1 - ∈0 < p < 1. The proof is obtained by a careful iteration of the Harnack inequality to obtain a nontrivial growth estimate in the negative phase, compensating for the apriori unknown nondegeneracy. © 2010 Springer-Verlag.

  17. Difference method for solving a nonlocal boundary value problem for a degenerating third-order pseudo-parabolic equation with variable coefficients

    Science.gov (United States)

    Beshtokov, M. Kh.

    2016-10-01

    A nonlocal boundary value problem for a degenerating third-order pseudo-parabolic equation with variable coefficients is considered. For solving this problem, a priori estimates in the differential and difference forms are obtained. The a priori estimates imply the uniqueness and stability of the solution on a layer with respect to the initial data and the right-hand side and the convergence of the solution of the difference problem to the solution of the differential problem.

  18. Indentations and Starting Points in Traveling Sales Tour Problems: Implications for Theory

    Science.gov (United States)

    MacGregor, James N.

    2012-01-01

    A complete, non-trivial, traveling sales tour problem contains at least one "indentation", where nodes in the interior of the point set are connected between two adjacent nodes on the boundary. Early research reported that human tours exhibited fewer such indentations than expected. A subsequent explanation proposed that this was because…

  19. Exact solution for a two-phase Stefan problem with variable latent heat and a convective boundary condition at the fixed face

    Science.gov (United States)

    Bollati, Julieta; Tarzia, Domingo A.

    2018-04-01

    Recently, in Tarzia (Thermal Sci 21A:1-11, 2017) for the classical two-phase Lamé-Clapeyron-Stefan problem an equivalence between the temperature and convective boundary conditions at the fixed face under a certain restriction was obtained. Motivated by this article we study the two-phase Stefan problem for a semi-infinite material with a latent heat defined as a power function of the position and a convective boundary condition at the fixed face. An exact solution is constructed using Kummer functions in case that an inequality for the convective transfer coefficient is satisfied generalizing recent works for the corresponding one-phase free boundary problem. We also consider the limit to our problem when that coefficient goes to infinity obtaining a new free boundary problem, which has been recently studied in Zhou et al. (J Eng Math 2017. https://doi.org/10.1007/s10665-017-9921-y).

  20. Exact multiplicity results for quasilinear boundary-value problems with cubic-like nonlinearities

    Directory of Open Access Journals (Sweden)

    Idris Addou

    2000-01-01

    Full Text Available We consider the boundary-value problem $$displaylines{ -(varphi_p (u'' =lambda f(u mbox{ in }(0,1 cr u(0 = u(1 =0,, }$$ where $p>1$, $lambda >0$ and $varphi_p (x =| x|^{p-2}x$. The nonlinearity $f$ is cubic-like with three distinct roots 0=a less than b less than c. By means of a quadrature method, we provide the exact number of solutions for all $lambda >0$. This way we extend a recent result, for $p=2$, by Korman et al. cite{KormanLiOuyang} to the general case $p>1$. We shall prove that when 1less than $pleq 2$ the structure of the solution set is exactly the same as that studied in the case $p=2$ by Korman et al. cite{KormanLiOuyang}, and strictly different in the case $p>2$.

  1. Boundary value problems of the circular cylinders in the strain-gradient theory of linear elasticity

    International Nuclear Information System (INIS)

    Kao, B.G.

    1979-11-01

    Three boundary value problems in the strain-gradient theory of linear elasticity are solved for circular cylinders. They are the twisting of circular cylinder, uniformly pressuring of concentric circular cylinder, and pure-bending of simply connected cylinder. The comparisons of these solutions with the solutions in classical elasticity and in couple-stress theory reveal the differences in the stress fields as well as the apparent stress fields due to the influences of the strain-gradient. These aspects of the strain-gradient theory could be important in modeling the failure behavior of structural materials

  2. Laplace Boundary-Value Problem in Paraboloidal Coordinates

    Science.gov (United States)

    Duggen, L.; Willatzen, M.; Voon, L. C. Lew Yan

    2012-01-01

    This paper illustrates both a problem in mathematical physics, whereby the method of separation of variables, while applicable, leads to three ordinary differential equations that remain fully coupled via two separation constants and a five-term recurrence relation for series solutions, and an exactly solvable problem in electrostatics, as a…

  3. Mixed problems for linear symmetric hyperbolic systems with characteristic boundary conditions

    International Nuclear Information System (INIS)

    Secchi, P.

    1994-01-01

    We consider the initial-boundary value problem for symmetric hyperbolic systems with characteristic boundary of constant multiplicity. In the linear case we give some results about the existence of regular solutions in suitable functions spaces which take in account the loss of regularity in the normal direction to the characteristic boundary. We also consider the equations of ideal magneto-hydrodynamics under perfectly conducting wall boundary conditions and give some results about the solvability of such mixed problem. (author). 16 refs

  4. Comparison of apparent diffusion coefficients (ADCs) between two-point and multi-point analyses using high-B-value diffusion MR imaging

    International Nuclear Information System (INIS)

    Kubo, Hitoshi; Maeda, Masayuki; Araki, Akinobu

    2001-01-01

    We evaluated the accuracy of calculating apparent diffusion coefficients (ADCs) using high-B-value diffusion images. Echo planar diffusion-weighted MR images were obtained at 1.5 tesla in five standard locations in six subjects using gradient strengths corresponding to B values from 0 to 3000 s/mm 2 . Estimation of ADCs was made using two methods: a nonlinear regression model using measurements from a full set of B values (multi-point method) and linear estimation using B values of 0 and max only (two-point method). A high correlation between the two methods was noted (r=0.99), and the mean percentage differences were -0.53% and 0.53% in phantom and human brain, respectively. These results suggest there is little error in estimating ADCs calculated by the two-point technique using high-B-value diffusion MR images. (author)

  5. On the radiative transfer problem in a spherical medium subject to Fresnel's reflective boundary conditions

    International Nuclear Information System (INIS)

    Mohammed, M.H.H.

    2012-01-01

    Radiation transfer problem for anisotropic scattering in a spherical homogeneous, turbid medium with angular dependent (specular) and diffuse reflecting boundary is considered. The angular dependent reflectivity of the boundary is considered as Fresnel's reflection probability function. The solution of the problem containing an energy source in a medium of specular and diffuse reflecting boundaries is given in terms of the solution of the source-free problem. The source-free problem for anisotropic scattering through a homogeneous solid sphere and two concentric spheres is solved by using the Pomraning- Eddington approximation method. This method transform the integro-differential equation into two differential equations for the radiance g (x) and net flux q (x) which has an analytical solution in terms of the modified Bessel function. Two different weight functions are used to verify the boundary conditions and so, find the solution constants. The partial heat fluxes at the boundaries of a solid sphere and spherical shell of transparent and reflecting boundaries are calculated. The media are taken with or without internal black-body radiation. The calculations are carried out for various values of refractive index and different radii. The results are compared with those of the Galerkin technique

  6. Zero-energy eigenstates for the Dirac boundary problem

    International Nuclear Information System (INIS)

    Hortacsu, M.; Rothe, K.D.; Schroer, B.

    1980-01-01

    As an alternative to the method of spherical compactification for the Dirac operator in instanton background fields we study the correct method of 'box-quantization': the Atiyah-Patodi-Singer spectral boundary condition. This is the only self-adjoint boundary condition which respects the charge conjugation property and the γ 5 symmetry, apart form the usual breaking due to zero modes. We point out the relevance of this approach to the computation of instanton determinants and other problems involving Dirac spinors. (orig.)

  7. Convergence Analysis of the Preconditioned Group Splitting Methods in Boundary Value Problems

    Directory of Open Access Journals (Sweden)

    Norhashidah Hj. Mohd Ali

    2012-01-01

    Full Text Available The construction of a specific splitting-type preconditioner in block formulation applied to a class of group relaxation iterative methods derived from the centred and rotated (skewed finite difference approximations has been shown to improve the convergence rates of these methods. In this paper, we present some theoretical convergence analysis on this preconditioner specifically applied to the linear systems resulted from these group iterative schemes in solving an elliptic boundary value problem. We will theoretically show the relationship between the spectral radiuses of the iteration matrices of the preconditioned methods which affects the rate of convergence of these methods. We will also show that the spectral radius of the preconditioned matrices is smaller than that of their unpreconditioned counterparts if the relaxation parameter is in a certain optimum range. Numerical experiments will also be presented to confirm the agreement between the theoretical and the experimental results.

  8. A finite difference method for free boundary problems

    KAUST Repository

    Fornberg, Bengt

    2010-04-01

    Fornberg and Meyer-Spasche proposed some time ago a simple strategy to correct finite difference schemes in the presence of a free boundary that cuts across a Cartesian grid. We show here how this procedure can be combined with a minimax-based optimization procedure to rapidly solve a wide range of elliptic-type free boundary value problems. © 2009 Elsevier B.V. All rights reserved.

  9. Dynamic Phase Boundary Estimation in Two-phase Flows Based on Electrical Impedance Tomography

    International Nuclear Information System (INIS)

    Lee, Jeong Seong; Muhammada, Nauman Malik; Kim, Kyung Youn; Kim, Sin

    2008-01-01

    For the dynamic visualization of the phase boundary in two-phase flows, the electrical impedance tomography (EIT) technique is introduced. In EIT, a set of predetermined electrical currents is injected through the electrodes placed on the boundary of the flow passage and the induced electrical potentials are measured on the electrodes. With the relationship between the injected currents and the induced voltages, the electrical conductivity distribution across the flow domain is estimated through the image reconstruction algorithm where the conductivity distribution corresponds to the phase distribution. In the application of EIT to two-phase flows where there are only two conductivity values, the conductivity distribution estimation problem can be transformed into the boundary estimation problem. This paper considers phase boundary estimation with EIT in annular two-phase flows. As the image reconstruction algorithm, the unscented Kalman filter (UKF) is adopted since from the control theory it is reported that the UKF shows better performance than the extended Kalman filter (EKF) that has been commonly used. For the present problem, the formulation of UKF algorithm involved its incorporation in the adopted image reconstruction algorithm. Also, phantom experiments have been conducted to evaluate the improvement reported by UKF

  10. Efficient Closed Form Cut-Off Planes and Propagation Planes Characteristics for Dielectric Slab Loaded Boundary Value Problems

    OpenAIRE

    Zafar, Junaid

    2012-01-01

    The geometrical relationship between the cut-off and propagating planes of any waveguide system is a prerequisite for any design process. The characterization of cut-off planes and optimisation are challenging for numerical methods, closed-form solutions are always preferred. In this paper Maxwells coupled field equations are used to characterise twin E-plane and H-plane slab loaded boundary value problems. The single mode bandwidths and dispersion characteristics of these structures are pres...

  11. Differential and Difference Boundary Value Problem for Loaded Third-Order Pseudo-Parabolic Differential Equations and Difference Methods for Their Numerical Solution

    Science.gov (United States)

    Beshtokov, M. Kh.

    2017-12-01

    Boundary value problems for loaded third-order pseudo-parabolic equations with variable coefficients are considered. A priori estimates for the solutions of the problems in the differential and difference formulations are obtained. These a priori estimates imply the uniqueness and stability of the solution with respect to the initial data and the right-hand side on a layer, as well as the convergence of the solution of each difference problem to the solution of the corresponding differential problem.

  12. On the Existence and Uniqueness of Rv-Generalized Solution for Dirichlet Problem with Singularity on All Boundary

    Directory of Open Access Journals (Sweden)

    V. Rukavishnikov

    2014-01-01

    Full Text Available The existence and uniqueness of the Rv-generalized solution for the first boundary value problem and a second order elliptic equation with coordinated and uncoordinated degeneracy of input data and with strong singularity solution on all boundary of a two-dimensional domain are established.

  13. Trace expansions for mixed boundary problems

    Energy Technology Data Exchange (ETDEWEB)

    Seeley, Robert T

    2002-01-01

    We discuss the heat trace expansion for a mixed boundary problem for the Laplace operator acting on sections of some bundle V over a manifold M of dimension d. The boundary is divided in two parts N{sub D} and N{sub N}, intersecting in a smooth submanifold {sigma}. Dirichlet conditions are imposed on N{sub D} - {sigma}, and Neumann conditions on N{sub N} - {sigma}. It turns out that it is also necessary to impose a condition along {sigma}. We then obtain an expansion of the trace of the heat operator with these boundary conditions, containing integrals of the usual terms over the interior and the two parts of the boundary, together with integrals over {sigma} of terms that are 'global' in certain operators on a semicircle. The first nonzero such term is computed; it involves the zeta function of an operator on the semicircle, and depends on the boundary condition along {sigma}. We find that no logarithmic terms occur in the expansion.

  14. Matrix-type multiple reciprocity boundary element method for solving three-dimensional two-group neutron diffusion equations

    International Nuclear Information System (INIS)

    Itagaki, Masafumi; Sahashi, Naoki.

    1997-01-01

    The multiple reciprocity boundary element method has been applied to three-dimensional two-group neutron diffusion problems. A matrix-type boundary integral equation has been derived to solve the first and the second group neutron diffusion equations simultaneously. The matrix-type fundamental solutions used here satisfy the equation which has a point source term and is adjoint to the neutron diffusion equations. A multiple reciprocity method has been employed to transform the matrix-type domain integral related to the fission source into an equivalent boundary one. The higher order fundamental solutions required for this formulation are composed of a series of two types of analytic functions. The eigenvalue itself is also calculated using only boundary integrals. Three-dimensional test calculations indicate that the present method provides stable and accurate solutions for criticality problems. (author)

  15. Hopf bifurcation of a free boundary problem modeling tumor growth with two time delays

    International Nuclear Information System (INIS)

    Xu Shihe

    2009-01-01

    In this paper, a free boundary problem modeling tumor growth with two discrete delays is studied. The delays respectively represents the time taken for cells to undergo mitosis and the time taken for the cell to modify the rate of cell loss due to apoptosis. We show the influence of time delays on the Hopf bifurcation when one of delays as a bifurcation parameter.

  16. Problems of matter-antimatter boundary layers

    International Nuclear Information System (INIS)

    Lehnert, B.

    1975-01-01

    This paper outlines the problems of the quasi-steady matter-antimatter boundary layers discussed in Klein-Alfven's cosmological theory, and a crude model of the corresponding ambiplasma balance is presented: (i) at interstellar particle densities, no well-defined boundary layer can exist in presence of neutral gas, nor can such a layer be sustained in an unmagnetized fully ionized ambiplasma. (ii) Within the limits of applicability of the present model, sharply defined boundary layers are under certain conditions found to exist in a magnetized ambiplasma. Thus, at beta values less than unity, a steep pressure drop of the low-energy components of matter and antimatter can be balanced by a magnetic field and the electric currents in the ambiplasma. (iii) The boundary layer thickness is of the order of 2x 0 approximately 10/BT 0 sup(1/4) meters, where B is the magnetic field strength in MKS units and T 0 the characteristic temperature of the low-energy components in the layer. (Auth.)

  17. On Motion Planning for Point-to-Point Maneuvers for a Class of Sailing Vehicles

    DEFF Research Database (Denmark)

    Xiao, Lin; Jouffroy, Jerome

    2011-01-01

    Despite their interesting dynamic and controllability properties, sailing vehicles have not been much studied in the control community. In this paper, we investigate motion planning of such vehicles. Starting from a simple dynamic model of sailing vessels in one dimension, this paper first...... considers their associated controllability issues, with the so-called no-sailing zone as a starting point, and it links them with a motion planning strategy using two-point boundary value problems as the main mathematical tool. This perspective is then expanded to do point-to-point maneuvers of sailing...

  18. Spectral combination of spherical gravitational curvature boundary-value problems

    Science.gov (United States)

    PitoÅák, Martin; Eshagh, Mehdi; Šprlák, Michal; Tenzer, Robert; Novák, Pavel

    2018-04-01

    Four solutions of the spherical gravitational curvature boundary-value problems can be exploited for the determination of the Earth's gravitational potential. In this article we discuss the combination of simulated satellite gravitational curvatures, i.e., components of the third-order gravitational tensor, by merging these solutions using the spectral combination method. For this purpose, integral estimators of biased- and unbiased-types are derived. In numerical studies, we investigate the performance of the developed mathematical models for the gravitational field modelling in the area of Central Europe based on simulated satellite measurements. Firstly, we verify the correctness of the integral estimators for the spectral downward continuation by a closed-loop test. Estimated errors of the combined solution are about eight orders smaller than those from the individual solutions. Secondly, we perform a numerical experiment by considering the Gaussian noise with the standard deviation of 6.5× 10-17 m-1s-2 in the input data at the satellite altitude of 250 km above the mean Earth sphere. This value of standard deviation is equivalent to a signal-to-noise ratio of 10. Superior results with respect to the global geopotential model TIM-r5 are obtained by the spectral downward continuation of the vertical-vertical-vertical component with the standard deviation of 2.104 m2s-2, but the root mean square error is the largest and reaches 9.734 m2s-2. Using the spectral combination of all gravitational curvatures the root mean square error is more than 400 times smaller but the standard deviation reaches 17.234 m2s-2. The combination of more components decreases the root mean square error of the corresponding solutions while the standard deviations of the combined solutions do not improve as compared to the solution from the vertical-vertical-vertical component. The presented method represents a weight mean in the spectral domain that minimizes the root mean square error

  19. Sources of spurious force oscillations from an immersed boundary method for moving-body problems

    Science.gov (United States)

    Lee, Jongho; Kim, Jungwoo; Choi, Haecheon; Yang, Kyung-Soo

    2011-04-01

    When a discrete-forcing immersed boundary method is applied to moving-body problems, it produces spurious force oscillations on a solid body. In the present study, we identify two sources of these force oscillations. One source is from the spatial discontinuity in the pressure across the immersed boundary when a grid point located inside a solid body becomes that of fluid with a body motion. The addition of mass source/sink together with momentum forcing proposed by Kim et al. [J. Kim, D. Kim, H. Choi, An immersed-boundary finite volume method for simulations of flow in complex geometries, Journal of Computational Physics 171 (2001) 132-150] reduces the spurious force oscillations by alleviating this pressure discontinuity. The other source is from the temporal discontinuity in the velocity at the grid points where fluid becomes solid with a body motion. The magnitude of velocity discontinuity decreases with decreasing the grid spacing near the immersed boundary. Four moving-body problems are simulated by varying the grid spacing at a fixed computational time step and at a constant CFL number, respectively. It is found that the spurious force oscillations decrease with decreasing the grid spacing and increasing the computational time step size, but they depend more on the grid spacing than on the computational time step size.

  20. Fictitious domain methods for elliptic problems with general boundary conditions with an application to the numerical simulation of two phase flows

    International Nuclear Information System (INIS)

    Ramiere, I.

    2006-09-01

    This work is dedicated to the introduction of two original fictitious domain methods for the resolution of elliptic problems (mainly convection-diffusion problems) with general and eventually mixed boundary conditions: Dirichlet, Robin or Neumann. The originality lies in the approximation of the immersed boundary by an approximate interface derived from the fictitious domain Cartesian mesh, which is generally not boundary-fitted to the physical domain. The same generic numerical scheme is used to impose the embedded boundary conditions. Hence, these methods require neither a surface mesh of the immersed boundary nor the local modification of the numerical scheme. We study two modelling of the immersed boundary. In the first one, called spread interface, the approximate immersed boundary is the union of the cells crossed by the physical immersed boundary. In the second one, called thin interface, the approximate immersed boundary lies on sides of mesh cells. Additional algebraic transmission conditions linking both flux and solution jumps through the thin approximate interface are introduced. The fictitious problem to solve as well as the treatment of the embedded boundary conditions are detailed for the two methods. A Q1 finite element scheme is implemented for the numerical validation of the spread interface approach while a new cell-centered finite volume scheme is derived for the thin interface approach with immersed jumps. Each method is then combined to multilevel local mesh refinement algorithms (with solution or flux residual) to increase the precision of the solution in the vicinity of the immersed interface. A convergence analysis of a Q1 finite element method with non-boundary fitted meshes is also presented. This study proves the convergence rates of the present methods. Among the various industrial applications, the simulation on a model of heat exchanger in french nuclear power plants enables us to appreciate the performances of the fictitious domain

  1. New Boundary Constraints for Elliptic Systems used in Grid Generation Problems

    Science.gov (United States)

    Kaul, Upender K.; Clancy, Daniel (Technical Monitor)

    2002-01-01

    This paper discusses new boundary constraints for elliptic partial differential equations as used in grid generation problems in generalized curvilinear coordinate systems. These constraints, based on the principle of local conservation of thermal energy in the vicinity of the boundaries, are derived using the Green's Theorem. They uniquely determine the so called decay parameters in the source terms of these elliptic systems. These constraints' are designed for boundary clustered grids where large gradients in physical quantities need to be resolved adequately. It is observed that the present formulation also works satisfactorily for mild clustering. Therefore, a closure for the decay parameter specification for elliptic grid generation problems has been provided resulting in a fully automated elliptic grid generation technique. Thus, there is no need for a parametric study of these decay parameters since the new constraints fix them uniquely. It is also shown that for Neumann type boundary conditions, these boundary constraints uniquely determine the solution to the internal elliptic problem thus eliminating the non-uniqueness of the solution of an internal Neumann boundary value grid generation problem.

  2. Numerical Solutions of Fifth Order Boundary Value Problems Using

    African Journals Online (AJOL)

    Dr A.B.Ahmed

    1Department of Mathematics Delta State University, Abraka, Nigeria. 2Department of ..... International Journal of Computational. Mathematics and ... Value Problems using Power Series Approximation Method.Applied. Mathematics,. 7,. 1215-.

  3. The Use of Source-Sink and Doublet Distributions Extended to the Solution of Boundary-Value Problems in Supersonic Flow

    Science.gov (United States)

    Heaslet, Max A; Lomax, Harvard

    1948-01-01

    A direct analogy is established between the use of source-sink and doublet distributions in the solution of specific boundary-value problems in subsonic wing theory and the corresponding problems in supersonic theory. The correct concept of the "finite part" of an integral is introduced and used in the calculation of the improper integrals associated with supersonic doublet distributions. The general equations developed are shown to include several previously published results and particular examples are given for the loading on rolling and pitching triangular wings with supersonic leading edges.

  4. Two (multi point nonlinear Lyapunov systems associated with an n th order nonlinear system of differential equations – existence and uniqueness

    Directory of Open Access Journals (Sweden)

    Murty K. N.

    2000-01-01

    Full Text Available This paper presents a criterion for the existence and uniqueness of solutions to two and multipoint boundary value problems associated with an n th order nonlinear Lyapunov system. A variation of parameters formula is developed and used as a tool to obtain existence and uniqueness. We discuss solution of the second order problem by the ADI method and develop a fixed point method to find the general solution of the n th order Lyapunov system. The results of Barnett (SIAM J. Appl. Anal. 24(1, 1973 are a particular case.

  5. Solutions to second order non-homogeneous multi-point BVPs using a fixed-point theorem

    Directory of Open Access Journals (Sweden)

    Yuji Liu

    2008-07-01

    Full Text Available In this article, we study five non-homogeneous multi-point boundary-value problems (BVPs of second order differential equations with the one-dimensional p-Laplacian. These problems have a common equation (in different function domains and different boundary conditions. We find conditions that guarantee the existence of at least three positive solutions. The results obtained generalize several known ones and are illustrated by examples. It is also shown that the approach for getting three positive solutions by using multi-fixed-point theorems can be extended to nonhomogeneous BVPs. The emphasis is on the nonhomogeneous boundary conditions and the nonlinear term involving first order derivative of the unknown. Some open problems are also proposed.

  6. The creation of geometrical plan on the boundary of two cadastral areas with a digitized cadastral map.

    Directory of Open Access Journals (Sweden)

    Jiří Bureš

    2005-06-01

    Full Text Available After reconstruction of communication passing through two cadastral areas, geometrical plans were made for the property dividing for each areas independently. The cadastral boundary is a water flow. The digitized cadastral maps of the former cadastre in the Cassini - soldner datum in the scale 1:2880, (the coordinate system St. Stephan, were used. The contact of drafting on the cadastral boundary was not adjusted. The changed boundary and reference points were surveyed in the field in the datum JTSK. The surveyed data were transformed into digitized maps separately for each cadastral area. The unadjusted cadastral boundary, many calculations and also the lack of reference points casued main difficulties. These problems are solved by digitized cadastral maps in datum JTSK with adjusted cadastral boundaries.

  7. Boundary integral equation methods in eigenvalue problems of elastodynamics and thin plates

    CERN Document Server

    Kitahara, M

    1985-01-01

    The boundary integral equation (BIE) method has been used more and more in the last 20 years for solving various engineering problems. It has important advantages over other techniques for numerical treatment of a wide class of boundary value problems and is now regarded as an indispensable tool for potential problems, electromagnetism problems, heat transfer, fluid flow, elastostatics, stress concentration and fracture problems, geomechanical problems, and steady-state and transient electrodynamics.In this book, the author gives a complete, thorough and detailed survey of the method. It pro

  8. Modified Taylor series method for solving nonlinear differential equations with mixed boundary conditions defined on finite intervals.

    Science.gov (United States)

    Vazquez-Leal, Hector; Benhammouda, Brahim; Filobello-Nino, Uriel Antonio; Sarmiento-Reyes, Arturo; Jimenez-Fernandez, Victor Manuel; Marin-Hernandez, Antonio; Herrera-May, Agustin Leobardo; Diaz-Sanchez, Alejandro; Huerta-Chua, Jesus

    2014-01-01

    In this article, we propose the application of a modified Taylor series method (MTSM) for the approximation of nonlinear problems described on finite intervals. The issue of Taylor series method with mixed boundary conditions is circumvented using shooting constants and extra derivatives of the problem. In order to show the benefits of this proposal, three different kinds of problems are solved: three-point boundary valued problem (BVP) of third-order with a hyperbolic sine nonlinearity, two-point BVP for a second-order nonlinear differential equation with an exponential nonlinearity, and a two-point BVP for a third-order nonlinear differential equation with a radical nonlinearity. The result shows that the MTSM method is capable to generate easily computable and highly accurate approximations for nonlinear equations. 34L30.

  9. Electrical Resistance Imaging of Bubble Boundary in Annular Two-Phase Flows Using Unscented Kalman Filter

    International Nuclear Information System (INIS)

    Lee, Jeong Seong; Chung, Soon Il; Ljaz, Umer Zeeshan; Khambampati, Anil Kumar; Kim, Kyung Youn; Kim, Sin Kim

    2007-01-01

    For the visualization of the phase boundary in annular two-phase flows, the electrical resistance tomography (ERT) technique is introduced. In ERT, a set of predetermined electrical currents is injected trough the electrodes placed on the boundary of the flow passage and the induced electrical potentials are measured on the electrode. With the relationship between the injected currents and the induced voltages, the electrical conductivity distribution across the flow domain is estimated through the image reconstruction algorithm. In this, the conductivity distribution corresponds to the phase distribution. In the application of ERT to two-phase flows where there are only two conductivity values, the conductivity distribution estimation problem can be transformed into the boundary estimation problem. This paper considers a bubble boundary estimation with ERT in annular two-phase flows. As the image reconstruction algorithm, the unscented Kalman filter (UKF) is adopted since from the control theory it is reported that the UKF shows better performance than the extended Kalman filter (EKF) that has been commonly used. We formulated the UKF algorithm to be incorporate into the image reconstruction algorithm for the present problem. Also, phantom experiments have been conducted to evaluate the improvement by UKF

  10. Solvability, regularity, and optimal control of boundary value problems for pdes in honour of Prof. Gianni Gilardi

    CERN Document Server

    Favini, Angelo; Rocca, Elisabetta; Schimperna, Giulio; Sprekels, Jürgen

    2017-01-01

    This volume gathers contributions in the field of partial differential equations, with a focus on mathematical models in phase transitions, complex fluids and thermomechanics. These contributions are dedicated to Professor Gianni Gilardi on the occasion of his 70th birthday. It particularly develops the following thematic areas: nonlinear dynamic and stationary equations; well-posedness of initial and boundary value problems for systems of PDEs; regularity properties for the solutions; optimal control problems and optimality conditions; feedback stabilization and stability results. Most of the articles are presented in a self-contained manner, and describe new achievements and/or the state of the art in their line of research, providing interested readers with an overview of recent advances and future research directions in PDEs.

  11. Unique solvability of a non-linear non-local boundary-value problem for systems of non-linear functional differential equations

    Czech Academy of Sciences Publication Activity Database

    Dilna, N.; Rontó, András

    2010-01-01

    Roč. 60, č. 3 (2010), s. 327-338 ISSN 0139-9918 R&D Projects: GA ČR(CZ) GA201/06/0254 Institutional research plan: CEZ:AV0Z10190503 Keywords : non-linear boundary value-problem * functional differential equation * non-local condition * unique solvability * differential inequality Subject RIV: BA - General Mathematics Impact factor: 0.316, year: 2010 http://link.springer.com/article/10.2478%2Fs12175-010-0015-9

  12. Boundary Fixed Points, Enhanced Gauge Symmetry and Singular Bundles on K3

    CERN Document Server

    Fuchs, J; Lerche, Wolfgang; Lütken, C A; Schweigert, C; Walcher, J

    2001-01-01

    We investigate certain fixed points in the boundary conformal field theory representation of type IIA D-branes on Gepner points of K3. They correspond geometrically to degenerate brane configurations, and physically lead to enhanced gauge symmetries on the world-volume. Non-abelian gauge groups arise if the stabilizer group of the fixed points is realized projectively, which is similar to D-branes on orbifolds with discrete torsion. Moreover, the fixed point boundary states can be resolved into several irreducible components. These correspond to bound states at threshold and can be viewed as (non-locally free) sub-sheaves of semi-stable sheaves. Thus, the BCFT fixed points appear to carry two-fold geometrical information: on the one hand they probe the boundary of the instanton moduli space on K3, on the other hand they probe discrete torsion in D-geometry.

  13. Numerical stability of finite difference algorithms for electrochemical kinetic simulations: Matrix stability analysis of the classic explicit, fully implicit and Crank-Nicolson methods and typical problems involving mixed boundary conditions

    DEFF Research Database (Denmark)

    Bieniasz, Leslaw K.; Østerby, Ole; Britz, Dieter

    1995-01-01

    The stepwise numerical stability of the classic explicit, fully implicit and Crank-Nicolson finite difference discretizations of example diffusional initial boundary value problems from electrochemical kinetics has been investigated using the matrix method of stability analysis. Special attention...... has been paid to the effect of the discretization of the mixed, linear boundary condition with time-dependent coefficients on stability, assuming the two-point forward-difference approximations for the gradient at the left boundary (electrode). Under accepted assumptions one obtains the usual...... stability criteria for the classic explicit and fully implicit methods. The Crank-Nicolson method turns out to be only conditionally stable in contrast to the current thought regarding this method....

  14. Solution for state constrained optimal control problems applied to power split control for hybrid vehicles

    NARCIS (Netherlands)

    Keulen, van T.A.C.; Gillot, J.; Jager, de A.G.; Steinbuch, M.

    2014-01-01

    This paper presents a numerical solution for scalar state constrained optimal control problems. The algorithm rewrites the constrained optimal control problem as a sequence of unconstrained optimal control problems which can be solved recursively as a two point boundary value problem. The solution

  15. Bubble boundary estimation in an annulus two-phase flow using electrical impedance tomography

    International Nuclear Information System (INIS)

    Lee, Jeong Seong

    2008-02-01

    For the visualization of the phase boundary in an annulus two-phase flows, the electrical impedance tomography (EIT) technique is introduced. In EIT, a set of predetermined electrical currents is injected trough the electrodes placed on the boundary of the flow passage and the induced electrical potentials are measured on the electrode. With the relationship between the injected currents and the induced voltages, the electrical conductivity distribution across the flow domain is estimated through the image reconstruction algorithm. In this, the conductivity distribution corresponds to the phase distribution. In the application of EIT to two-phase flows where there are only two conductivity values, the conductivity distribution estimation problem can be transformed into the boundary estimation problem. This paper considers a bubble boundary estimation with EIT in an annulus two-phase flows. And in many industrial cases there are a priori known internal structures inside the vessels which could be used as internal electrodes in tomographical imaging. In this paper internal electrodes were considered in electrical impedance tomography. As the image reconstruction algorithm, the unscented Kalman filter (UKF) is adopted since from the control theory it is reported that the UKF shows better performance than the extended Kalman filter (EKF) that has been commonly used. The UKF algorithm was formulated to be incorporate into the image reconstruction algorithm for the present problem. Also, phantom experiments have been conducted to evaluate the improvement by UKF

  16. Multiplicity results for classes of one-dimensional p-Laplacian boundary-value problems with cubic-like nonlinearities

    Directory of Open Access Journals (Sweden)

    Idris Addou

    2000-07-01

    Full Text Available We study boundary-value problems of the type $$displaylines{ -(varphi_{p}( u' ' =lambda f( u ,hbox{ in }(0,1 cr u( 0 =u( 1 =0, }$$ where $p>1$, $varphi_{p}( x =left| x ight| ^{p-2}x$, and $lambda >0$. We provide multiplicity results when $f$ behaves like a cubic with three distinct roots, at which it satisfies Lipschitz-type conditions involving a parameter $q>1$. We shall show how changes in the position of $q$ with respect to $p$ lead to different behavior of the solution set. When dealing with sign-changing solutions, we assume that $f$ is {it half-odd}; a condition generalizing the usual oddness. We use a quadrature method.

  17. The theory of discrete barriers and its applications to linear boundary-value problems of the 'Dirichlet type'; Theorie des barrieres discretes et applications a des problemes lineaires elliptiques du ''type de dirichlet''

    Energy Technology Data Exchange (ETDEWEB)

    Jamet, P [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

    1967-07-01

    This report gives a general presentation of barrier theory for finite difference operators, with its applications to some boundary value problems. (author) [French] Ce rapport est un expose synthetique de la theorie des barrieres pour les operateurs aux differences finies et ses applications a certaines classes de problemes lineaires elliptiques du 'type de Dirichlet'. (auteur)

  18. The quantum-field renormalization group in the problem of a growing phase boundary

    International Nuclear Information System (INIS)

    Antonov, N.V.; Vasil'ev, A.N.

    1995-01-01

    Within the quantum-field renormalization-group approach we examine the stochastic equation discussed by S.I. Pavlik in describing a randomly growing phase boundary. We show that, in contrast to Pavlik's assertion, the model is not multiplicatively renormalizable and that its consistent renormalization-group analysis requires introducing an infinite number of counterterms and the respective coupling constants (open-quotes chargeclose quotes). An explicit calculation in the one-loop approximation shows that a two-dimensional surface of renormalization-group points exits in the infinite-dimensional charge space. If the surface contains an infrared stability region, the problem allows for scaling with the nonuniversal critical dimensionalities of the height of the phase boundary and time, δ h and δ t , which satisfy the exact relationship 2 δ h = δ t + d, where d is the dimensionality of the phase boundary. 23 refs., 1 tab

  19. The mixed boundary value problem, Krein resolvent formulas and spectral asymptotic estimates

    DEFF Research Database (Denmark)

    Grubb, Gerd

    2011-01-01

    For a second-order symmetric strongly elliptic operator A on a smooth bounded open set in Rn, the mixed problem is defined by a Neumann-type condition on a part Σ+ of the boundary and a Dirichlet condition on the other part Σ−. We show a Kreĭn resolvent formula, where the difference between its...... to the area of Σ+, in the case where A is principally equal to the Laplacian...

  20. Einstein boundary conditions in relation to constraint propagation for the initial-boundary value problem of the Einstein equations

    International Nuclear Information System (INIS)

    Frittelli, Simonetta; Gomez, Roberto

    2004-01-01

    We show how the use of the normal projection of the Einstein tensor as a set of boundary conditions relates to the propagation of the constraints, for two representations of the Einstein equations with vanishing shift vector: the Arnowitt-Deser-Misner formulation, which is ill posed, and the Einstein-Christoffel formulation, which is symmetric hyperbolic. Essentially, the components of the normal projection of the Einstein tensor that act as nontrivial boundary conditions are linear combinations of the evolution equations with the constraints that are not preserved at the boundary, in both cases. In the process, the relationship of the normal projection of the Einstein tensor to the recently introduced 'constraint-preserving' boundary conditions becomes apparent

  1. Universal equations of unsteady two-dimensional MHD boundary layer whose temperature varies with time

    Directory of Open Access Journals (Sweden)

    Boričić Zoran

    2009-01-01

    Full Text Available This paper concerns with unsteady two-dimensional temperature laminar magnetohydrodynamic (MHD boundary layer of incompressible fluid. It is assumed that induction of outer magnetic field is function of longitudinal coordinate with force lines perpendicular to the body surface on which boundary layer forms. Outer electric filed is neglected and magnetic Reynolds number is significantly lower then one i.e. considered problem is in inductionless approximation. Characteristic properties of fluid are constant because velocity of flow is much lower than speed of light and temperature difference is small enough (under 50ºC . Introduced assumptions simplify considered problem in sake of mathematical solving, but adopted physical model is interesting from practical point of view, because its relation with large number of technically significant MHD flows. Obtained partial differential equations can be solved with modern numerical methods for every particular problem. Conclusions based on these solutions are related only with specific temperature MHD boundary layer problem. In this paper, quite different approach is used. First new variables are introduced and then sets of similarity parameters which transform equations on the form which don't contain inside and in corresponding boundary conditions characteristics of particular problems and in that sense equations are considered as universal. Obtained universal equations in appropriate approximation can be solved numerically once for all. So-called universal solutions of equations can be used to carry out general conclusions about temperature MHD boundary layer and for calculation of arbitrary particular problems. To calculate any particular problem it is necessary also to solve corresponding momentum integral equation.

  2. Boundary value problems of finite elasticity local theorems on existence, uniqueness, and analytic dependence on data

    CERN Document Server

    Valent, Tullio

    1988-01-01

    In this book I present, in a systematic form, some local theorems on existence, uniqueness, and analytic dependence on the load, which I have recently obtained for some types of boundary value problems of finite elasticity. Actually, these results concern an n-dimensional (n ~ 1) formal generalization of three-dimensional elasticity. Such a generalization, be­ sides being quite spontaneous, allows us to consider a great many inter­ esting mathematical situations, and sometimes allows us to clarify certain aspects of the three-dimensional case. Part of the matter presented is unpublished; other arguments have been only partially published and in lesser generality. Note that I concentrate on simultaneous local existence and uniqueness; thus, I do not deal with the more general theory of exis­ tence. Moreover, I restrict my discussion to compressible elastic bodies and I do not treat unilateral problems. The clever use of the inverse function theorem in finite elasticity made by STOPPELLI [1954, 1957a, 1957b]...

  3. On two-spectra inverse problems

    OpenAIRE

    Guliyev, Namig J.

    2018-01-01

    We consider a two-spectra inverse problem for the one-dimensional Schr\\"{o}dinger equation with boundary conditions containing rational Herglotz--Nevanlinna functions of the eigenvalue parameter and provide a complete solution of this problem.

  4. Applications of Voronoi and Delaunay Diagrams in the solution of the geodetic boundary value problem

    Directory of Open Access Journals (Sweden)

    C. A. B. Quintero

    Full Text Available Voronoi and Delaunay structures are presented as discretization tools to be used in numerical surface integration aiming the computation of geodetic problems solutions, when under the integral there is a non-analytical function (e. g., gravity anomaly and height. In the Voronoi approach, the target area is partitioned into polygons which contain the observed point and no interpolation is necessary, only the original data is used. In the Delaunay approach, the observed points are vertices of triangular cells and the value for a cell is interpolated for its barycenter. If the amount and distribution of the observed points are adequate, gridding operation is not required and the numerical surface integration is carried out by point-wise. Even when the amount and distribution of the observed points are not enough, the structures of Voronoi and Delaunay can combine grid with observed points in order to preserve the integrity of the original information. Both schemes are applied to the computation of the Stokes' integral, the terrain correction, the indirect effect and the gradient of the gravity anomaly, in the State of Rio de Janeiro, Brazil area.

  5. Solution of the Stokes system by boundary integral equations and fixed point iterative schemes

    International Nuclear Information System (INIS)

    Chidume, C.E.; Lubuma, M.S.

    1990-01-01

    The solution to the exterior three dimensional Stokes problem is sought in the form of a single layer potential of unknown density. This reduces the problem to a boundary integral equation of the first kind whose operator is the velocity component of the single layer potential. It is shown that this component is an isomorphism between two appropriate Sobolev spaces containing the unknown densities and the data respectively. The isomorphism corresponds to a variational problem with coercive bilinear form. The latter property allows us to consider various fixed point iterative schemes that converge to the unique solution of the integral equation. Explicit error estimates are also obtained. The successive approximations are also considered in a more computable form by using the product integration method of Atkinson. (author). 47 refs

  6. Existence of solutions to boundary value problems arising from the fractional advection dispersion equation

    Directory of Open Access Journals (Sweden)

    Lingju Kong

    2013-04-01

    Full Text Available We study the existence of multiple solutions to the boundary value problem $$displaylines{ frac{d}{dt}Big(frac12{}_0D_t^{-eta}(u'(t+frac12{}_tD_T^{-eta}(u'(t Big+lambda abla F(t,u(t=0,quad tin [0,T],cr u(0=u(T=0, }$$ where $T>0$, $lambda>0$ is a parameter, $0leqeta<1$, ${}_0D_t^{-eta}$ and ${}_tD_T^{-eta}$ are, respectively, the left and right Riemann-Liouville fractional integrals of order $eta$, $F: [0,T]imesmathbb{R}^Nomathbb{R}$ is a given function. Our interest in the above system arises from studying the steady fractional advection dispersion equation. By applying variational methods, we obtain sufficient conditions under which the above equation has at least three solutions. Our results are new even for the special case when $eta=0$. Examples are provided to illustrate the applicability of our results.

  7. A nonlinear free boundary problem with a self-driven Bernoulli condition

    OpenAIRE

    Dipierro, Serena; Karakhanyan, Aram; Valdinoci, Enrico

    2017-01-01

    We study a Bernoulli type free boundary problem with two phases J[u]=∫Ω|∇u(x)|2dx+Φ(M−(u),M+(u)),u−u¯∈W1,20(Ω), where u¯∈W1,2(Ω) is a given boundary datum. Here, M1 and M2 are weighted volumes of {u≤0}∩Ω and {u>0}∩Ω, respectively, and Φ is a nonnegative function of two real variables. We show that, for this problem, the Bernoulli constant, which determines the gradient jump condition across the free boundary, is of global type and it is indeed determined by the weighted volumes of the phas...

  8. Thin-film superconducting rings in the critical state: the mixed boundary value approach

    Science.gov (United States)

    Brambilla, Roberto; Grilli, Francesco

    2015-02-01

    In this paper, we describe the critical state of a thin superconducting ring (and of a perfectly conducting ring as a limiting case) as a mixed boundary value problem. The disc is characterized by a three-part boundary division of the positive real axis, so this work is an extension of the procedure used in a previous work of ours for describing superconducting discs and strips, which are characterized by a two-part boundary division of the real axis. Here, we present the mathematical tools to solve this kind of problems—the Erdélyi-Kober operators—in a frame that can be immediately used. Contrary to the two-part problems considered in our previous work, three-part problems do not generally have analytical solutions and the numerical work takes on a significant heaviness. Nevertheless, this work is remunerated by three clear advantages: firstly, all the cases are afforded in the same way, without the necessity of any brilliant invention or ability; secondly, in the case of superconducting rings, the penetration of the magnetic field in the internal/external rims is a result of the method itself and does not have to be imposed, as it is commonly done with other methods presented in the literature; thirdly, the method can be extended to investigate even more complex cases (four-part problems). In this paper, we consider the cases of rings in uniform field and with transport current, with or without flux trapping in the hole and the case without net current, corresponding to a cut ring (washer), as used in some SQUID applications.

  9. A boundary-value inverse model and its application to the calculation of tidal oscillation systems in the Western South Atlantic Ocean

    International Nuclear Information System (INIS)

    Miranda-Alonso, S.

    1991-01-01

    A Cauchy-Riemann problem is solved for the case of the linearized equations for long waves. The initial-values are amplitudes and phases measured at the coast. No boundary values are made use of. This inverse-problem is solved by starting the calculations at the coast and continuing outwards to the open ocean in a rectangular areas with one side at the coast and the other three at the open ocean. The initial values were expanded into the complex plane to get a platform to perform with the calculations. This non-well-posed problem was solved by means of two different mathematical techniques for comparison. The results produced with the inverse model were compared with those produced with a 'classical' model initialized at the three open boundaries with the results of the inverse model. The oscillating systems produced by both models were quite similar, giving validity to this invese modeling approach which should be a useful technique to solve problems when only initial values are known. (orig.)

  10. Boundary layer and fundamental problems of hydrodynamics (compatibility of a logarithmic velocity profile in a turbulent boundary layer with the experience values)

    Science.gov (United States)

    Zaryankin, A. E.

    2017-11-01

    The compatibility of the semiempirical turbulence theory of L. Prandtl with the actual flow pattern in a turbulent boundary layer is considered in this article, and the final calculation results of the boundary layer is analyzed based on the mentioned theory. It shows that accepted additional conditions and relationships, which integrate the differential equation of L. Prandtl, associating the turbulent stresses in the boundary layer with the transverse velocity gradient, are fulfilled only in the near-wall region where the mentioned equation loses meaning and are inconsistent with the physical meaning on the main part of integration. It is noted that an introduced concept about the presence of a laminar sublayer between the wall and the turbulent boundary layer is the way of making of a physical meaning to the logarithmic velocity profile, and can be defined as adjustment of the actual flow to the formula that is inconsistent with the actual boundary conditions. It shows that coincidence of the experimental data with the actual logarithmic profile is obtained as a result of the use of not particular physical value, as an argument, but function of this value.

  11. An asymptotic analytical solution to the problem of two moving boundaries with fractional diffusion in one-dimensional drug release devices

    International Nuclear Information System (INIS)

    Yin Chen; Xu Mingyu

    2009-01-01

    We set up a one-dimensional mathematical model with a Caputo fractional operator of a drug released from a polymeric matrix that can be dissolved into a solvent. A two moving boundaries problem in fractional anomalous diffusion (in time) with order α element of (0, 1] under the assumption that the dissolving boundary can be dissolved slowly is presented in this paper. The two-parameter regular perturbation technique and Fourier and Laplace transform methods are used. A dimensionless asymptotic analytical solution is given in terms of the Wright function

  12. LiveWire interactive boundary extraction algorithm based on Haar wavelet transform and control point set direction search

    Science.gov (United States)

    Cheng, Jun; Zhang, Jun; Tian, Jinwen

    2015-12-01

    Based on deep analysis of the LiveWire interactive boundary extraction algorithm, a new algorithm focusing on improving the speed of LiveWire algorithm is proposed in this paper. Firstly, the Haar wavelet transform is carried on the input image, and the boundary is extracted on the low resolution image obtained by the wavelet transform of the input image. Secondly, calculating LiveWire shortest path is based on the control point set direction search by utilizing the spatial relationship between the two control points users provide in real time. Thirdly, the search order of the adjacent points of the starting node is set in advance. An ordinary queue instead of a priority queue is taken as the storage pool of the points when optimizing their shortest path value, thus reducing the complexity of the algorithm from O[n2] to O[n]. Finally, A region iterative backward projection method based on neighborhood pixel polling has been used to convert dual-pixel boundary of the reconstructed image to single-pixel boundary after Haar wavelet inverse transform. The algorithm proposed in this paper combines the advantage of the Haar wavelet transform and the advantage of the optimal path searching method based on control point set direction search. The former has fast speed of image decomposition and reconstruction and is more consistent with the texture features of the image and the latter can reduce the time complexity of the original algorithm. So that the algorithm can improve the speed in interactive boundary extraction as well as reflect the boundary information of the image more comprehensively. All methods mentioned above have a big role in improving the execution efficiency and the robustness of the algorithm.

  13. Cost-effective computations with boundary interface operators in elliptic problems

    International Nuclear Information System (INIS)

    Khoromskij, B.N.; Mazurkevich, G.E.; Nikonov, E.G.

    1993-01-01

    The numerical algorithm for fast computations with interface operators associated with the elliptic boundary value problems (BVP) defined on step-type domains is presented. The algorithm is based on the asymptotically almost optimal technique developed for treatment of the discrete Poincare-Steklov (PS) operators associated with the finite-difference Laplacian on rectangles when using the uniform grid with a 'displacement by h/2'. The approach can be regarded as an extension of the method proposed for the partial solution of the finite-difference Laplace equation to the case of displaced grids and mixed boundary conditions. It is shown that the action of the PS operator for the Dirichlet problem and mixed BVP can be computed with expenses of the order of O(Nlog 2 N) both for arithmetical operations and computer memory needs, where N is the number of unknowns on the rectangle boundary. The single domain algorithm is applied to solving the multidomain elliptic interface problems with piecewise constant coefficients. The numerical experiments presented confirm almost linear growth of the computational costs and memory needs with respect to the dimension of the discrete interface problem. 14 refs., 3 figs., 4 tabs

  14. Sectio Aurea Conditions for Mityuk's Radius of Two-Connected Domains

    Directory of Open Access Journals (Sweden)

    A.V. Kazantsev

    2017-03-01

    Full Text Available Connection of an exterior inverse boundary value problem with the critical points of some surface is one of the central themes in the theory of exterior inverse boundary value problems for analytic functions. In the simply connected case, such a surface is defined by the inner mapping radius; in the multiply connected one, by the function Ω(w such that M(w = (2π–1ln Ω(w is Mityuk's version of a generalized reduced module. In the present paper, the relation between the curvature of the surface Ω = Ω(w with the Schwarzian derivatives of the mapping functions and with the Bergman kernel functions k0(w,ω and l0(w,ω is established for an arbitrary multiply connected domain. When passing to two-connected domains, due to the choice of the ring as a canonical domain, we construct the conditions for the critical points of Mityuk's radius to concentrate on the golden section circle of the ring. Finally, we show that the minimal collection of the critical points of the Mityuk radius in the two-connected case, consisting of one maximum and one saddle, is attained for the linear-fractional solution of the exterior inverse boundary value problem.

  15. Simulating a singularity-free universe outside the problem boundary in poisson

    International Nuclear Information System (INIS)

    Halbach, K.; Schlueter, R.

    1992-01-01

    An exact analytical solution developed from the Dirichlet problem exterior to a circle is employed in the magnetostatics code POISSON to provide a boundary condition option which simulates a singularity-free universe external to the problem domain. Problems with domains of large unequal extents in perpendicular directions are treated by first conformally mapping the exterior of an ellipse onto the exterior of the unit circle. Problems exhibiting symmetry in one or two planes are modeled using a semi or quarter, respectively, in conjunction with the singularity-free rest-of-universe boundary condition

  16. An Investigation of Starting Point Preferences in Human Performance on Traveling Salesman Problems

    Science.gov (United States)

    MacGregor, James N.

    2014-01-01

    Previous studies have shown that people start traveling sales problem tours significantly more often from boundary than from interior nodes. There are a number of possible reasons for such a tendency: first, it may arise as a direct result of the processes involved in tour construction; second, boundary points may be perceptually more salient than…

  17. Numerical experiments using CHIEF to treat the nonuniqueness in solving acoustic axisymmetric exterior problems via boundary integral equations

    Directory of Open Access Journals (Sweden)

    Adel A.K. Mohsen

    2010-07-01

    Full Text Available The problem of nonuniqueness (NU of the solution of exterior acoustic problems via boundary integral equations is discussed in this article. The efficient implementation of the CHIEF (Combined Helmholtz Integral Equations Formulation method to axisymmetric problems is studied. Interior axial fields are used to indicate the solution error and to select proper CHIEF points. The procedure makes full use of LU-decomposition as well as the forward solution derived in the solution. Implementations of the procedure for hard spheres are presented. Accurate results are obtained up to a normalised radius of ka = 20.983, using only one CHIEF point. The radiation from a uniformly vibrating sphere is also considered. Accurate results for ka up to 16.927 are obtained using two CHIEF points.

  18. A note on a boundary sine-Gordon model at the free-Fermion point

    Science.gov (United States)

    Murgan, Rajan

    2018-02-01

    We investigate the free-Fermion point of a boundary sine-Gordon model with nondiagonal boundary interactions for the ground state using auxiliary functions obtained from T  -  Q equations of a corresponding inhomogeneous open spin-\\frac{1}{2} XXZ chain with nondiagonal boundary terms. In particular, we obtain the Casimir energy. Our result for the Casimir energy is shown to agree with the result from the TBA approach. The analytical result for the effective central charge in the ultraviolet (UV) limit is also verified from the plots of effective central charge for intermediate values of volume.

  19. New complex variable meshless method for advection—diffusion problems

    International Nuclear Information System (INIS)

    Wang Jian-Fei; Cheng Yu-Min

    2013-01-01

    In this paper, an improved complex variable meshless method (ICVMM) for two-dimensional advection—diffusion problems is developed based on improved complex variable moving least-square (ICVMLS) approximation. The equivalent functional of two-dimensional advection—diffusion problems is formed, the variation method is used to obtain the equation system, and the penalty method is employed to impose the essential boundary conditions. The difference method for two-point boundary value problems is used to obtain the discrete equations. Then the corresponding formulas of the ICVMM for advection—diffusion problems are presented. Two numerical examples with different node distributions are used to validate and inestigate the accuracy and efficiency of the new method in this paper. It is shown that ICVMM is very effective for advection—diffusion problems, and has a good convergent character, accuracy, and computational efficiency

  20. On solution of Lame equations in axisymmetric domains with conical points

    International Nuclear Information System (INIS)

    Nkemzi, Boniface

    2003-10-01

    Partial Fourier series expansion is applied to the Dirichlet problem for the Lame equations in axisymmetric domains Ω-circumflex is a subset of R 3 with conical points on the rotation axis. This leads to dimension reduction of the three-dimensional boundary value problem resulting to an infinite sequence of two-dimensional boundary value problems on the plane meridian domain Ω a is a subset of R + 2 of Ω-circumflex with solutions u n (n = 0,1,2, ...) being the Fourier coefficients of the solution u-circumflex of the 3D BVP. The asymptotic behavior of the Fourier coefficients u n (n = 0,1,2, ...) near the angular points of the meridian domain Ω a is fully described by singular vector-functions which are related to the zeros α n of some transcendental equations involving Legendre functions of the first kind. Equations which determine the values of α n are given and a numerical algorithm for the computation of α n is proposed with some plots of values obtained presented. The singular vector functions for the solution of the 3D BVP is obtained by Fourier synthesis. (author)

  1. Matrix product density operators: Renormalization fixed points and boundary theories

    Energy Technology Data Exchange (ETDEWEB)

    Cirac, J.I. [Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, D-85748 Garching (Germany); Pérez-García, D., E-mail: dperezga@ucm.es [Departamento de Análisis Matemático, Universidad Complutense de Madrid, Plaza de Ciencias 3, 28040 Madrid (Spain); ICMAT, Nicolas Cabrera, Campus de Cantoblanco, 28049 Madrid (Spain); Schuch, N. [Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, D-85748 Garching (Germany); Verstraete, F. [Department of Physics and Astronomy, Ghent University (Belgium); Vienna Center for Quantum Technology, University of Vienna (Austria)

    2017-03-15

    We consider the tensors generating matrix product states and density operators in a spin chain. For pure states, we revise the renormalization procedure introduced in (Verstraete et al., 2005) and characterize the tensors corresponding to the fixed points. We relate them to the states possessing zero correlation length, saturation of the area law, as well as to those which generate ground states of local and commuting Hamiltonians. For mixed states, we introduce the concept of renormalization fixed points and characterize the corresponding tensors. We also relate them to concepts like finite correlation length, saturation of the area law, as well as to those which generate Gibbs states of local and commuting Hamiltonians. One of the main result of this work is that the resulting fixed points can be associated to the boundary theories of two-dimensional topological states, through the bulk-boundary correspondence introduced in (Cirac et al., 2011).

  2. Nonlinear fractional differential equations and inclusions of arbitrary order and multi-strip boundary conditions

    Directory of Open Access Journals (Sweden)

    Bashir Ahmad

    2012-06-01

    Full Text Available We study boundary value problems of nonlinear fractional differential equations and inclusions of order $q in (m-1, m]$, $m ge 2$ with multi-strip boundary conditions. Multi-strip boundary conditions may be regarded as the generalization of multi-point boundary conditions. Our problem is new in the sense that we consider a nonlocal strip condition of the form: $$ x(1=sum_{i=1}^{n-2}alpha_i int^{eta_i}_{zeta_i} x(sds, $$ which can be viewed as an extension of a multi-point nonlocal boundary condition: $$ x(1=sum_{i=1}^{n-2}alpha_i x(eta_i. $$ In fact, the strip condition corresponds to a continuous distribution of the values of the unknown function on arbitrary finite segments $(zeta_i,eta_i$ of the interval $[0,1]$ and the effect of these strips is accumulated at $x=1$. Such problems occur in the applied fields such as wave propagation and geophysics. Some new existence and uniqueness results are obtained by using a variety of fixed point theorems. Some illustrative examples are also discussed.

  3. Inverse Problem for Two-Dimensional Discrete Schr`dinger Equation

    CERN Document Server

    Serdyukova, S I

    2000-01-01

    For two-dimensional discrete Schroedinger equation the boundary-value problem in rectangle M times N with zero boundary conditions is solved. It's stated in this work, that inverse problem reduces to reconstruction of C symmetric five-diagonal matrix with given spectrum and given first k(M,N), 1<-kproblem to the end in the process of concrete calculations. Deriving and solving the huge polynomial systems had been perfor...

  4. The boundary element method for the solution of the multidimensional inverse heat conduction problem

    International Nuclear Information System (INIS)

    Lagier, Guy-Laurent

    1999-01-01

    This work focuses on the solution of the inverse heat conduction problem (IHCP), which consists in the determination of boundary conditions from a given set of internal temperature measurements. This problem is difficult to solve due to its ill-posedness and high sensitivity to measurement error. As a consequence, numerical regularization procedures are required to solve this problem. However, most of these methods depend on the dimension and the nature, stationary or transient, of the problem. Furthermore, these methods introduce parameters, called hyper-parameters, which have to be chosen optimally, but can not be determined a priori. So, a new general method is proposed for solving the IHCP. This method is based on a Boundary Element Method formulation, and the use of the Singular Values Decomposition as a regularization procedure. Thanks to this method, it's possible to identify and eliminate the directions of the solution where the measurement error plays the major role. This algorithm is first validated on two-dimensional stationary and one-dimensional transient problems. Some criteria are presented in order to choose the hyper-parameters. Then, the methodology is applied to two-dimensional and three-dimensional, theoretical or experimental, problems. The results are compared with those obtained by a standard method and show the accuracy of the method, its generality, and the validity of the proposed criteria. (author) [fr

  5. Discontinuous Sturm-Liouville Problems with Eigenvalue Dependent Boundary Condition

    Energy Technology Data Exchange (ETDEWEB)

    Amirov, R. Kh., E-mail: emirov@cumhuriyet.edu.tr; Ozkan, A. S., E-mail: sozkan@cumhuriyet.edu.tr [Cumhuriyet University, Department of Mathematics Faculty of Art and Science (Turkey)

    2014-12-15

    In this study, an inverse problem for Sturm-Liouville differential operators with discontinuities is studied when an eigenparameter appears not only in the differential equation but it also appears in the boundary condition. Uniqueness theorems of inverse problems according to the Prüfer angle, the Weyl function and two different eigenvalues sets are proved.

  6. Two-phase semilinear free boundary problem with a degenerate phase

    KAUST Repository

    Matevosyan, Norayr; Petrosyan, Arshak

    2010-01-01

    states that in dimension two the free boundaries Γ+ = ∂{u > 0} ∩ D andΓ- = ∂{u < 0} ∩ D are C1,α-regular, provided 1 - ∈0 < p < 1. The proof is obtained by a careful iteration of the Harnack inequality to obtain a nontrivial growth estimate

  7. A Duality Approach for the Boundary Variation of Neumann Problems

    DEFF Research Database (Denmark)

    Bucur, Dorin; Varchon, Nicolas

    2002-01-01

    In two dimensions, we study the stability of the solution of an elliptic equation with Neumann boundary conditions for nonsmooth perturbations of the geometric domain. Using harmonic conjugates, we relate this problem to the shape stability of the solution of an elliptic equation with Dirichlet b...... boundary conditions. As a particular case, we prove the stability of the solution under a topological constraint ( uniform number of holes), which is analogous to Sverak's result for Dirichlet boundary conditions....

  8. A duality approach or the boundary variation of Neumann problems

    DEFF Research Database (Denmark)

    Bucur, D.; Varchon, Nicolas

    2002-01-01

    In two dimensions, we study the stability of the solution of an elliptic equation with Neumann boundary conditions for nonsmooth perturbations of the geometric domain. Using harmonic conjugates, we relate this problem to the shape stability of the solution of an elliptic equation with Dirichlet b...... boundary conditions. As a particular case, we prove the stability of the solution under a topological constraint ( uniform number of holes), which is analogous to Sverak's result for Dirichlet boundary conditions....

  9. A scheme to calculate higher-order homogenization as applied to micro-acoustic boundary value problems

    Science.gov (United States)

    Vagh, Hardik A.; Baghai-Wadji, Alireza

    2008-12-01

    Current technological challenges in materials science and high-tech device industry require the solution of boundary value problems (BVPs) involving regions of various scales, e.g. multiple thin layers, fibre-reinforced composites, and nano/micro pores. In most cases straightforward application of standard variational techniques to BVPs of practical relevance necessarily leads to unsatisfactorily ill-conditioned analytical and/or numerical results. To remedy the computational challenges associated with sub-sectional heterogeneities various sophisticated homogenization techniques need to be employed. Homogenization refers to the systematic process of smoothing out the sub-structural heterogeneities, leading to the determination of effective constitutive coefficients. Ordinarily, homogenization involves a sophisticated averaging and asymptotic order analysis to obtain solutions. In the majority of the cases only zero-order terms are constructed due to the complexity of the processes involved. In this paper we propose a constructive scheme for obtaining homogenized solutions involving higher order terms, and thus, guaranteeing higher accuracy and greater robustness of the numerical results. We present

  10. Multidimensional phase change problems by the dual-reciprocity boundary-element method

    International Nuclear Information System (INIS)

    Jo, J.C.; Shin, W.K.; Choi, C.Y.

    1999-01-01

    Transient heat transfer problems with phase changes (Stefan problems) occur in many engineering situations, including potential core melting and solidification during pressurized-water-reactor severe accidents, ablation of thermal shields, melting and solidification of alloys, and many others. This article addresses the numerical analysis of nonlinear transient heat transfer with melting or solidification. An effective and simple procedure is presented for the simulation of the motion of the boundary and the transient temperature field during the phase change process. To accomplish this purpose, an iterative implicit solution algorithm has been developed by employing the dual-reciprocity boundary-element method. The dual-reciprocity boundary-element approach provided in this article is much simpler than the usual boundary-element method in applying a reciprocity principle and an available technique for dealing with the domain integral of the boundary element formulation simultaneously. In this article, attention is focused on two-dimensional melting (ablation)/solidification problems for simplicity. The accuracy and effectiveness of the present analysis method have been illustrated through comparisons of the calculation results of some examples of one-phase ablation/solidification problems with their known semianalytical or numerical solutions where available

  11. Immersed Boundary-Lattice Boltzmann Method Using Two Relaxation Times

    Directory of Open Access Journals (Sweden)

    Kosuke Hayashi

    2012-06-01

    Full Text Available An immersed boundary-lattice Boltzmann method (IB-LBM using a two-relaxation time model (TRT is proposed. The collision operator in the lattice Boltzmann equation is modeled using two relaxation times. One of them is used to set the fluid viscosity and the other is for numerical stability and accuracy. A direct-forcing method is utilized for treatment of immersed boundary. A multi-direct forcing method is also implemented to precisely satisfy the boundary conditions at the immersed boundary. Circular Couette flows between a stationary cylinder and a rotating cylinder are simulated for validation of the proposed method. The method is also validated through simulations of circular and spherical falling particles. Effects of the functional forms of the direct-forcing term and the smoothed-delta function, which interpolates the fluid velocity to the immersed boundary and distributes the forcing term to fixed Eulerian grid points, are also examined. As a result, the following conclusions are obtained: (1 the proposed method does not cause non-physical velocity distribution in circular Couette flows even at high relaxation times, whereas the single-relaxation time (SRT model causes a large non-physical velocity distortion at a high relaxation time, (2 the multi-direct forcing reduces the errors in the velocity profile of a circular Couette flow at a high relaxation time, (3 the two-point delta function is better than the four-point delta function at low relaxation times, but worse at high relaxation times, (4 the functional form of the direct-forcing term does not affect predictions, and (5 circular and spherical particles falling in liquids are well predicted by using the proposed method both for two-dimensional and three-dimensional cases.

  12. Two-point resistance of a resistor network embedded on a globe.

    Science.gov (United States)

    Tan, Zhi-Zhong; Essam, J W; Wu, F Y

    2014-07-01

    We consider the problem of two-point resistance in an (m-1) × n resistor network embedded on a globe, a geometry topologically equivalent to an m × n cobweb with its boundary collapsed into one single point. We deduce a concise formula for the resistance between any two nodes on the globe using a method of direct summation pioneered by one of us [Z.-Z. Tan, L. Zhou, and J. H. Yang, J. Phys. A: Math. Theor. 46, 195202 (2013)]. This method is contrasted with the Laplacian matrix approach formulated also by one of us [F. Y. Wu, J. Phys. A: Math. Gen. 37, 6653 (2004)], which is difficult to apply to the geometry of a globe. Our analysis gives the result in the form of a single summation.

  13. Stabilizing local boundary conditions for two-dimensional shallow water equations

    KAUST Repository

    Dia, Ben Mansour; Oppelstrup, Jesper

    2018-01-01

    In this article, we present a sub-critical two-dimensional shallow water flow regulation. From the energy estimate of a set of one-dimensional boundary stabilization problems, we obtain a set of polynomial equations with respect to the boundary

  14. Numerical Methods for Free Boundary Problems

    CERN Document Server

    1991-01-01

    About 80 participants from 16 countries attended the Conference on Numerical Methods for Free Boundary Problems, held at the University of Jyviiskylii, Finland, July 23-27, 1990. The main purpose of this conference was to provide up-to-date information on important directions of research in the field of free boundary problems and their numerical solutions. The contributions contained in this volume cover the lectures given in the conference. The invited lectures were given by H.W. Alt, V. Barbu, K-H. Hoffmann, H. Mittelmann and V. Rivkind. In his lecture H.W. Alt considered a mathematical model and existence theory for non-isothermal phase separations in binary systems. The lecture of V. Barbu was on the approximate solvability of the inverse one phase Stefan problem. K-H. Hoff­ mann gave an up-to-date survey of several directions in free boundary problems and listed several applications, but the material of his lecture is not included in this proceedings. H.D. Mittelmann handled the stability of thermo capi...

  15. Analytic Approximations to the Free Boundary and Multi-dimensional Problems in Financial Derivatives Pricing

    Science.gov (United States)

    Lau, Chun Sing

    This thesis studies two types of problems in financial derivatives pricing. The first type is the free boundary problem, which can be formulated as a partial differential equation (PDE) subject to a set of free boundary condition. Although the functional form of the free boundary condition is given explicitly, the location of the free boundary is unknown and can only be determined implicitly by imposing continuity conditions on the solution. Two specific problems are studied in details, namely the valuation of fixed-rate mortgages and CEV American options. The second type is the multi-dimensional problem, which involves multiple correlated stochastic variables and their governing PDE. One typical problem we focus on is the valuation of basket-spread options, whose underlying asset prices are driven by correlated geometric Brownian motions (GBMs). Analytic approximate solutions are derived for each of these three problems. For each of the two free boundary problems, we propose a parametric moving boundary to approximate the unknown free boundary, so that the original problem transforms into a moving boundary problem which can be solved analytically. The governing parameter of the moving boundary is determined by imposing the first derivative continuity condition on the solution. The analytic form of the solution allows the price and the hedging parameters to be computed very efficiently. When compared against the benchmark finite-difference method, the computational time is significantly reduced without compromising the accuracy. The multi-stage scheme further allows the approximate results to systematically converge to the benchmark results as one recasts the moving boundary into a piecewise smooth continuous function. For the multi-dimensional problem, we generalize the Kirk (1995) approximate two-asset spread option formula to the case of multi-asset basket-spread option. Since the final formula is in closed form, all the hedging parameters can also be derived in

  16. Two numerical methods for the solution of two-dimensional eddy current problems

    International Nuclear Information System (INIS)

    Biddlecombe, C.S.

    1978-07-01

    A general method for the solution of eddy current problems in two dimensions - one component of current density and two of magnetic field, is reported. After examining analytical methods two numerical methods are presented. Both solve the two dimensional, low frequency limit of Maxwell's equations for transient eddy currents in conducting material, which may be permeable, in the presence of other non-conducting permeable material. Both solutions are expressed in terms of the magnetic vector potential. The first is an integral equation method, using zero order elements in the discretisation of the unknown source regions. The other is a differential equation method, using a first order finite element mesh, and the Galerkin weighted residual procedure. The resulting equations are solved as initial-value problems. Results from programs based on each method are presented showing the power and limitations of the methods and the range of problems solvable. The methods are compared and recommendations are made for choosing between them. Suggestions are made for improving both methods, involving boundary integral techniques. (author)

  17. A New Spectral Local Linearization Method for Nonlinear Boundary Layer Flow Problems

    Directory of Open Access Journals (Sweden)

    S. S. Motsa

    2013-01-01

    Full Text Available We propose a simple and efficient method for solving highly nonlinear systems of boundary layer flow problems with exponentially decaying profiles. The algorithm of the proposed method is based on an innovative idea of linearizing and decoupling the governing systems of equations and reducing them into a sequence of subsystems of differential equations which are solved using spectral collocation methods. The applicability of the proposed method, hereinafter referred to as the spectral local linearization method (SLLM, is tested on some well-known boundary layer flow equations. The numerical results presented in this investigation indicate that the proposed method, despite being easy to develop and numerically implement, is very robust in that it converges rapidly to yield accurate results and is more efficient in solving very large systems of nonlinear boundary value problems of the similarity variable boundary layer type. The accuracy and numerical stability of the SLLM can further be improved by using successive overrelaxation techniques.

  18. What do we actually mean by 'sociotechnical'? On values, boundaries and the problems of language.

    Science.gov (United States)

    Klein, Lisl

    2014-03-01

    The term 'sociotechnical' was first coined in the context of industrial democracy. In comparing two projects on shipping in Esso to help define the concept, the essential categories were found to be where systems boundaries were set, and what factors were considered to be relevant 'human' characteristics. This is often discussed in terms of values. During the nineteen-sixties and seventies sociotechnical theory related to the shop-floor work system, and contingency theory to the organisation as a whole, the two levels being distinct. With the coming of information technology, this distinction became blurred; the term 'socio-structural' is proposed to describe the whole system. IT sometimes is the operating technology, it sometimes supports the operating technology, or it may sometimes be mistaken for the operating technology. This is discussed with reference to recent air accidents. Copyright © 2013 Elsevier Ltd and The Ergonomics Society. All rights reserved.

  19. Performance improvement of extended boundary node method for solving elliptic boundary-value problems

    International Nuclear Information System (INIS)

    Saitoh, Ayumu; Kamitani, Atsushi; Takayama, Teruou; Nakamura, Hiroaki

    2016-01-01

    The extended boundary-node method (X-BNM) with the hierarchical-matrix (H-matrix) method has been developed and its performance has been investigated numerically. The results of computations show that the solver speed of the X-BNM with the H-matrix method is much faster than that of the standard X-BNM for the case where the number of boundary nodes exceeds a certain limit. Furthermore, the accuracy of the X-BNM with the H-matrix method is almost equal to that of the standard X-BNM. From these results, it is found that the H-matrix method is useful as the acceleration technique of the X-BNM. (author)

  20. Shooting method for third order simultaneous ordinary differential equations with application to magnetohydrodynamic boundary layer

    International Nuclear Information System (INIS)

    Srivastava, A.C.; Hazarika, G.C.

    1990-01-01

    An algorithm based on the shooting method has been developed for the solution of a two-point boundary value problem consisting of a system of third order simultaneous ordinary differential equations. The Falkner-Skan equations for electrically conducting viscous fluid with applied magnetic field has been solved by using this algorithm for various values of the wedge angle and magnetic parameters. The shooting method seems to be well convergent for a system as the results are in good agreement with those obtained by other methods. It is observed that both viscous boundary layer and magnetic boundary layer decrease while velocity as well as magnetic field increase with the increase of the wedge angle. (author). 6 tabs., 7 refs

  1. Mathematical simulation of point defect interaction with grain boundaries

    International Nuclear Information System (INIS)

    Bojko, V.S.

    1987-01-01

    Published works, where the interaction of point defects and grain boundaries was studied by mathematical simulation methods, have been analysed. Energetics of the vacancy formation both in nuclei of large-angle special grain boundaries and in lattice regions adjoining them has been considered. The data obtained permit to explain specific features of grain-boundary diffusion processes. Results of mathematical simulation of the interaction of impurity atoms and boundaries have been considered. Specific features of the helium atom interaction with large-angle grain boundaries are analysed as well

  2. A minimax inequality for a class of functionals and applications to the existence of solutions for two-point boundary-value problems

    Directory of Open Access Journals (Sweden)

    Ghasem Alizadeh Afrouzi

    2006-10-01

    Full Text Available In this paper, we establish an equivalent statement to minimax inequality for a special class of functionals. As an application, we prove the existence of three solutions to the Dirichlet problem $$displaylines{ -u''(x+m(xu(x =lambda f(x,u(x,quad xin (a,b,cr u(a=u(b=0, }$$ where $lambda>0$, $f:[a,b]imes mathbb{R}o mathbb{R}$ is a continuous function which changes sign on $[a,b]imes mathbb{R}$ and $m(xin C([a,b]$ is a positive function.

  3. Uniqueness of solution to a stationary boundary kinetic problem

    International Nuclear Information System (INIS)

    Zhykharsky, A.V.

    1992-01-01

    The paper treats the question of uniqueness of solution to the boundary kinetic problem. This analysis is based on the accurate solutions to the stationary one-dimensional boundary kinetic problem for the limited plasma system. In the paper a simplified problem statement is used (no account is taken of the external magnetic field, a simplest form of boundary conditions is accepted) which, however, covers all features of the problem considered. Omitting the details of the conclusion we will write a set of Vlasov stationary kinetic equations for the cases of plane, cylindrical and spherical geometry of the problem. (author) 1 ref

  4. Solution to Two-Dimensional Steady Inverse Heat Transfer Problems with Interior Heat Source Based on the Conjugate Gradient Method

    Directory of Open Access Journals (Sweden)

    Shoubin Wang

    2017-01-01

    Full Text Available The compound variable inverse problem which comprises boundary temperature distribution and surface convective heat conduction coefficient of two-dimensional steady heat transfer system with inner heat source is studied in this paper applying the conjugate gradient method. The introduction of complex variable to solve the gradient matrix of the objective function obtains more precise inversion results. This paper applies boundary element method to solve the temperature calculation of discrete points in forward problems. The factors of measuring error and the number of measuring points zero error which impact the measurement result are discussed and compared with L-MM method in inverse problems. Instance calculation and analysis prove that the method applied in this paper still has good effectiveness and accuracy even if measurement error exists and the boundary measurement points’ number is reduced. The comparison indicates that the influence of error on the inversion solution can be minimized effectively using this method.

  5. Dual reciprocity boundary element analysis for the laminar forced heat convection problem in concentric annulus

    International Nuclear Information System (INIS)

    Choi, Chang Yong

    1999-01-01

    This paper presents a study of the Dual Reciprocity Boundary Element Method (DRBEM) for the laminar heat convection problem in a concentric annulus with constant heat flux boundary condition. DRBEM is one of the most successful technique used to transform the domain integrals arising from the nonhomogeneous term of the poisson equation into equivalent boundary only integrals. This recently developed and highly efficient numerical method is tested for the solution accuracy of the fluid flow and heat transfer study in a concentric annulus. Since their exact solutions are available, DRBEM solutions are verified with different number of boundary element discretization and internal points. The results obtained in this study are discussed with the relative error percentage of velocity and temperature solutions, and potential applicability of the method for the more complicated heat convection problems with arbitrary duct geometries

  6. Boundary Value Problems and Approximate Solutions

    African Journals Online (AJOL)

    Tadesse

    Department of Mathematics, College of Natural and Computational Scineces, Mekelle ..... In this section, the Variational Iteration Method is applied to different forms of .... Some problems in non-Newtonian fluid mechanics, Ph.D. thesis, Wales.

  7. Equivalence-point electromigration acid-base titration via moving neutralization boundary electrophoresis.

    Science.gov (United States)

    Yang, Qing; Fan, Liu-Yin; Huang, Shan-Sheng; Zhang, Wei; Cao, Cheng-Xi

    2011-04-01

    In this paper, we developed a novel method of acid-base titration, viz. the electromigration acid-base titration (EABT), via a moving neutralization boundary (MNR). With HCl and NaOH as the model strong acid and base, respectively, we conducted the experiments on the EABT via the method of moving neutralization boundary for the first time. The experiments revealed that (i) the concentration of agarose gel, the voltage used and the content of background electrolyte (KCl) had evident influence on the boundary movement; (ii) the movement length was a function of the running time under the constant acid and base concentrations; and (iii) there was a good linearity between the length and natural logarithmic concentration of HCl under the optimized conditions, and the linearity could be used to detect the concentration of acid. The experiments further manifested that (i) the RSD values of intra-day and inter-day runs were less than 1.59 and 3.76%, respectively, indicating similar precision and stability in capillary electrophoresis or HPLC; (ii) the indicators with different pK(a) values had no obvious effect on EABT, distinguishing strong influence on the judgment of equivalence-point titration in the classic one; and (iii) the constant equivalence-point titration always existed in the EABT, rather than the classic volumetric analysis. Additionally, the EABT could be put to good use for the determination of actual acid concentrations. The experimental results achieved herein showed a new general guidance for the development of classic volumetric analysis and element (e.g. nitrogen) content analysis in protein chemistry. Copyright © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

  8. Regularization of the Boundary-Saddle-Node Bifurcation

    Directory of Open Access Journals (Sweden)

    Xia Liu

    2018-01-01

    Full Text Available In this paper we treat a particular class of planar Filippov systems which consist of two smooth systems that are separated by a discontinuity boundary. In such systems one vector field undergoes a saddle-node bifurcation while the other vector field is transversal to the boundary. The boundary-saddle-node (BSN bifurcation occurs at a critical value when the saddle-node point is located on the discontinuity boundary. We derive a local topological normal form for the BSN bifurcation and study its local dynamics by applying the classical Filippov’s convex method and a novel regularization approach. In fact, by the regularization approach a given Filippov system is approximated by a piecewise-smooth continuous system. Moreover, the regularization process produces a singular perturbation problem where the original discontinuous set becomes a center manifold. Thus, the regularization enables us to make use of the established theories for continuous systems and slow-fast systems to study the local behavior around the BSN bifurcation.

  9. Problem of the Moving Boundary in Continuous Casting Solved by The Analytic-Numerical Method

    Directory of Open Access Journals (Sweden)

    Grzymkowski R.

    2013-03-01

    Full Text Available Mathematical modeling of thermal processes combined with the reversible phase transitions of type: solid phase - liquid phase leads to formulation of the parabolic or elliptic moving boundary problem. Solution of such defined problem requires, most often, to use some sophisticated numerical techniques and far advanced mathematical tools. The paper presents an analytic-numerical method, especially attractive from the engineer’s point of view, applied for finding the approximate solutions of the selected class of problems which can be reduced to the one-phase solidification problem of a plate with the unknown a priori, varying in time boundary of the region in which the solution is sought. Proposed method is based on the known formalism of initial expansion of a sought function, describing the field of temperature, into the power series, some coefficients of which are determined with the aid of boundary conditions, and on the approximation of a function defining the freezing front location with the broken line, parameters of which are determined numerically. The method represents a combination of the analytical and numerical techniques and seems to be an effective and relatively easy in using tool for solving problems of considered kind.

  10. Problem of the Moving Boundary in Continuous Casting Solved by the Analytic-Numerical Method

    Directory of Open Access Journals (Sweden)

    R. Grzymkowski

    2013-01-01

    Full Text Available Mathematical modeling of thermal processes combined with the reversible phase transitions of type: solid phase – liquid phase leads to formulation of the parabolic or elliptic moving boundary problem. Solution of such defined problem requires, most often, to use some sophisticated numerical techniques and far advanced mathematical tools. The paper presents an analytic-numerical method, especially attractive from the engineer’s point of view, applied for finding the approximate solutions of the selected class of problems which can be reduced to the one-phase solidification problem of a plate with the unknown a priori, varying in time boundary of the region in which the solution is sought. Proposed method is based on the known formalism of initial expansion of a sought function, describing the field of temperature, into the power series, some coefficients of which are determined with the aid of boundary conditions, and on the approximation of a function defining the freezing front location with the broken line, parameters of which are determined numerically. The method represents a combination of the analytical and numerical techniques and seems to be an effective and relatively easy in using tool for solving problems of considered kind.

  11. A Matlab-based finite-difference solver for the Poisson problem with mixed Dirichlet-Neumann boundary conditions

    Science.gov (United States)

    Reimer, Ashton S.; Cheviakov, Alexei F.

    2013-03-01

    A Matlab-based finite-difference numerical solver for the Poisson equation for a rectangle and a disk in two dimensions, and a spherical domain in three dimensions, is presented. The solver is optimized for handling an arbitrary combination of Dirichlet and Neumann boundary conditions, and allows for full user control of mesh refinement. The solver routines utilize effective and parallelized sparse vector and matrix operations. Computations exhibit high speeds, numerical stability with respect to mesh size and mesh refinement, and acceptable error values even on desktop computers. Catalogue identifier: AENQ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENQ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License v3.0 No. of lines in distributed program, including test data, etc.: 102793 No. of bytes in distributed program, including test data, etc.: 369378 Distribution format: tar.gz Programming language: Matlab 2010a. Computer: PC, Macintosh. Operating system: Windows, OSX, Linux. RAM: 8 GB (8, 589, 934, 592 bytes) Classification: 4.3. Nature of problem: To solve the Poisson problem in a standard domain with “patchy surface”-type (strongly heterogeneous) Neumann/Dirichlet boundary conditions. Solution method: Finite difference with mesh refinement. Restrictions: Spherical domain in 3D; rectangular domain or a disk in 2D. Unusual features: Choice between mldivide/iterative solver for the solution of large system of linear algebraic equations that arise. Full user control of Neumann/Dirichlet boundary conditions and mesh refinement. Running time: Depending on the number of points taken and the geometry of the domain, the routine may take from less than a second to several hours to execute.

  12. A non-standard optimal control problem arising in an economics application

    Directory of Open Access Journals (Sweden)

    Alan Zinober

    2013-04-01

    Full Text Available A recent optimal control problem in the area of economics has mathematical properties that do not fall into the standard optimal control problem formulation. In our problem the state value at the final time the state, y(T = z, is free and unknown, and additionally the Lagrangian integrand in the functional is a piecewise constant function of the unknown value y(T. This is not a standard optimal control problem and cannot be solved using Pontryagin's Minimum Principle with the standard boundary conditions at the final time. In the standard problem a free final state y(T yields a necessary boundary condition p(T = 0, where p(t is the costate. Because the integrand is a function of y(T, the new necessary condition is that y(T should be equal to a certain integral that is a continuous function of y(T. We introduce a continuous approximation of the piecewise constant integrand function by using a hyperbolic tangent approach and solve an example using a C++ shooting algorithm with Newton iteration for solving the Two Point Boundary Value Problem (TPBVP. The minimising free value y(T is calculated in an outer loop iteration using the Golden Section or Brent algorithm. Comparative nonlinear programming (NP discrete-time results are also presented.

  13. Causal boundary for stably causal space-times

    International Nuclear Information System (INIS)

    Racz, I.

    1987-12-01

    The usual boundary constructions for space-times often yield an unsatisfactory boundary set. This problem is reviewed and a new solution is proposed. An explicit identification rule is given on the set of the ideal points of the space-time. This construction leads to a satisfactory boundary point set structure for stably causal space-times. The topological properties of the resulting causal boundary construction are examined. For the stably causal space-times each causal curve has a unique endpoint on the boundary set according to the extended Alexandrov topology. The extension of the space-time through the boundary is discussed. To describe the singularities the defined boundary sets have to be separated into two disjoint sets. (D.Gy.) 8 refs

  14. Bibliography on moving boundary problems with key word index

    International Nuclear Information System (INIS)

    Wilson, D.G.; Solomon, A.D.; Trent, J.S.

    1979-10-01

    This bibliography concentrates mainly on time-dependent moving-boundary problems of heat and mass transfer. The bibliography is in two parts, a list of the references ordered by last name of the first author and a key word index to the titles. Few references from before 1965 are included

  15. Triple solutions for a Dirichlet boundary value problem involving a perturbed discrete p(k-Laplacian operator

    Directory of Open Access Journals (Sweden)

    Khaleghi Moghadam Mohsen

    2017-08-01

    Full Text Available Triple solutions are obtained for a discrete problem involving a nonlinearly perturbed one-dimensional p(k-Laplacian operator and satisfying Dirichlet boundary conditions. The methods for existence rely on a Ricceri-local minimum theorem for differentiable functionals. Several examples are included to illustrate the main results.

  16. A Probabilistic Approach for Breast Boundary Extraction in Mammograms

    Directory of Open Access Journals (Sweden)

    Hamed Habibi Aghdam

    2013-01-01

    Full Text Available The extraction of the breast boundary is crucial to perform further analysis of mammogram. Methods to extract the breast boundary can be classified into two categories: methods based on image processing techniques and those based on models. The former use image transformation techniques such as thresholding, morphological operations, and region growing. In the second category, the boundary is extracted using more advanced techniques, such as the active contour model. The problem with thresholding methods is that it is a hard to automatically find the optimal threshold value by using histogram information. On the other hand, active contour models require defining a starting point close to the actual boundary to be able to successfully extract the boundary. In this paper, we propose a probabilistic approach to address the aforementioned problems. In our approach we use local binary patterns to describe the texture around each pixel. In addition, the smoothness of the boundary is handled by using a new probability model. Experimental results show that the proposed method reaches 38% and 50% improvement with respect to the results obtained by the active contour model and threshold-based methods respectively, and it increases the stability of the boundary extraction process up to 86%.

  17. Contrasting Boundary Scavenging in two Eastern Boundary Current Regimes

    Science.gov (United States)

    Anderson, R. F.; Fleisher, M. Q.; Pavia, F. J.; Vivancos, S. M.; Lu, Y.; Zhang, P.; Cheng, H.; Edwards, R. L.

    2016-02-01

    We use data from two US GEOTRACES expeditions to compare boundary scavenging intensity in two eastern boundary current systems: the Canary Current off Mauritania and the Humboldt Current off Peru. Boundary scavenging refers to the enhanced removal of trace elements from the ocean by sorption to sinking particles in regions of greater than average particle abundance. Both regimes experience high rates of biological productivity and generation of biogenic particles, with rates of productivity potentially a little greater off Peru, whereas dust fluxes are an order of magnitude greater off NW Africa (see presentation by Vivancos et al., this meeting). Despite greater productivity off Peru, we find greater intensity of scavenging off NW Africa as measured by the residence time of dissolved 230Th integrated from the surface to a depth of 2500 m (10-11 years off NW Africa vs. 15-17 years off Peru). Dissolved 231Pa/230Th ratios off NW Africa (Hayes et al., Deep Sea Res.-II 116 (2015) 29-41) are nearly twice the values observed off Peru. We attribute this difference to the well-known tendency for lithogenic phases (dust) to strongly fractionate in favor of Th uptake during scavenging and removal, leaving the dissolved phase enriched in Pa. This behavior needs to be considered when interpreting sedimentary 231Pa/230Th ratios as a paleo proxy.

  18. Bibliography on moving boundary problems with key word index

    Energy Technology Data Exchange (ETDEWEB)

    Wilson, D.G.; Solomon, A.D.; Trent, J.S.

    1979-10-01

    This bibliography concentrates mainly on time-dependent moving-boundary problems of heat and mass transfer. The bibliography is in two parts, a list of the references ordered by last name of the first author and a key word index to the titles. Few references from before 1965 are included. (RWR)

  19. Existence and Nonexistence of Positive Solutions for Coupled Riemann-Liouville Fractional Boundary Value Problems

    Directory of Open Access Journals (Sweden)

    Johnny Henderson

    2016-01-01

    Full Text Available We investigate the existence and nonexistence of positive solutions for a system of nonlinear Riemann-Liouville fractional differential equations with two parameters, subject to coupled integral boundary conditions.

  20. Appling a Novel Cost Function to Hopfield Neural Network for Defects Boundaries Detection of Wood Image

    Directory of Open Access Journals (Sweden)

    Qi Dawei

    2010-01-01

    Full Text Available A modified Hopfield neural network with a novel cost function was presented for detecting wood defects boundary in the image. Different from traditional methods, the boundary detection problem in this paper was formulated as an optimization process that sought the boundary points to minimize a cost function. An initial boundary was estimated by Canny algorithm first. The pixel gray value was described as a neuron state of Hopfield neural network. The state updated till the cost function touches the minimum value. The designed cost function ensured that few neurons were activated except the neurons corresponding to actual boundary points and ensured that the activated neurons are positioned in the points which had greatest change in gray value. The tools of Matlab were used to implement the experiment. The results show that the noises of the image are effectively removed, and our method obtains more noiseless and vivid boundary than those of the traditional methods.

  1. Lubricated immersed boundary method in two dimensions

    Science.gov (United States)

    Fai, Thomas G.; Rycroft, Chris H.

    2018-03-01

    Many biological examples of fluid-structure interaction, including the transit of red blood cells through the narrow slits in the spleen and the intracellular trafficking of vesicles into dendritic spines, involve the near-contact of elastic structures separated by thin layers of fluid. Motivated by such problems, we introduce an immersed boundary method that uses elements of lubrication theory to resolve thin fluid layers between immersed boundaries. We demonstrate 2nd-order accurate convergence for simple two-dimensional flows with known exact solutions to showcase the increased accuracy of this method compared to the standard immersed boundary method. Motivated by the phenomenon of wall-induced migration, we apply the lubricated immersed boundary method to simulate an elastic vesicle near a wall in shear flow. We also simulate the dynamics of a vesicle traveling through a narrow channel and observe the ability of the lubricated method to capture the vesicle motion on relatively coarse fluid grids.

  2. Method of interior boundaries in a mixed problem of acoustic scattering

    Directory of Open Access Journals (Sweden)

    P. A. Krutitskii

    1999-01-01

    Full Text Available The mixed problem for the Helmholtz equation in the exterior of several bodies (obstacles is studied in 2 and 3 dimensions. The Dirichlet boundary condition is given on some obstacles and the impedance boundary condition is specified on the rest. The problem is investigated by a special modification of the boundary integral equation method. This modification can be called ‘Method of interior boundaries’, because additional boundaries are introduced inside scattering bodies, where impedance boundary condition is given. The solution of the problem is obtained in the form of potentials on the whole boundary. The density in the potentials satisfies the uniquely solvable Fredholm equation of the second kind and can be computed by standard codes. In fact our method holds for any positive wave numbers. The Neumann, Dirichlet, impedance problems and mixed Dirichlet–Neumann problem are particular cases of our problem.

  3. The complex variable boundary element method: Applications in determining approximative boundaries

    Science.gov (United States)

    Hromadka, T.V.

    1984-01-01

    The complex variable boundary element method (CVBEM) is used to determine approximation functions for boundary value problems of the Laplace equation such as occurs in potential theory. By determining an approximative boundary upon which the CVBEM approximator matches the desired constant (level curves) boundary conditions, the CVBEM is found to provide the exact solution throughout the interior of the transformed problem domain. Thus, the acceptability of the CVBEM approximation is determined by the closeness-of-fit of the approximative boundary to the study problem boundary. ?? 1984.

  4. Heat transfer in boundary layer stagnation-point flow towards a shrinking sheet with non-uniform heat flux

    International Nuclear Information System (INIS)

    Bhattacharyya Krishnendu

    2013-01-01

    In this paper, the effect of non-uniform heat flux on heat transfer in boundary layer stagnation-point flow over a shrinking sheet is studied. The variable boundary heat fluxes are considered of two types: direct power-law variation with the distance along the sheet and inverse power-law variation with the distance. The governing partial differential equations (PDEs) are transformed into non linear self-similar ordinary differential equations (ODEs) by similarity transformations, and then those are solved using very efficient shooting method. The direct variation and inverse variation of heat flux along the sheet have completely different effects on the temperature distribution. Moreover, the heat transfer characteristics in the presence of non-uniform heat flux for several values of physical parameters are also found to be interesting

  5. Classical solutions for discrete potential boundary value problems with generalized Leray-Lions type operator and variable exponent

    Directory of Open Access Journals (Sweden)

    Bila Adolphe Kyelem

    2017-04-01

    Full Text Available In this article, we prove the existence of solutions for some discrete nonlinear difference equations subjected to a potential boundary type condition. We use a variational technique that relies on Szulkin's critical point theory, which ensures the existence of solutions by ground state and mountain pass methods.

  6. On Nonlinear Inverse Problems of Heat Transfer with Radiation Boundary Conditions: Application to Dehydration of Gypsum Plasterboards Exposed to Fire

    OpenAIRE

    Belmiloudi, A.; Mahé, F.

    2014-01-01

    International audience; The paper investigates boundary optimal controls and parameter estimates to the well-posedness nonlinear model of dehydration of thermic problems. We summarize the general formulations for the boundary control for initial-boundary value problem for nonlinear partial differential equations modeling the heat transfer and derive necessary optimality conditions, including the adjoint equation, for the optimal set of parameters minimizing objective functions J. Numerical si...

  7. A boundary value approach for solving three-dimensional elliptic and hyperbolic partial differential equations.

    Science.gov (United States)

    Biala, T A; Jator, S N

    2015-01-01

    In this article, the boundary value method is applied to solve three dimensional elliptic and hyperbolic partial differential equations. The partial derivatives with respect to two of the spatial variables (y, z) are discretized using finite difference approximations to obtain a large system of ordinary differential equations (ODEs) in the third spatial variable (x). Using interpolation and collocation techniques, a continuous scheme is developed and used to obtain discrete methods which are applied via the Block unification approach to obtain approximations to the resulting large system of ODEs. Several test problems are investigated to elucidate the solution process.

  8. Integral Boundary Value Problems for Fractional Impulsive Integro Differential Equations in Banach Spaces

    Directory of Open Access Journals (Sweden)

    A. Anguraj

    2014-02-01

    Full Text Available We study in this paper,the existence of solutions for fractional integro differential equations with impulsive and integral conditions by using fixed point method. We establish the Sufficient conditions and unique solution for given problem. An Example is also explained to the main results.

  9. Solution of moving boundary problems with implicit boundary condition

    International Nuclear Information System (INIS)

    Moyano, E.A.

    1990-01-01

    An algorithm that solves numerically a model for studying one dimensional moving boundary problems, with implicit boundary condition, is described. Landau's transformation is used, in order to work with a fixed number of nodes at each instant. Then, it is necessary to deal with a parabolic partial differential equation, whose diffusive and convective terms have variable coefficients. The partial differential equation is implicitly discretized, using Laasonen's scheme, always stable, instead of employing Crank-Nicholson sheme, as it has been done by Ferris and Hill. Fixed time and space steps (Δt, Δξ) are used, and the iteration is made with variable positions of the interface, i.e. varying δs until a boundary condition is satisfied. The model has the same features of the oxygen diffusion in absorbing tissue. It would be capable of estimating time variant radiation treatments of cancerous tumors. (Author) [es

  10. Lectures on nonlinear evolution equations initial value problems

    CERN Document Server

    Racke, Reinhard

    2015-01-01

    This book mainly serves as an elementary, self-contained introduction to several important aspects of the theory of global solutions to initial value problems for nonlinear evolution equations. The book employs the classical method of continuation of local solutions with the help of a priori estimates obtained for small data. The existence and uniqueness of small, smooth solutions that are defined for all values of the time parameter are investigated. Moreover, the asymptotic behavior of the solutions is described as time tends to infinity. The methods for nonlinear wave equations are discussed in detail. Other examples include the equations of elasticity, heat equations, the equations of thermoelasticity, Schrödinger equations, Klein-Gordon equations, Maxwell equations and plate equations. To emphasize the importance of studying the conditions under which small data problems offer global solutions, some blow-up results are briefly described. Moreover, the prospects for corresponding initial-boundary value p...

  11. Two transparent boundary conditions for the electromagnetic scattering from two-dimensional overfilled cavities

    Science.gov (United States)

    Du, Kui

    2011-07-01

    We consider electromagnetic scattering from two-dimensional (2D) overfilled cavities embedded in an infinite ground plane. The unbounded computational domain is truncated to a bounded one by using a transparent boundary condition (TBC) proposed on a semi-ellipse. For overfilled rectangular cavities with homogeneous media, another TBC is introduced on the cavity apertures, which produces a smaller computational domain. The existence and uniqueness of the solutions of the variational formulations for the transverse magnetic and transverse electric polarizations are established. In the exterior domain, the 2D scattering problem is solved in the elliptic coordinate system using the Mathieu functions. In the interior domain, the problem is solved by a finite element method. Numerical experiments show the efficiency and accuracy of the new boundary conditions.

  12. Boundary value problemfor multidimensional fractional advection-dispersion equation

    Directory of Open Access Journals (Sweden)

    Khasambiev Mokhammad Vakhaevich

    2015-05-01

    Full Text Available In recent time there is a very great interest in the study of differential equations of fractional order, in which the unknown function is under the symbol of fractional derivative. It is due to the development of the theory of fractional integro-differential theory and application of it in different fields.The fractional integrals and derivatives of fractional integro-differential equations are widely used in modern investigations of theoretical physics, mechanics, and applied mathematics. The fractional calculus is a very powerful tool for describing physical systems, which have a memory and are non-local. Many processes in complex systems have nonlocality and long-time memory. Fractional integral operators and fractional differential operators allow describing some of these properties. The use of the fractional calculus will be helpful for obtaining the dynamical models, in which integro-differential operators describe power long-time memory by time and coordinates, and three-dimensional nonlocality for complex medium and processes.Differential equations of fractional order appear when we use fractal conception in physics of the condensed medium. The transfer, described by the operator with fractional derivatives at a long distance from the sources, leads to other behavior of relatively small concentrations as compared with classic diffusion. This fact redefines the existing ideas about safety, based on the ideas on exponential velocity of damping. Fractional calculus in the fractal theory and the systems with memory have the same importance as the classic analysis in mechanics of continuous medium.In recent years, the application of fractional derivatives for describing and studying the physical processes of stochastic transfer is very popular too. Many problems of filtration of liquids in fractal (high porous medium lead to the need to study boundary value problems for partial differential equations in fractional order.In this paper the

  13. The boundary conditions for point transformed electromagnetic invisibility cloaks

    International Nuclear Information System (INIS)

    Weder, Ricardo

    2008-01-01

    In this paper we study point transformed electromagnetic invisibility cloaks in transformation media that are obtained by transformation from general anisotropic media. We assume that there are several point transformed electromagnetic cloaks located in different points in space. Our results apply in particular to the first-order invisibility cloaks introduced by Pendry et al and to the high-order invisibility cloaks introduced by Hendi et al and by Cai et al. We identify the appropriate cloaking boundary conditions that the solutions of Maxwell equations have to satisfy at the outside, ∂K + , and at the inside, ∂K - , of the boundary of the cloaked object K in the case where the permittivity and the permeability are bounded below and above in K. Namely, that the tangential components of the electric and the magnetic fields have to vanish at ∂K + -which is always true-and that the normal components of the curl of the electric and the magnetic fields have to vanish at ∂K - . These results are proven requiring that energy be conserved. In the case of one spherical cloak with a spherically stratified K and a radial current at ∂K we verify by an explicit calculation that our cloaking boundary conditions are satisfied and that cloaking of active devices holds, even if the current is at the boundary of the cloaked object. As we prove our results for media that are obtained by transformation from general anisotropic media, our results apply to the cloaking of objects with passive and active devices contained in general anisotropic media, in particular to objects with passive and active devices contained inside general crystals. Our results suggest a method to enhance cloaking in the approximate transformation media that are used in practice. Namely, to coat the boundary of the cloaked object (the inner boundary of the cloak) with a material that imposes the boundary conditions above. As these boundary conditions have to be satisfied for exact transformation

  14. Functional geometric method for solving free boundary problems for harmonic functions

    Energy Technology Data Exchange (ETDEWEB)

    Demidov, Aleksander S [M. V. Lomonosov Moscow State University, Moscow (Russian Federation)

    2010-01-01

    A survey is given of results and approaches for a broad spectrum of free boundary problems for harmonic functions of two variables. The main results are obtained by the functional geometric method. The core of these methods is an interrelated analysis of the functional and geometric characteristics of the problems under consideration and of the corresponding non-linear Riemann-Hilbert problems. An extensive list of open questions is presented. Bibliography: 124 titles.

  15. Boundary value problems for multi-term fractional differential equations

    Science.gov (United States)

    Daftardar-Gejji, Varsha; Bhalekar, Sachin

    2008-09-01

    Multi-term fractional diffusion-wave equation along with the homogeneous/non-homogeneous boundary conditions has been solved using the method of separation of variables. It is observed that, unlike in the one term case, solution of multi-term fractional diffusion-wave equation is not necessarily non-negative, and hence does not represent anomalous diffusion of any kind.

  16. A Value Chain Analysis of ghost nets in the Arafura Sea: identifying trans-boundary stakeholders, intervention points and livelihood trade-offs.

    Science.gov (United States)

    Butler, J R A; Gunn, R; Berry, H L; Wagey, G A; Hardesty, B D; Wilcox, C

    2013-07-15

    Lost or discarded fishing nets are a significant component of marine debris which has trans-boundary impacts in large marine ecosystems. Such 'ghost nets' cause the by-catch of marine fauna and require retrieval from coastlines where they wash up. Identifying the causes of discarded nets and feasible intervention points requires analysis of a complex value chain and the stakeholders within it, yet no studies have attempted this. In this paper we combine Value Chain Analysis, commonly applied to understand value-adding for a commodity, with elements of Life Cycle Assessment and social network analysis to examine the drivers, stakeholders, economic, environmental and social costs and benefits in the life of a trawl net. We use the Arafura Sea as a case study, which is shared by Indonesia, Papua New Guinea and Australia, and is the focus of a Trans-boundary Diagnostic Assessment (TDA) within the Arafura-Timor Seas Ecosystem Action program (ATSEA). We follow a trawl net through four sub-systems: manufacture of webbing in South Korea, fishing and loss by an Indonesian vessel, retrieval as ghost net on the northern Australian coastline by Indigenous rangers, and disposal or re-cycling as 'GhostNet Art' by Indigenous artists. Primary stakeholders along the value chain incur economic and social benefits, and economic and environmental costs. There is an anomaly in the chain between Indonesian fishermen and Indigenous rangers, artists and communities due to the lack of market linkages between these primary stakeholders. The first 'nexus of influence' where reductions in net losses and environmental costs can be achieved is through interactions between GhostNets Australia, the World Wide Fund for Nature and the Australian Government, which can influence Indonesian fishery management institutions and fishing crews. The second nexus is via the international art market which by publicising GhostNet Art can raise awareness amongst fish consumers about the impacts of ghost nets

  17. Wake structures of two side by side spheres in a tripped boundary layer flow

    Directory of Open Access Journals (Sweden)

    Canli Eyüb

    2014-03-01

    Full Text Available Two independent spheres were placed in a side by side arrangement and flow structure in the wake region of the spheres was investigated with a Particle Image Velocimetry (PIV system when the spheres were in a boundary layer over a flat plate as a special case. Reynolds number was 5000 based on the sphere diameter which was 42.5 mm. Boundary layer was tripped 8mm away from the leading edge of the flat plate with a 5 mm trip wire. The thickness of the hydrodynamically developed boundary layer was determined as 63mm which was larger than the sphere diameter of D=42.5mm. Wake region of the spheres was examined from point of flow physics for the different sphere locations in the ranges of 0≤G/D ≤1.5 and 0≤S/D ≤1.5 where G and S were the distance between the spheres and the distance between the bottom point of the spheres and the flat plate surface, respectively. Depending on the different sphere locations, instantaneous and time averaged vorticity data, scalar values of time-averaged velocity components and their root mean square (rms values and time averaged vorticity data are presented in the study for the evaluation of wake region of the spheres. It is demonstrated that the gap between the two spheres and the interaction between the gap and the boundary layer greatly affects flow pattern, especially when spheres are located near to the flat plate surface, i.e. S/D=0.1 for 0≤G/D ≤1.5. Different distances between the spheres resulted in various flow patterns as the spheres were approached to the flat plate. The distance S/D=0.1 for all gap values has the strongest effect on the wake structures. Beyond G/D=1.0, the sphere wakes tend to be similar to single sphere case. The instantaneous vorticity fields of the side by side arrangements comprised wavy structures in higher level comparing to an individual sphere case. The gap flow intensifies the occurrence of small scale eddies in the wake region. The submersion rate of the spheres

  18. Vector-valued measure and the necessary conditions for the optimal control problems of linear systems

    International Nuclear Information System (INIS)

    Xunjing, L.

    1981-12-01

    The vector-valued measure defined by the well-posed linear boundary value problems is discussed. The maximum principle of the optimal control problem with non-convex constraint is proved by using the vector-valued measure. Especially, the necessary conditions of the optimal control of elliptic systems is derived without the convexity of the control domain and the cost function. (author)

  19. Integro-differential equations of fractional order with nonlocal fractional boundary conditions associated with financial asset model

    Directory of Open Access Journals (Sweden)

    Bashir Ahmad

    2013-02-01

    Full Text Available In this article, we discuss the existence of solutions for a boundary-value problem of integro-differential equations of fractional order with nonlocal fractional boundary conditions by means of some standard tools of fixed point theory. Our problem describes a more general form of fractional stochastic dynamic model for financial asset. An illustrative example is also presented.

  20. Boundary value problems and Fourier expansions

    CERN Document Server

    MacCluer, Charles R

    2004-01-01

    Based on modern Sobolev methods, this text for advanced undergraduates and graduate students is highly physical in its orientation. It integrates numerical methods and symbolic manipulation into an elegant viewpoint that is consonant with implementation by digital computer. The first five sections form an informal introduction that develops students' physical and mathematical intuition. The following section introduces Hilbert space in its natural environment, and the next six sections pose and solve the standard problems. The final seven sections feature concise introductions to selected topi

  1. The SMM Model as a Boundary Value Problem Using the Discrete Diffusion Equation

    Science.gov (United States)

    Campbell, Joel

    2007-01-01

    A generalized single step stepwise mutation model (SMM) is developed that takes into account an arbitrary initial state to a certain partial difference equation. This is solved in both the approximate continuum limit and the more exact discrete form. A time evolution model is developed for Y DNA or mtDNA that takes into account the reflective boundary modeling minimum microsatellite length and the original difference equation. A comparison is made between the more widely known continuum Gaussian model and a discrete model, which is based on modified Bessel functions of the first kind. A correction is made to the SMM model for the probability that two individuals are related that takes into account a reflecting boundary modeling minimum microsatellite length. This method is generalized to take into account the general n-step model and exact solutions are found. A new model is proposed for the step distribution.

  2. Image mosaicking based on feature points using color-invariant values

    Science.gov (United States)

    Lee, Dong-Chang; Kwon, Oh-Seol; Ko, Kyung-Woo; Lee, Ho-Young; Ha, Yeong-Ho

    2008-02-01

    In the field of computer vision, image mosaicking is achieved using image features, such as textures, colors, and shapes between corresponding images, or local descriptors representing neighborhoods of feature points extracted from corresponding images. However, image mosaicking based on feature points has attracted more recent attention due to the simplicity of the geometric transformation, regardless of distortion and differences in intensity generated by camera motion in consecutive images. Yet, since most feature-point matching algorithms extract feature points using gray values, identifying corresponding points becomes difficult in the case of changing illumination and images with a similar intensity. Accordingly, to solve these problems, this paper proposes a method of image mosaicking based on feature points using color information of images. Essentially, the digital values acquired from a real digital color camera are converted to values of a virtual camera with distinct narrow bands. Values based on the surface reflectance and invariant to the chromaticity of various illuminations are then derived from the virtual camera values and defined as color-invariant values invariant to changing illuminations. The validity of these color-invariant values is verified in a test using a Macbeth Color-Checker under simulated illuminations. The test also compares the proposed method using the color-invariant values with the conventional SIFT algorithm. The accuracy of the matching between the feature points extracted using the proposed method is increased, while image mosaicking using color information is also achieved.

  3. Mathematical and numerical study of nonlinear boundary problems related to plasma physics

    International Nuclear Information System (INIS)

    Sermange, M.

    1982-06-01

    After the study of some equations based on the Hodgkin-Huxley model, the work presented here is concerned with nonlinear boundary problems in MHD. They are gathered in two subjects: equilibrium equations and stability equations. The axisymmetric MHD equilibrium equations with free boundary have been studied by different authors, particularly the existence, regularity, unicity and non-unicity. Here, bifurcation, convergence of calculation methods existence of solutions in a discontinuous frame are studied. MHD stability can be determined by the principle of Bernstein et al; the mathematical work concerned here bears on the equivalence, in the case of two-dimensional or axisymmetric stability, between this model and a scalar eigenvalue problem which is introduced. At last, modules for computing MHD equilibrium for the simulation of plasma confinement in a tokamak are described [fr

  4. A Novel Approach to Calculation of Reproducing Kernel on Infinite Interval and Applications to Boundary Value Problems

    Directory of Open Access Journals (Sweden)

    Jing Niu

    2013-01-01

    reproducing kernel on infinite interval is obtained concisely in polynomial form for the first time. Furthermore, as a particular effective application of this method, we give an explicit representation formula for calculation of reproducing kernel in reproducing kernel space with boundary value conditions.

  5. Nonlinear $q$-fractional differential equations with nonlocal and sub-strip type boundary conditions

    Directory of Open Access Journals (Sweden)

    Bashir Ahmad

    2014-06-01

    Full Text Available This paper is concerned with new boundary value problems of nonlinear $q$-fractional differential equations with nonlocal and sub-strip type boundary conditions. Our results are new in the present setting and rely on the contraction mapping principle and a fixed point theorem due to O'Regan. Some illustrative examples are also presented.

  6. Antireflective Boundary Conditions for Deblurring Problems

    Directory of Open Access Journals (Sweden)

    Marco Donatelli

    2010-01-01

    Full Text Available This survey paper deals with the use of antireflective boundary conditions for deblurring problems where the issues that we consider are the precision of the reconstruction when the noise is not present, the linear algebra related to these boundary conditions, the iterative and noniterative regularization solvers when the noise is considered, both from the viewpoint of the computational cost and from the viewpoint of the quality of the reconstruction. In the latter case, we consider a reblurring approach that replaces the transposition operation with correlation. For many of the considered items, the anti-reflective algebra coming from the given boundary conditions is the optimal choice. Numerical experiments corroborating the previous statement and a conclusion section end the paper.

  7. Three Boundary Conditions for Computing the Fixed-Point Property in Binary Mixture Data.

    Directory of Open Access Journals (Sweden)

    Leendert van Maanen

    Full Text Available The notion of "mixtures" has become pervasive in behavioral and cognitive sciences, due to the success of dual-process theories of cognition. However, providing support for such dual-process theories is not trivial, as it crucially requires properties in the data that are specific to mixture of cognitive processes. In theory, one such property could be the fixed-point property of binary mixture data, applied-for instance- to response times. In that case, the fixed-point property entails that response time distributions obtained in an experiment in which the mixture proportion is manipulated would have a common density point. In the current article, we discuss the application of the fixed-point property and identify three boundary conditions under which the fixed-point property will not be interpretable. In Boundary condition 1, a finding in support of the fixed-point will be mute because of a lack of difference between conditions. Boundary condition 2 refers to the case in which the extreme conditions are so different that a mixture may display bimodality. In this case, a mixture hypothesis is clearly supported, yet the fixed-point may not be found. In Boundary condition 3 the fixed-point may also not be present, yet a mixture might still exist but is occluded due to additional changes in behavior. Finding the fixed-property provides strong support for a dual-process account, yet the boundary conditions that we identify should be considered before making inferences about underlying psychological processes.

  8. Second-order wave diffraction by a circular cylinder using scaled boundary finite element method

    International Nuclear Information System (INIS)

    Song, H; Tao, L

    2010-01-01

    The scaled boundary finite element method (SBFEM) has achieved remarkable success in structural mechanics and fluid mechanics, combing the advantage of both FEM and BEM. Most of the previous works focus on linear problems, in which superposition principle is applicable. However, many physical problems in the real world are nonlinear and are described by nonlinear equations, challenging the application of the existing SBFEM model. A popular idea to solve a nonlinear problem is decomposing the nonlinear equation to a number of linear equations, and then solves them individually. In this paper, second-order wave diffraction by a circular cylinder is solved by SBFEM. By splitting the forcing term into two parts, the physical problem is described as two second-order boundary-value problems with different asymptotic behaviour at infinity. Expressing the velocity potentials as a series of depth-eigenfunctions, both of the 3D boundary-value problems are decomposed to a number of 2D boundary-value sub-problems, which are solved semi-analytically by SBFEM. Only the cylinder boundary is discretised with 1D curved finite-elements on the circumference of the cylinder, while the radial differential equation is solved completely analytically. The method can be extended to solve more complex wave-structure interaction problems resulting in direct engineering applications.

  9. Standard deviation of vertical two-point longitudinal velocity differences in the atmospheric boundary layer.

    Science.gov (United States)

    Fichtl, G. H.

    1971-01-01

    Statistical estimates of wind shear in the planetary boundary layer are important in the design of V/STOL aircraft, and for the design of the Space Shuttle. The data analyzed in this study consist of eleven sets of longitudinal turbulent velocity fluctuation time histories digitized at 0.2 sec intervals with approximately 18,000 data points per time history. The longitudinal velocity fluctuations were calculated with horizontal wind and direction data collected at the 18-, 30-, 60-, 90-, 120-, and 150-m levels. The data obtained confirm the result that Eulerian time spectra transformed to wave-number spectra with Taylor's frozen eddy hypothesis possess inertial-like behavior at wave-numbers well out of the inertial subrange.

  10. Use Residual Correction Method and Monotone Iterative Technique to Calculate the Upper and Lower Approximate Solutions of Singularly Perturbed Non-linear Boundary Value Problems

    Directory of Open Access Journals (Sweden)

    Chi-Chang Wang

    2013-09-01

    Full Text Available This paper seeks to use the proposed residual correction method in coordination with the monotone iterative technique to obtain upper and lower approximate solutions of singularly perturbed non-linear boundary value problems. First, the monotonicity of a non-linear differential equation is reinforced using the monotone iterative technique, then the cubic-spline method is applied to discretize and convert the differential equation into the mathematical programming problems of an inequation, and finally based on the residual correction concept, complex constraint solution problems are transformed into simpler questions of equational iteration. As verified by the four examples given in this paper, the method proposed hereof can be utilized to fast obtain the upper and lower solutions of questions of this kind, and to easily identify the error range between mean approximate solutions and exact solutions.

  11. Solving eigenvalue problems on curved surfaces using the Closest Point Method

    KAUST Repository

    Macdonald, Colin B.

    2011-06-01

    Eigenvalue problems are fundamental to mathematics and science. We present a simple algorithm for determining eigenvalues and eigenfunctions of the Laplace-Beltrami operator on rather general curved surfaces. Our algorithm, which is based on the Closest Point Method, relies on an embedding of the surface in a higher-dimensional space, where standard Cartesian finite difference and interpolation schemes can be easily applied. We show that there is a one-to-one correspondence between a problem defined in the embedding space and the original surface problem. For open surfaces, we present a simple way to impose Dirichlet and Neumann boundary conditions while maintaining second-order accuracy. Convergence studies and a series of examples demonstrate the effectiveness and generality of our approach. © 2011 Elsevier Inc.

  12. A Boundary Value Problem for Hermitian Monogenic Functions

    Directory of Open Access Journals (Sweden)

    Ricardo Abreu Blaya

    2008-02-01

    Full Text Available We study the problem of finding a Hermitian monogenic function with a given jump on a given hypersurface in ℝm, m=2n. Necessary and sufficient conditions for the solvability of this problem are obtained.

  13. Second order finite-difference ghost-point multigrid methods for elliptic problems with discontinuous coefficients on an arbitrary interface

    Science.gov (United States)

    Coco, Armando; Russo, Giovanni

    2018-05-01

    In this paper we propose a second-order accurate numerical method to solve elliptic problems with discontinuous coefficients (with general non-homogeneous jumps in the solution and its gradient) in 2D and 3D. The method consists of a finite-difference method on a Cartesian grid in which complex geometries (boundaries and interfaces) are embedded, and is second order accurate in the solution and the gradient itself. In order to avoid the drop in accuracy caused by the discontinuity of the coefficients across the interface, two numerical values are assigned on grid points that are close to the interface: a real value, that represents the numerical solution on that grid point, and a ghost value, that represents the numerical solution extrapolated from the other side of the interface, obtained by enforcing the assigned non-homogeneous jump conditions on the solution and its flux. The method is also extended to the case of matrix coefficient. The linear system arising from the discretization is solved by an efficient multigrid approach. Unlike the 1D case, grid points are not necessarily aligned with the normal derivative and therefore suitable stencils must be chosen to discretize interface conditions in order to achieve second order accuracy in the solution and its gradient. A proper treatment of the interface conditions will allow the multigrid to attain the optimal convergence factor, comparable with the one obtained by Local Fourier Analysis for rectangular domains. The method is robust enough to handle large jump in the coefficients: order of accuracy, monotonicity of the errors and good convergence factor are maintained by the scheme.

  14. Iterative method for solving a problem with mixed boundary conditions for biharmonic equation arising in fracture mechanics

    Directory of Open Access Journals (Sweden)

    Dang Quang A

    2013-02-01

    Full Text Available In this paper we consider a mixed boundary value problem for biharmonic equation of the Airy stress function which models a crack problem of a solid elastic plate. An iterative method for reducing the problem to a sequence of mixed problems for Poisson equations is proposed and investigated. The convergence of the method is established theoretically and illustrated on many numerical experiments.

  15. Free boundary problems in PDEs and particle systems

    CERN Document Server

    Carinci, Gioia; Giardinà, Cristian; Presutti, Errico

    2016-01-01

    In this volume a theory for models of transport in the presence of a free boundary is developed. Macroscopic laws of transport are described by PDE's. When the system is open, there are several mechanisms to couple the system with the external forces. Here a class of systems where the interaction with the exterior takes place in correspondence of a free boundary is considered. Both continuous and discrete models sharing the same structure are analysed. In Part I a free boundary problem related to the Stefan Problem is worked out in all details. For this model a new notion of relaxed solution is proposed for which global existence and uniqueness is proven. It is also shown that this is the hydrodynamic limit of the empirical mass density of the associated particle system. In Part II several other models are discussed. The expectation is that the results proved for the basic model extend to these other cases. All the models discussed in this volume have an interest in problems arising in several research fields...

  16. Robust Wavelet Estimation to Eliminate Simultaneously the Effects of Boundary Problems, Outliers, and Correlated Noise

    Directory of Open Access Journals (Sweden)

    Alsaidi M. Altaher

    2012-01-01

    Full Text Available Classical wavelet thresholding methods suffer from boundary problems caused by the application of the wavelet transformations to a finite signal. As a result, large bias at the edges and artificial wiggles occur when the classical boundary assumptions are not satisfied. Although polynomial wavelet regression and local polynomial wavelet regression effectively reduce the risk of this problem, the estimates from these two methods can be easily affected by the presence of correlated noise and outliers, giving inaccurate estimates. This paper introduces two robust methods in which the effects of boundary problems, outliers, and correlated noise are simultaneously taken into account. The proposed methods combine thresholding estimator with either a local polynomial model or a polynomial model using the generalized least squares method instead of the ordinary one. A primary step that involves removing the outlying observations through a statistical function is considered as well. The practical performance of the proposed methods has been evaluated through simulation experiments and real data examples. The results are strong evidence that the proposed method is extremely effective in terms of correcting the boundary bias and eliminating the effects of outliers and correlated noise.

  17. Boundary-value problems with integral conditions for a system of Lame equations in the space of almost periodic functions

    Directory of Open Access Journals (Sweden)

    Volodymyr S. Il'kiv

    2016-11-01

    Full Text Available We study a problem with integral boundary conditions in the time coordinate for a system of Lame equations of dynamic elasticity theory of an arbitrary dimension. We find necessary and sufficient conditions for the existence and uniqueness of solution in the class of almost periodic functions in the spatial variables. To solve the problem of small denominators arising while constructing solutions, we use the metric approach.

  18. Material equations for rock salt under mechanical and thermal load including treatment of boundary value problems by the finite element method

    International Nuclear Information System (INIS)

    Olschewski, J.; Stein, E.; Wagner, W.; Wetjen, D.

    1981-01-01

    This paper is a first step in the development of thermodynamically consistent material equations for inelastic materials, such as polycrystalline rock salt. In this context it is of particular importance to reduce the number and the structure of the internal variables, in order to allow for a fit with available experimental data. As an example this is demonstrated in detail in the case of the so-called dislocation model. As physical non-linearities and in addition also geometrical non-linearities lead to an inhomogeneous deformation - and stress state even in the case of simple samples, boundary value problems have to be studied, in order to test the material equations. For this purpose the finite element method has been used. (orig./HP) [de

  19. Effect of Rotation for Two-Temperature Generalized Thermoelasticity of Two-Dimensional under Thermal Shock Problem

    Directory of Open Access Journals (Sweden)

    Kh. Lotfy

    2013-01-01

    Full Text Available The theory of two-temperature generalized thermoelasticity based on the theory of Youssef is used to solve boundary value problems of two-dimensional half-space. The governing equations are solved using normal mode method under the purview of the Lord-Şhulman (LS and the classical dynamical coupled theory (CD. The general solution obtained is applied to a specific problem of a half-space subjected to one type of heating, the thermal shock type. We study the influence of rotation on the total deformation of thermoelastic half-space and the interaction with each other under the influence of two temperature theory. The material is homogeneous isotropic elastic half-space. The methodology applied here is use of the normal mode analysis techniques that are used to solve the resulting nondimensional coupled field equations for the two theories. Numerical results for the displacement components, force stresses, and temperature distribution are presented graphically and discussed. The conductive temperature, the dynamical temperature, the stress, and the strain distributions are shown graphically with some comparisons.

  20. Best Proximity Point Results in Complex Valued Metric Spaces

    Directory of Open Access Journals (Sweden)

    Binayak S. Choudhury

    2014-01-01

    complex valued metric spaces. We treat the problem as that of finding the global optimal solution of a fixed point equation although the exact solution does not in general exist. We also define and use the concept of P-property in such spaces. Our results are illustrated with examples.

  1. Modification of the Riemann problem and the application for the boundary conditions in computational fluid dynamics

    Directory of Open Access Journals (Sweden)

    Kyncl Martin

    2017-01-01

    Full Text Available We work with the system of partial differential equations describing the non-stationary compressible turbulent fluid flow. It is a characteristic feature of the hyperbolic equations, that there is a possible raise of discontinuities in solutions, even in the case when the initial conditions are smooth. The fundamental problem in this area is the solution of the so-called Riemann problem for the split Euler equations. It is the elementary problem of the one-dimensional conservation laws with the given initial conditions (LIC - left-hand side, and RIC - right-hand side. The solution of this problem is required in many numerical methods dealing with the 2D/3D fluid flow. The exact (entropy weak solution of this hyperbolical problem cannot be expressed in a closed form, and has to be computed by an iterative process (to given accuracy, therefore various approximations of this solution are being used. The complicated Riemann problem has to be further modified at the close vicinity of boundary, where the LIC is given, while the RIC is not known. Usually, this boundary problem is being linearized, or roughly approximated. The inaccuracies implied by these simplifications may be small, but these have a huge impact on the solution in the whole studied area, especially for the non-stationary flow. Using the thorough analysis of the Riemann problem we show, that the RIC for the local problem can be partially replaced by the suitable complementary conditions. We suggest such complementary conditions accordingly to the desired preference. This way it is possible to construct the boundary conditions by the preference of total values, by preference of pressure, velocity, mass flow, temperature. Further, using the suitable complementary conditions, it is possible to simulate the flow in the vicinity of the diffusible barrier. On the contrary to the initial-value Riemann problem, the solution of such modified problems can be written in the closed form for some

  2. Heading off boundary problems: clinical supervision as risk management.

    Science.gov (United States)

    Walker, R; Clark, J J

    1999-11-01

    The effective management of risk in clinical practice includes steps to limit harm to clients resulting from ethical violations or professional misconduct. Boundary problems constitute some of the most damaging ethical violations. The authors propose an active use of clinical supervision to anticipate and head off possible ethical violations by intervening when signs of boundary problems appear. The authors encourage a facilitative, Socratic method, rather than directive approaches, to help supervisees maximize their learning about ethical complexities. Building on the idea of a slippery slope, in which seemingly insignificant acts can lead to unethical patterns of behavior, the authors discuss ten cues to potential boundary problems, including strong feelings about a client; extended sessions with clients; gift giving between clinician and client; loans, barter, and sale of goods; clinician self-disclosures; and touching and sex. The authors outline supervisory interventions to be made when the cues are detected.

  3. The massless two-loop two-point function

    International Nuclear Information System (INIS)

    Bierenbaum, I.; Weinzierl, S.

    2003-01-01

    We consider the massless two-loop two-point function with arbitrary powers of the propagators and derive a representation from which we can obtain the Laurent expansion to any desired order in the dimensional regularization parameter ε. As a side product, we show that in the Laurent expansion of the two-loop integral only rational numbers and multiple zeta values occur. Our method of calculation obtains the two-loop integral as a convolution product of two primitive one-loop integrals. We comment on the generalization of this product structure to higher loop integrals. (orig.)

  4. Coupled diffusion of two species in a slab with an eroding boundary

    International Nuclear Information System (INIS)

    Leite, S.B.; Ozisik, M.N.; Verghese, K.

    1981-01-01

    The diffusion of two interchangeable species in a medium with an eroding boundary is analyzed by modeling the problem as the solution of two diffusion equations coupled at the source term for a slab with a moving boundary. Formal solutions are developed for the concentration of the two species as a function of time and position in the slab for arbitrary initial distributions of the diffusing species, arbitrary sources within the medium and boundary conditions of the third kind at the bounding surfaces. It is shown with an illustrative example, that the resulting coupled integral equations for the species can be solved very efficiently by an approach employing both a lower- and upper-bound starting function for the concentrations. (author)

  5. A New Iterative Method for Equilibrium Problems and Fixed Point Problems

    Directory of Open Access Journals (Sweden)

    Abdul Latif

    2013-01-01

    Full Text Available Introducing a new iterative method, we study the existence of a common element of the set of solutions of equilibrium problems for a family of monotone, Lipschitz-type continuous mappings and the sets of fixed points of two nonexpansive semigroups in a real Hilbert space. We establish strong convergence theorems of the new iterative method for the solution of the variational inequality problem which is the optimality condition for the minimization problem. Our results improve and generalize the corresponding recent results of Anh (2012, Cianciaruso et al. (2010, and many others.

  6. Boundary Shape Control of the Navier-Stokes Equations and Applications

    Institute of Scientific and Technical Information of China (English)

    Kaitai LI; Jian SU; Aixiang HUANG

    2010-01-01

    In this paper,the geometrical design for the blade's surface(s)in an impeller or for the profile of an aircraft,is modeled from the mathematical point of view by a boundary shape control problem for the Navier-Stokes equations.The objective function is the sum of a global dissipative function and the power of the fluid.The control variables are the geometry of the boundary and the state equations are the Navier-Stokes equations.The Euler-Lagrange equations of the optimal control problem are derived,which are an elliptic boundary value system of fourth order,coupled with the Navier-Stokes equations.The authors also prove the existence of the solution of the optimal control problem,the existence of the solution of the Navier-Stokes equations with mixed boundary conditions,the weak continuity of the solution of the Navier-Stokes equations with respect to the geometry shape of the blade's surface and the existence of solutions of the equations for the G(a)teaux derivative of the solution of the Navier-Stokes equations with respect to the geometry of the boundary.

  7. Well-posedness of nonlocal parabolic differential problems with dependent operators.

    Science.gov (United States)

    Ashyralyev, Allaberen; Hanalyev, Asker

    2014-01-01

    The nonlocal boundary value problem for the parabolic differential equation v'(t) + A(t)v(t) = f(t) (0 ≤ t ≤ T), v(0) = v(λ) + φ, 0 exact estimates in Hölder norms for the solution of two nonlocal boundary value problems for parabolic equations with dependent coefficients are established.

  8. Provisional-Ideal-Point-Based Multi-objective Optimization Method for Drone Delivery Problem

    Science.gov (United States)

    Omagari, Hiroki; Higashino, Shin-Ichiro

    2018-04-01

    In this paper, we proposed a new evolutionary multi-objective optimization method for solving drone delivery problems (DDP). It can be formulated as a constrained multi-objective optimization problem. In our previous research, we proposed the "aspiration-point-based method" to solve multi-objective optimization problems. However, this method needs to calculate the optimal values of each objective function value in advance. Moreover, it does not consider the constraint conditions except for the objective functions. Therefore, it cannot apply to DDP which has many constraint conditions. To solve these issues, we proposed "provisional-ideal-point-based method." The proposed method defines a "penalty value" to search for feasible solutions. It also defines a new reference solution named "provisional-ideal point" to search for the preferred solution for a decision maker. In this way, we can eliminate the preliminary calculations and its limited application scope. The results of the benchmark test problems show that the proposed method can generate the preferred solution efficiently. The usefulness of the proposed method is also demonstrated by applying it to DDP. As a result, the delivery path when combining one drone and one truck drastically reduces the traveling distance and the delivery time compared with the case of using only one truck.

  9. Analytical study of the non orthogonal stagnation point flow of a micro polar fluid

    Directory of Open Access Journals (Sweden)

    M. Ali. Abbas

    2017-01-01

    Full Text Available In this paper we consider the steady two dimensional flow of micro polar fluids on a flat plate. The flow under discussion is the modified Hiemenz flow for a micro polar fluid which occurs in the hjkns + skms boundary layer near an orthogonal stagnation point. The full governing equation reduced to a modified Hiemenz flow. The solution to the boundary value problem is governed by two non dimensional parameters, the material parameter K and the ratio of the micro rotation to skin friction parameter n. The obtained nonlinear coupled ordinary differential equations are solved by using the Homotopy perturbation method. Comparison between numerical and analytical solutions of the problem is shown in tables form for different values of the governing parameters K and n. Effects of the material parameter K on the velocity profile and microrotation profiles for different cases of n are discussed graphically as well as numerically. Velocity profile decreases as the material parameter K increases and the microrotation profile increases as the material parameter K increases for different cases of n.

  10. Analysis of stagnation point flow of an upper-convected Maxwell fluid

    Directory of Open Access Journals (Sweden)

    Joseph E. Paullet

    2017-12-01

    Full Text Available Several recent papers have investigated the two-dimensional stagnation point flow of an upper-convected Maxwell fluid by employing a similarity change of variable to reduce the governing PDEs to a nonlinear third order ODE boundary value problem (BVP. In these previous works, the BVP was studied numerically and several conjectures regarding the existence and behavior of the solutions were made. The purpose of this article is to mathematically verify these conjectures. We prove the existence of a solution to the BVP for all relevant values of the elasticity parameter. We also prove that this solution has monotonically increasing first derivative, thus verifying the conjecture that no ``overshoot'' of the boundary condition occurs. Uniqueness results are presented for a large range of parameter space and bounds on the skin friction coefficient are calculated.

  11. Algorithms for solving common fixed point problems

    CERN Document Server

    Zaslavski, Alexander J

    2018-01-01

    This book details approximate solutions to common fixed point problems and convex feasibility problems in the presence of perturbations. Convex feasibility problems search for a common point of a finite collection of subsets in a Hilbert space; common fixed point problems pursue a common fixed point of a finite collection of self-mappings in a Hilbert space. A variety of algorithms are considered in this book for solving both types of problems, the study of which has fueled a rapidly growing area of research. This monograph is timely and highlights the numerous applications to engineering, computed tomography, and radiation therapy planning. Totaling eight chapters, this book begins with an introduction to foundational material and moves on to examine iterative methods in metric spaces. The dynamic string-averaging methods for common fixed point problems in normed space are analyzed in Chapter 3. Dynamic string methods, for common fixed point problems in a metric space are introduced and discussed in Chapter ...

  12. Using reciprocity in Boundary Element Calculations

    DEFF Research Database (Denmark)

    Juhl, Peter Møller; Cutanda Henriquez, Vicente

    2010-01-01

    The concept of reciprocity is widely used in both theoretical and experimental work. In Boundary Element calculations reciprocity is sometimes employed in the solution of computationally expensive scattering problems, which sometimes can be more efficiently dealt with when formulated...... as the reciprocal radiation problem. The present paper concerns the situation of having a point source (which is reciprocal to a point receiver) at or near a discretized boundary element surface. The accuracy of the original and the reciprocal problem is compared in a test case for which an analytical solution...

  13. Fictitious domain methods for elliptic problems with general boundary conditions with an application to the numerical simulation of two phase flows; Methodes de domaine fictif pour des problemes elliptiques avec conditions aux limites generales en vue de la simulation numerique d'ecoulements diphasiques

    Energy Technology Data Exchange (ETDEWEB)

    Ramiere, I

    2006-09-15

    This work is dedicated to the introduction of two original fictitious domain methods for the resolution of elliptic problems (mainly convection-diffusion problems) with general and eventually mixed boundary conditions: Dirichlet, Robin or Neumann. The originality lies in the approximation of the immersed boundary by an approximate interface derived from the fictitious domain Cartesian mesh, which is generally not boundary-fitted to the physical domain. The same generic numerical scheme is used to impose the embedded boundary conditions. Hence, these methods require neither a surface mesh of the immersed boundary nor the local modification of the numerical scheme. We study two modelling of the immersed boundary. In the first one, called spread interface, the approximate immersed boundary is the union of the cells crossed by the physical immersed boundary. In the second one, called thin interface, the approximate immersed boundary lies on sides of mesh cells. Additional algebraic transmission conditions linking both flux and solution jumps through the thin approximate interface are introduced. The fictitious problem to solve as well as the treatment of the embedded boundary conditions are detailed for the two methods. A Q1 finite element scheme is implemented for the numerical validation of the spread interface approach while a new cell-centered finite volume scheme is derived for the thin interface approach with immersed jumps. Each method is then combined to multilevel local mesh refinement algorithms (with solution or flux residual) to increase the precision of the solution in the vicinity of the immersed interface. A convergence analysis of a Q1 finite element method with non-boundary fitted meshes is also presented. This study proves the convergence rates of the present methods. Among the various industrial applications, the simulation on a model of heat exchanger in french nuclear power plants enables us to appreciate the performances of the fictitious domain

  14. High angle grain boundaries as sources or sinks for point defects

    Energy Technology Data Exchange (ETDEWEB)

    Balluffi, R.W.

    1979-09-01

    A secondary grain boundary dislocation climb model for high angle grain boundaries as sources/sinks for point defects is described in the light of recent advances in our knowledge of grain boundary structure. Experimental results are reviewed and are then compared with the expected behavior of the proposed model. Reasonably good consistency is found at the level of our present understanding of the subject. However, several gaps in our present knowledge still exist, and these are identified and discussed briefly.

  15. Two-Dimensional Steady-State Boundary Shape Inversion of CGM-SPSO Algorithm on Temperature Information

    Directory of Open Access Journals (Sweden)

    Shoubin Wang

    2017-01-01

    Full Text Available Addressing the problem of two-dimensional steady-state thermal boundary recognition, a hybrid algorithm of conjugate gradient method and social particle swarm optimization (CGM-SPSO algorithm is proposed. The global search ability of particle swarm optimization algorithm and local search ability of gradient algorithm are effectively combined, which overcomes the shortcoming that the conjugate gradient method tends to converge to the local solution and relies heavily on the initial approximation of the iterative process. The hybrid algorithm also avoids the problem that the particle swarm optimization algorithm requires a large number of iterative steps and a lot of time. The experimental results show that the proposed algorithm is feasible and effective in solving the problem of two-dimensional steady-state thermal boundary shape.

  16. Adaptive algorithm for solution of early exercise boundary problem of American put option implemented in Mathematica

    Directory of Open Access Journals (Sweden)

    Lukáš Ladislav

    2017-01-01

    Full Text Available The paper is focused on American option pricing problem. Assuming non-dividend paying American put option leads to two disjunctive regions, a continuation one and a stopping one, which are separated by an early exercise boundary. We present variational formulation of American option problem with special attention to early exercise action effect. Next, we discuss financially motivated additive decomposition of American option price into a European option price and another part due to the extra premium required by early exercising the option contract. As the optimal exercise boundary is a free boundary, its determination is coupled with the determination of the option price. Therefore, a closed-form expression of the free boundary is not attainable in general. We discuss in detail a derivation of an asymptotic expression of the early exercise boundary. Finally, we present some numerical results of determination of free boundary based upon this approach. All computations are performed by sw Mathematica, and suitable numerical procedure is discussed in detail, as well.

  17. Singular integral equations boundary problems of function theory and their application to mathematical physics

    CERN Document Server

    Muskhelishvili, N I

    2011-01-01

    Singular integral equations play important roles in physics and theoretical mechanics, particularly in the areas of elasticity, aerodynamics, and unsteady aerofoil theory. They are highly effective in solving boundary problems occurring in the theory of functions of a complex variable, potential theory, the theory of elasticity, and the theory of fluid mechanics.This high-level treatment by a noted mathematician considers one-dimensional singular integral equations involving Cauchy principal values. Its coverage includes such topics as the Hölder condition, Hilbert and Riemann-Hilbert problem

  18. Numerical solution of pipe flow problems for generalized Newtonian fluids

    International Nuclear Information System (INIS)

    Samuelsson, K.

    1993-01-01

    In this work we study the stationary laminar flow of incompressible generalized Newtonian fluids in a pipe with constant arbitrary cross-section. The resulting nonlinear boundary value problems can be written in a variational formulation and solved using finite elements and the augmented Lagrangian method. The solution of the boundary value problem is obtained by finding a saddle point of the augmented Lagrangian. In the algorithm the nonlinear part of the equations is treated locally and the solution is obtained by iteration between this nonlinear problem and a global linear problem. For the solution of the linear problem we use the SSOR preconditioned conjugate gradient method. The approximating problem is solved on a sequence of adaptively refined grids. A scheme for adjusting the value of the crucial penalization parameter of the augmented Lagrangian is proposed. Applications to pipe flow and a problem from the theory of capacities are given. (author) (34 refs.)

  19. A finite-volume method for convection problems with embedded moving boundaries

    NARCIS (Netherlands)

    Y.J. Hassen (Yunus); B. Koren (Barry)

    2009-01-01

    htmlabstractAn accurate method, using a novel immersed-boundary approach, is presented for numerically solving linear, scalar convection problems. Moving interior boundary conditions are embedded in the fixed-grid fluxes in the direct neighborhood of the moving boundaries. Tailor-made limiters are

  20. Electrostatic point charge fitting as an inverse problem: Revealing the underlying ill-conditioning

    International Nuclear Information System (INIS)

    Ivanov, Maxim V.; Talipov, Marat R.; Timerghazin, Qadir K.

    2015-01-01

    Atom-centered point charge (PC) model of the molecular electrostatics—a major workhorse of the atomistic biomolecular simulations—is usually parameterized by least-squares (LS) fitting of the point charge values to a reference electrostatic potential, a procedure that suffers from numerical instabilities due to the ill-conditioned nature of the LS problem. To reveal the origins of this ill-conditioning, we start with a general treatment of the point charge fitting problem as an inverse problem and construct an analytical model with the point charges spherically arranged according to Lebedev quadrature which is naturally suited for the inverse electrostatic problem. This analytical model is contrasted to the atom-centered point-charge model that can be viewed as an irregular quadrature poorly suited for the problem. This analysis shows that the numerical problems of the point charge fitting are due to the decay of the curvatures corresponding to the eigenvectors of LS sum Hessian matrix. In part, this ill-conditioning is intrinsic to the problem and is related to decreasing electrostatic contribution of the higher multipole moments, that are, in the case of Lebedev grid model, directly associated with the Hessian eigenvectors. For the atom-centered model, this association breaks down beyond the first few eigenvectors related to the high-curvature monopole and dipole terms; this leads to even wider spread-out of the Hessian curvature values. Using these insights, it is possible to alleviate the ill-conditioning of the LS point-charge fitting without introducing external restraints and/or constraints. Also, as the analytical Lebedev grid PC model proposed here can reproduce multipole moments up to a given rank, it may provide a promising alternative to including explicit multipole terms in a force field

  1. A boundary-Fitted Coordinate Code for General Two-Dimensional Regions with Obstacles and Boundary Intrusions.

    Science.gov (United States)

    1983-03-01

    values of these functions on the two sides of the slits. The acceleration parameters for the iteration at each point are in the field array WACC (I,J...code will calculate a locally optimum value at each point in the field, these values being placed in the field array WACC . This calculation is...changes in x and y, are calculated by calling subroutine ERROR.) The acceleration parameter is placed in the field 65 array WACC . The addition to the

  2. Solving free-plasma-boundary problems with the SIESTA MHD code

    Science.gov (United States)

    Sanchez, R.; Peraza-Rodriguez, H.; Reynolds-Barredo, J. M.; Tribaldos, V.; Geiger, J.; Hirshman, S. P.; Cianciosa, M.

    2017-10-01

    SIESTA is a recently developed MHD equilibrium code designed to perform fast and accurate calculations of ideal MHD equilibria for 3D magnetic configurations. It is an iterative code that uses the solution obtained by the VMEC code to provide a background coordinate system and an initial guess of the solution. The final solution that SIESTA finds can exhibit magnetic islands and stochastic regions. In its original implementation, SIESTA addressed only fixed-boundary problems. This fixed boundary condition somewhat restricts its possible applications. In this contribution we describe a recent extension of SIESTA that enables it to address free-plasma-boundary situations, opening up the possibility of investigating problems with SIESTA in which the plasma boundary is perturbed either externally or internally. As an illustration, the extended version of SIESTA is applied to a configuration of the W7-X stellarator.

  3. Mesoscopic current transport in two-dimensional materials with grain boundaries: Four-point probe resistance and Hall effect

    DEFF Research Database (Denmark)

    Lotz, Mikkel Rønne; Boll, Mads; Østerberg, Frederik Westergaard

    2016-01-01

    -configurations depends on the dimensionality of the current transport (i.e., one- or two-dimensional). At low grain density or low grain boundary resistivity, two-dimensional transport is observed. In contrast, at moderate grain density and high grain resistivity, one-dimensional transport is seen. Ultimately...

  4. Hierarchical random additive process and logarithmic scaling of generalized high order, two-point correlations in turbulent boundary layer flow

    Science.gov (United States)

    Yang, X. I. A.; Marusic, I.; Meneveau, C.

    2016-06-01

    Townsend [Townsend, The Structure of Turbulent Shear Flow (Cambridge University Press, Cambridge, UK, 1976)] hypothesized that the logarithmic region in high-Reynolds-number wall-bounded flows consists of space-filling, self-similar attached eddies. Invoking this hypothesis, we express streamwise velocity fluctuations in the inertial layer in high-Reynolds-number wall-bounded flows as a hierarchical random additive process (HRAP): uz+=∑i=1Nzai . Here u is the streamwise velocity fluctuation, + indicates normalization in wall units, z is the wall normal distance, and ai's are independently, identically distributed random additives, each of which is associated with an attached eddy in the wall-attached hierarchy. The number of random additives is Nz˜ln(δ /z ) where δ is the boundary layer thickness and ln is natural log. Due to its simplified structure, such a process leads to predictions of the scaling behaviors for various turbulence statistics in the logarithmic layer. Besides reproducing known logarithmic scaling of moments, structure functions, and correlation function [" close="]3/2 uz(x ) uz(x +r ) >, new logarithmic laws in two-point statistics such as uz4(x ) > 1 /2, 1/3, etc. can be derived using the HRAP formalism. Supporting empirical evidence for the logarithmic scaling in such statistics is found from the Melbourne High Reynolds Number Boundary Layer Wind Tunnel measurements. We also show that, at high Reynolds numbers, the above mentioned new logarithmic laws can be derived by assuming the arrival of an attached eddy at a generic point in the flow field to be a Poisson process [Woodcock and Marusic, Phys. Fluids 27, 015104 (2015), 10.1063/1.4905301]. Taken together, the results provide new evidence supporting the essential ingredients of the attached eddy hypothesis to describe streamwise velocity fluctuations of large, momentum transporting eddies in wall-bounded turbulence, while observed deviations suggest the need for further extensions of the

  5. The effect of guide-field and boundary conditions on collisionless magnetic reconnection in a stressed X-point collapse

    Energy Technology Data Exchange (ETDEWEB)

    Graf von der Pahlen, J.; Tsiklauri, D. [School of Physics and Astronomy, Queen Mary University of London, London E1 4NS (United Kingdom)

    2014-01-15

    Works of Tsiklauri and Haruki [Phys. Plasmas 15, 102902 (2008); 14, 112905 (2007)] are extended by inclusion of the out-of-plane magnetic (guide) field. In particular, magnetic reconnection during collisionless, stressed X-point collapse for varying out-of-plane guide-fields is studied using a kinetic, 2.5D, fully electromagnetic, relativistic particle-in-cell numerical code. For zero guide-field, cases for both open and closed boundary conditions are investigated, where magnetic flux and particles are lost and conserved, respectively. It is found that reconnection rates, out-of-plane currents and density in the X-point increase more rapidly and peak sooner in the closed boundary case, but higher values are reached in the open boundary case. The normalized reconnection rate is fast: 0.10-0.25. In the open boundary case it is shown that an increase of guide-field yields later onsets in the reconnection peak rates, while in the closed boundary case initial peak rates occur sooner but are suppressed. The reconnection current changes similarly with increasing guide-field; however for low guide-fields the reconnection current increases, giving an optimal value for the guide-field between 0.1 and 0.2 times the in-plane field in both cases. Also, in the open boundary case, it is found that for guide-fields of the order of the in-plane magnetic field, the generation of electron vortices occurs. Possible causes of the vortex generation, based on the flow of decoupled particles in the diffusion region and localized plasma heating, are discussed. Before peak reconnection onset, oscillations in the out-of-plane electric field at the X-point are found, ranging in frequency from approximately 1 to 2 ω{sub pe} and coinciding with oscillatory reconnection. These oscillations are found to be part of a larger wave pattern in the simulation domain. Mapping the out-of-plane electric field along the central lines of the domain over time and applying a 2D Fourier transform reveal that

  6. Computation of Charged-Particle Transfer Maps for General Fields and Geometries Using Electromagnetic Boundary-Value Data

    OpenAIRE

    Dragt, A. J.; Roberts, P.; Stasevich, T. J.; Dragt, A. Bodoh-Creed A. J.; Roberts, P.; Stasevich, T. J.; Bodoh-Creed, A.; Walstrom, P. L.

    2010-01-01

    Three-dimensional field distributions from realistic beamline elements can be obtained only by measurement or by numerical solution of a boundary-value problem. In numerical charged-particle map generation, fields along a reference trajectory are differentiated multiple times. Any attempt to differentiate directly such field data multiple times is soon dominated by "noise" due to finite meshing and/or measurement errors. This problem can be overcome by the use of field data on a surface outsi...

  7. Numerical Treatment of Degenerate Diffusion Equations via Feller's Boundary Classification, and Applications

    Science.gov (United States)

    Cacio, Emanuela; Cohn, Stephen E.; Spigler, Renato

    2011-01-01

    A numerical method is devised to solve a class of linear boundary-value problems for one-dimensional parabolic equations degenerate at the boundaries. Feller theory, which classifies the nature of the boundary points, is used to decide whether boundary conditions are needed to ensure uniqueness, and, if so, which ones they are. The algorithm is based on a suitable preconditioned implicit finite-difference scheme, grid, and treatment of the boundary data. Second-order accuracy, unconditional stability, and unconditional convergence of solutions of the finite-difference scheme to a constant as the time-step index tends to infinity are further properties of the method. Several examples, pertaining to financial mathematics, physics, and genetics, are presented for the purpose of illustration.

  8. Assessment of Two Analytical Methods in Solving the Linear and Nonlinear Elastic Beam Deformation Problems

    DEFF Research Database (Denmark)

    Barari, Amin; Ganjavi, B.; Jeloudar, M. Ghanbari

    2010-01-01

    and fluid mechanics. Design/methodology/approach – Two new but powerful analytical methods, namely, He's VIM and HPM, are introduced to solve some boundary value problems in structural engineering and fluid mechanics. Findings – Analytical solutions often fit under classical perturbation methods. However......, as with other analytical techniques, certain limitations restrict the wide application of perturbation methods, most important of which is the dependence of these methods on the existence of a small parameter in the equation. Disappointingly, the majority of nonlinear problems have no small parameter at all......Purpose – In the last two decades with the rapid development of nonlinear science, there has appeared ever-increasing interest of scientists and engineers in the analytical techniques for nonlinear problems. This paper considers linear and nonlinear systems that are not only regarded as general...

  9. Change Point Estimation in Panel Data without Boundary Issue

    Czech Academy of Sciences Publication Activity Database

    Peštová, Barbora; Pešta, M.

    2017-01-01

    Roč. 5, č. 1 (2017), č. článku 7. E-ISSN 2227-9091 Institutional support: RVO:67985807 Keywords : change point * estimation * consistency * panel data * short panels * boundary issue * structural change * bootstrap * non-life insurance * change in claim amounts Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics

  10. A Hierarchical Bayesian Setting for an Inverse Problem in Linear Parabolic PDEs with Noisy Boundary Conditions

    KAUST Repository

    Ruggeri, Fabrizio

    2016-05-12

    In this work we develop a Bayesian setting to infer unknown parameters in initial-boundary value problems related to linear parabolic partial differential equations. We realistically assume that the boundary data are noisy, for a given prescribed initial condition. We show how to derive the joint likelihood function for the forward problem, given some measurements of the solution field subject to Gaussian noise. Given Gaussian priors for the time-dependent Dirichlet boundary values, we analytically marginalize the joint likelihood using the linearity of the equation. Our hierarchical Bayesian approach is fully implemented in an example that involves the heat equation. In this example, the thermal diffusivity is the unknown parameter. We assume that the thermal diffusivity parameter can be modeled a priori through a lognormal random variable or by means of a space-dependent stationary lognormal random field. Synthetic data are used to test the inference. We exploit the behavior of the non-normalized log posterior distribution of the thermal diffusivity. Then, we use the Laplace method to obtain an approximated Gaussian posterior and therefore avoid costly Markov Chain Monte Carlo computations. Expected information gains and predictive posterior densities for observable quantities are numerically estimated using Laplace approximation for different experimental setups.

  11. Streamline topologies near simple degenerate critical points in two-dimensional flow away from boundaries

    DEFF Research Database (Denmark)

    Brøns, Morten; Hartnack, Johan Nicolai

    1998-01-01

    Streamline patterns and their bifurcations in two-dimensional incompressible flow are investigated from a topological point of view. The velocity field is expanded at a point in the fluid, and the expansion coefficients are considered as bifurcation parameters. A series of non-linear coordinate c...

  12. Streamline topologies near simple degenerate critical points in two-dimensional flow away from boundaries

    DEFF Research Database (Denmark)

    Brøns, Morten; Hartnack, Johan Nicolai

    1999-01-01

    Streamline patterns and their bifurcations in two-dimensional incompressible flow are investigated from a topological point of view. The velocity field is expanded at a point in the fluid, and the expansion coefficients are considered as bifurcation parameters. A series of nonlinear coordinate ch...

  13. Two-media boundary layer on a flat plate

    OpenAIRE

    Nikolay Ilyich Klyuev; Asgat Gatyatovich Gimadiev; Yuriy Alekseevich Kryukov

    2014-01-01

    The present paper provides a solution to the problem of a flow over a flat semi-infinite plate set at an angle to the horizon, and having a thin liquid film on its surface by external airflow. The film is formed by extrusion of liquid from the porous wall. The paper proposes a mathematical model of a two-media boundary layer flow. The main characteristics of the flow to a zero and a first approximation are determined. A drop of frictional stress is obtained.

  14. More on boundary holographic Witten diagrams

    Science.gov (United States)

    Sato, Yoshiki

    2018-01-01

    In this paper we discuss geodesic Witten diagrams in general holographic conformal field theories with boundary or defect. In boundary or defect conformal field theory, two-point functions are nontrivial and can be decomposed into conformal blocks in two distinct ways; ambient channel decomposition and boundary channel decomposition. In our previous work [A. Karch and Y. Sato, J. High Energy Phys. 09 (2017) 121., 10.1007/JHEP09(2017)121] we only consider two-point functions of same operators. We generalize our previous work to a situation where operators in two-point functions are different. We obtain two distinct decomposition for two-point functions of different operators.

  15. Propagation of Boundary-Induced Discontinuity in Stationary Radiative Transfer

    Science.gov (United States)

    Kawagoe, Daisuke; Chen, I.-Kun

    2018-01-01

    We consider the boundary value problem of the stationary transport equation in the slab domain of general dimensions. In this paper, we discuss the relation between discontinuity of the incoming boundary data and that of the solution to the stationary transport equation. We introduce two conditions posed on the boundary data so that discontinuity of the boundary data propagates along positive characteristic lines as that of the solution to the stationary transport equation. Our analysis does not depend on the celebrated velocity averaging lemma, which is different from previous works. We also introduce an example in two dimensional case which shows that piecewise continuity of the boundary data is not a sufficient condition for the main result.

  16. On non-linear boundary value problems and parametrisation at multiple nodes

    Czech Academy of Sciences Publication Activity Database

    Rontó, András; Rontó, M.; Varha, J.

    2016-01-01

    Roč. 2016, Č. 80 (2016), s. 1-18 ISSN 1417-3875 Institutional support: RVO:67985840 Keywords : non-local boundary conditions * parametrisation * successive approximations * interval division Subject RIV: BA - General Mathematics Impact factor: 0.926, year: 2016 http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=5302

  17. The unified method: III. Nonlinearizable problems on the interval

    International Nuclear Information System (INIS)

    Lenells, J; Fokas, A S

    2012-01-01

    Boundary value problems for integrable nonlinear evolution PDEs formulated on the finite interval can be analyzed by the unified method introduced by one of the authors and extensively used in the literature. The implementation of this general method to this particular class of problems yields the solution in terms of the unique solution of a matrix Riemann–Hilbert problem formulated in the complex k-plane (the Fourier plane), which has a jump matrix with explicit (x, t)-dependence involving six scalar functions of k, called the spectral functions. Two of these functions depend on the initial data, whereas the other four depend on all boundary values. The most difficult step of the new method is the characterization of the latter four spectral functions in terms of the given initial and boundary data, i.e. the elimination of the unknown boundary values. Here, we present an effective characterization of the spectral functions in terms of the given initial and boundary data. We present two different characterizations of this problem. One is based on the analysis of the so-called global relation, on the analysis of the equations obtained from the global relation via certain transformations leaving the dispersion relation of the associated linearized PDE invariant and on the computation of the large k asymptotics of the eigenfunctions defining the relevant spectral functions. The other is based on the analysis of the global relation and on the introduction of the so-called Gelfand–Levitan–Marchenko representations of the eigenfunctions defining the relevant spectral functions. We also show that these two different characterizations are equivalent and that in the limit when the length of the interval tends to infinity, the relevant formulas reduce to the analogous formulas obtained recently for the case of boundary value problems formulated on the half-line. (paper)

  18. Variable and space steps solution of a two phase moving boundary ...

    African Journals Online (AJOL)

    Equations of a two phase moving boundary problem in cylindrical coordinates are obtained from the formulation of a transient shrinking core model of whole tree combustion in a one dimensional steady state fixed-bed reactor. An hybrid Variable Grid Method is developed to solve the non linear equations and the results are ...

  19. Multiple positive solutions of nonlinear singular m-point boundary value problem for second-order dynamic equations with sign changing coefficients on time scales

    Directory of Open Access Journals (Sweden)

    Fuyi Xu

    2010-04-01

    \\end{array}\\right.$$ where $1\\leq k\\leq s\\leq m-2, a_i, b_i\\in(0,+\\infty$ with $0<\\sum_{i=1}^{k}b_{i}-\\sum_{i=k+1}^{s}b_{i}<1, 0<\\sum_{i=1}^{m-2}a_{i}<1, 0<\\xi_1<\\xi_2<\\cdots<\\xi_{m-2}<\\rho(T$, $f\\in C( [0,+\\infty,[0,+\\infty$, $a(t$ may be singular at $t=0$. We show that there exist two positive solutions by using two different fixed point theorems respectively. As an application, some examples are included to illustrate the main results. In particular, our criteria extend and improve some known results.

  20. Regularity of p(ṡ)-superharmonic functions, the Kellogg property and semiregular boundary points

    Science.gov (United States)

    Adamowicz, Tomasz; Björn, Anders; Björn, Jana

    2014-11-01

    We study various boundary and inner regularity questions for $p(\\cdot)$-(super)harmonic functions in Euclidean domains. In particular, we prove the Kellogg property and introduce a classification of boundary points for $p(\\cdot)$-harmonic functions into three disjoint classes: regular, semiregular and strongly irregular points. Regular and especially semiregular points are characterized in many ways. The discussion is illustrated by examples. Along the way, we present a removability result for bounded $p(\\cdot)$-harmonic functions and give some new characterizations of $W^{1, p(\\cdot)}_0$ spaces. We also show that $p(\\cdot)$-superharmonic functions are lower semicontinuously regularized, and characterize them in terms of lower semicontinuously regularized supersolutions.

  1. High order methods for incompressible fluid flow: Application to moving boundary problems

    Energy Technology Data Exchange (ETDEWEB)

    Bjoentegaard, Tormod

    2008-04-15

    Fluid flows with moving boundaries are encountered in a large number of real life situations, with two such types being fluid-structure interaction and free-surface flows. Fluid-structure phenomena are for instance apparent in many hydrodynamic applications; wave effects on offshore structures, sloshing and fluid induced vibrations, and aeroelasticity; flutter and dynamic response. Free-surface flows can be considered as a special case of a fluid-fluid interaction where one of the fluids are practically inviscid, such as air. This type of flows arise in many disciplines such as marine hydrodynamics, chemical engineering, material processing, and geophysics. The driving forces for free-surface flows may be of large scale such as gravity or inertial forces, or forces due to surface tension which operate on a much smaller scale. Free-surface flows with surface tension as a driving mechanism include the flow of bubbles and droplets, and the evolution of capillary waves. In this work we consider incompressible fluid flow, which are governed by the incompressible Navier-Stokes equations. There are several challenges when simulating moving boundary problems numerically, and these include - Spatial discretization - Temporal discretization - Imposition of boundary conditions - Solution strategy for the linear equations. These are some of the issues which will be addressed in this introduction. We will first formulate the problem in the arbitrary Lagrangian-Eulerian framework, and introduce the weak formulation of the problem. Next, we discuss the spatial and temporal discretization before we move to the imposition of surface tension boundary conditions. In the final section we discuss the solution of the resulting linear system of equations. (Author). refs., figs., tabs

  2. Uniqueness theorems for variational problems by the method of transformation groups

    CERN Document Server

    Reichel, Wolfgang

    2004-01-01

    A classical problem in the calculus of variations is the investigation of critical points of functionals {\\cal L} on normed spaces V. The present work addresses the question: Under what conditions on the functional {\\cal L} and the underlying space V does {\\cal L} have at most one critical point? A sufficient condition for uniqueness is given: the presence of a "variational sub-symmetry", i.e., a one-parameter group G of transformations of V, which strictly reduces the values of {\\cal L}. The "method of transformation groups" is applied to second-order elliptic boundary value problems on Riemannian manifolds. Further applications include problems of geometric analysis and elasticity.

  3. Determination of boundaries between ranges of high and low gradient of beam profile.

    Science.gov (United States)

    Wendykier, Jacek; Bieniasiewicz, Marcin; Grządziel, Aleksandra; Jedynak, Tadeusz; Kośniewski, Wiktor; Reudelsdorf, Marta; Wendykier, Piotr

    2016-01-01

    This work addresses the problem of treatment planning system commissioning by introducing a new method of determination of boundaries between high and low gradient in beam profile. The commissioning of a treatment planning system is a very important task in the radiation therapy. One of the main goals of this task is to compare two field profiles: measured and calculated. Applying points of 80% and 120% of nominal field size can lead to the incorrect determination of boundaries, especially for small field sizes. The method that is based on the beam profile gradient allows for proper assignment of boundaries between high and low gradient regions even for small fields. TRS 430 recommendations for commissioning were used. The described method allows a separation between high and low gradient, because it directly uses the value of the gradient of a profile. For small fields, the boundaries determined by the new method allow a commissioning of a treatment planning system according to the TRS 430, while the point of 80% of nominal field size is already in the high gradient region. The method of determining the boundaries by using the beam profile gradient can be extremely helpful during the commissioning of the treatment planning system for Intensity Modulated Radiation Therapy or for other techniques which require very small field sizes.

  4. Axisymmetric capillary-gravity waves at the interface of two viscous, immiscible fluids - Initial value problem

    Science.gov (United States)

    Farsoiya, Palas Kumar; Dasgupta, Ratul

    2017-11-01

    When the interface between two radially unbounded, viscous fluids lying vertically in a stable configuration (denser fluid below) at rest, is perturbed, radially propagating capillary-gravity waves are formed which damp out with time. We study this process analytically using a recently developed linearised theory. For small amplitude initial perturbations, the analytical solution to the initial value problem, represented as a linear superposition of Bessel modes at time t = 0 , is found to agree very well with results obtained from direct numerical simulations of the Navier-Stokes equations, for a range of initial conditions. Our study extends the earlier work by John W. Miles who studied this initial value problem analytically, taking into account, a single viscous fluid only. Implications of this study for the mechanistic understanding of droplet impact into a deep pool, will be discussed. Some preliminary, qualitative comparison with experiments will also be presented. We thank SERB Dept. Science & Technology, Govt. of India, Grant No. EMR/2016/000830 for financial support.

  5. Spectral collocation for multiparameter eigenvalue problems arising from separable boundary value problems

    Science.gov (United States)

    Plestenjak, Bor; Gheorghiu, Călin I.; Hochstenbach, Michiel E.

    2015-10-01

    In numerous science and engineering applications a partial differential equation has to be solved on some fairly regular domain that allows the use of the method of separation of variables. In several orthogonal coordinate systems separation of variables applied to the Helmholtz, Laplace, or Schrödinger equation leads to a multiparameter eigenvalue problem (MEP); important cases include Mathieu's system, Lamé's system, and a system of spheroidal wave functions. Although multiparameter approaches are exploited occasionally to solve such equations numerically, MEPs remain less well known, and the variety of available numerical methods is not wide. The classical approach of discretizing the equations using standard finite differences leads to algebraic MEPs with large matrices, which are difficult to solve efficiently. The aim of this paper is to change this perspective. We show that by combining spectral collocation methods and new efficient numerical methods for algebraic MEPs it is possible to solve such problems both very efficiently and accurately. We improve on several previous results available in the literature, and also present a MATLAB toolbox for solving a wide range of problems.

  6. Solutions Stability of Initial Boundary Problem, Modeling of Dynamics of Some Discrete Continuum Mechanical System

    Directory of Open Access Journals (Sweden)

    D. A. Eliseev

    2015-01-01

    Full Text Available The solution stability of an initial boundary problem for a linear hybrid system of differential equations, which models the rotation of a rigid body with two elastic rods located in the same plane is studied in the paper. To an axis passing through the mass center of the rigid body perpendicularly to the rods location plane is applied the stabilizing moment proportional to the angle of the system rotation, derivative of the angle, integral of the angle. The external moment provides a feedback. A method of studying the behavior of solutions of the initial boundary problem is proposed. This method allows to exclude from the hybrid system of differential equations partial differential equations, which describe the dynamics of distributed elements of a mechanical system. It allows us to build one equation for an angle of the system rotation. Its characteristic equation defines the stability of solutions of all the system. In the space of feedback-coefficients the areas that provide the asymptotic stability of solutions of the initial boundary problem are built up.

  7. Boundary Element Solution of Geometrical Inverse Heat Conduction Problems for Development of IR CAT Scan

    International Nuclear Information System (INIS)

    Choi, C. Y.; Park, C. T.; Kim, T. H.; Han, K. N.; Choe, S. H.

    1995-01-01

    A geometrical inverse heat conduction problem is solved for the development of Infrared Computerized-Axial-Tomography (IR CAT) Scan by using a boundary element method in conjunction with regularization procedure. In this problem, an overspecified temperature condition by infrared scanning is provided on the surface, and is used together with other conditions to solve the position of an unknown boundary (cavity). An auxiliary problem is introduced in the solution of this problem. By defining a hypothetical inner boundary for the auxiliary problem domain, the cavity is located interior to the domain and its position is determined by solving a potential problem. Boundary element method with regularization procedure is used to solve this problem, and the effects of regularization on the inverse solution method are investigated by means of numerical analysis

  8. Mixed problem with nonlocal boundary conditions for a third-order partial differential equation of mixed type

    OpenAIRE

    Denche, M.; Marhoune, A. L.

    2001-01-01

    We study a mixed problem with integral boundary conditions for a third-order partial differential equation of mixed type. We prove the existence and uniqueness of the solution. The proof is based on two-sided a priori estimates and on the density of the range of the operator generated by the considered problem.

  9. Moving boundary - Oxygen diffusion. Two algorithms using Landau transformation

    International Nuclear Information System (INIS)

    Moyano, E.A.

    1991-01-01

    A description is made of two algorithms which solve a mathematical model destinated for the study of one-dimensional problems with moving boundaries and implicit boundary conditions. The Landau transformation is used in both methods for each temporal level so as to work all through with the same amount of nodes. Thus, it is necessary to deal with a partial differential equation whose diffusive and convective terms are accompanied by variable coefficients. The partial differential equation is made discrete implicitly, using the Laasonen scheme -which is always stable- instead of the Crank-Nicholson scheme, as performed by Ferris and Hill (5), in the fixed time passing method. The second method employs the tridiagonal algorithm. The first algorithm uses fixed time passing and iterates with variable interface positions, that is to say, it varies δs until it satisfies the boundary condition. The mathematical model describes oxygen diffusion in live tissues. Its numerical solution is obtained by finite differences. An important application of this method could be the estimation of the radiation dose in cancerous tumor treatment. (Author) [es

  10. The unified method: I. Nonlinearizable problems on the half-line

    International Nuclear Information System (INIS)

    Fokas, A S; Lenells, J

    2012-01-01

    Boundary value problems for integrable nonlinear evolution PDEs formulated on the half-line can be analyzed by the unified method introduced by one of the authors and used extensively in the literature. The implementation of this general method to this particular class of problems yields the solution in terms of the unique solution of a matrix Riemann–Hilbert problem formulated in the complex k-plane (the Fourier plane), which has a jump matrix with explicit (x, t)-dependence involving four scalar functions of k, called the spectral functions. Two of these functions depend on the initial data, whereas the other two depend on all boundary values. The most difficult step of the new method is the characterization of the latter two spectral functions in terms of the given initial and boundary data, i.e. the elimination of the unknown boundary values. For certain boundary conditions, called linearizable, this can be achieved simply using algebraic manipulations. Here, we present an effective characterization of the spectral functions in terms of the given initial and boundary data for the general case of non-linearizable boundary conditions. This characterization is based on the analysis of the so-called global relation, on the analysis of the equations obtained from the global relation via certain transformations leaving the dispersion relation of the associated linearized PDE invariant and on the computation of the large k asymptotics of the eigenfunctions defining the relevant spectral functions. (paper)

  11. Applying inversion to construct planar, rational spirals that satisfy two-point G(2) Hermite data

    CERN Document Server

    Kurnosenko, A

    2010-01-01

    A method of two-point G(2) Hermite interpolation with spirals is proposed. To construct a sought for curve, the inversion is applied to an arc of some other spiral. To illustrate the method, inversions of parabola are considered in detail. The resulting curve is 4th degree rational. The method allows the matching of a wide range of boundary conditions, including those which require an inflection. Although not all G(2) Hermite data can be matched with a spiral generated from a parabolic arc, introducing one intermediate G(2) data solves the problem. Expanding the method by involving other spirals arcs is also discussed. (C) 2009 Elsevier B.V. All rights reserved.

  12. The environmental zero-point problem in evolutionary reaction norm modeling.

    Science.gov (United States)

    Ergon, Rolf

    2018-04-01

    There is a potential problem in present quantitative genetics evolutionary modeling based on reaction norms. Such models are state-space models, where the multivariate breeder's equation in some form is used as the state equation that propagates the population state forward in time. These models use the implicit assumption of a constant reference environment, in many cases set to zero. This zero-point is often the environment a population is adapted to, that is, where the expected geometric mean fitness is maximized. Such environmental reference values follow from the state of the population system, and they are thus population properties. The environment the population is adapted to, is, in other words, an internal population property, independent of the external environment. It is only when the external environment coincides with the internal reference environment, or vice versa, that the population is adapted to the current environment. This is formally a result of state-space modeling theory, which is an important theoretical basis for evolutionary modeling. The potential zero-point problem is present in all types of reaction norm models, parametrized as well as function-valued, and the problem does not disappear when the reference environment is set to zero. As the environmental reference values are population characteristics, they ought to be modeled as such. Whether such characteristics are evolvable is an open question, but considering the complexity of evolutionary processes, such evolvability cannot be excluded without good arguments. As a straightforward solution, I propose to model the reference values as evolvable mean traits in their own right, in addition to other reaction norm traits. However, solutions based on an evolvable G matrix are also possible.

  13. Magnetostratigraphy of a Marine Triassic-Jurassic Boundary Section, Kennecott Point, Queen Charlotte Islands: Implications for the Temporal Correlation of a 'Big Five' Mass Extinction Event.

    Science.gov (United States)

    Hilburn, I. A.; Kirschvink, J. L.; Ward, P. D.; Haggart, J. W.; Raub, T. D.

    2008-12-01

    Several causes have been proposed for Triassic-Jurassic (T-J) boundary extinctions, including global ocean anoxia/euxinia, an impact event, and/or eruption of the massive Central Atlantic Magmatic Province (CAMP), but poor intercontinental correlation makes testing these difficult. Sections at Kennecott Point, Queen Charlotte Islands, British Columbia span the late Norian through Rhaetian (Triassic) and into the earliest Hettangian (Jurassic) and provide the best integrated magneto- and chemostratigraphic framework for placing necessary temporal constraints upon the T-J mass extinctions. At Kennecott Point, turnover of radiolaria and ammonoids define the T-J boundary marine extinction and are coincident with a 2 ‰ negative excursion in δ13Corg similar in magnitude to that observed at Ferguson Hill (Muller Canyon), Nevada (1, 2). With Conodont Alteration Index values in the 1-2 range, Kennecott Point provides the ideal setting for use of magnetostratigraphy to tie the marine isotope excursion into the chronostratigraphic framework of the Newark, Hartford, and Fundy Basins. In the summer of 2005, we collected a ~1m resolution magnetostratigraphic section from 105 m of deep marine, silt- and sandstone turbidites and interbedded mudstones, spanning the T-J boundary at Kennecott Point. Hybrid progressive demagnetization - including zero-field, low-temperature cycling; low-field AF cleaning; and thermal demagnetization in ~25°C steps to 445°C under flowing N2 gas (3) - first removed a Northerly, steeply inclined component interpreted to be a Tertiary overprint, revealing an underlying dual-polarity component of moderate inclination. Five major polarity zones extend through our section, with several short, one-sample reversals interspersed amongst them. Comparison of this pattern with other T-J boundary sections (4-6) argues for a Northern hemisphere origin of our site, albeit with large vertical-axis rotations. A long normal chron bounds the T-J boundary punctuated

  14. An efficient computer based wavelets approximation method to solve Fuzzy boundary value differential equations

    Science.gov (United States)

    Alam Khan, Najeeb; Razzaq, Oyoon Abdul

    2016-03-01

    In the present work a wavelets approximation method is employed to solve fuzzy boundary value differential equations (FBVDEs). Essentially, a truncated Legendre wavelets series together with the Legendre wavelets operational matrix of derivative are utilized to convert FB- VDE into a simple computational problem by reducing it into a system of fuzzy algebraic linear equations. The capability of scheme is investigated on second order FB- VDE considered under generalized H-differentiability. Solutions are represented graphically showing competency and accuracy of this method.

  15. On solutions of some fractional $m$-point boundary value problems at resonance

    Directory of Open Access Journals (Sweden)

    Zhanbing Bai

    2010-06-01

    is considered, where $1< \\alpha \\leq 2,$ is a real number, $D_{0+}^\\alpha$ and $I_{0+}^{\\alpha}$ are the standard Riemann-Liouville differentiation and integration, and $f:[0,1]\\times R^2 \\to R$ is continuous and $e \\in L^1[0,1]$, and $\\eta_i \\in (0, 1, \\beta_i \\in R, i=1,2, \\cdots, m-2$, are given constants such that $\\sum_{i=1}^{m-2}\\beta_i=1$. By using the coincidence degree theory, some existence results of solutions are established.

  16. Application of the perturbation iteration method to boundary layer type problems.

    Science.gov (United States)

    Pakdemirli, Mehmet

    2016-01-01

    The recently developed perturbation iteration method is applied to boundary layer type singular problems for the first time. As a preliminary work on the topic, the simplest algorithm of PIA(1,1) is employed in the calculations. Linear and nonlinear problems are solved to outline the basic ideas of the new solution technique. The inner and outer solutions are determined with the iteration algorithm and matched to construct a composite expansion valid within all parts of the domain. The solutions are contrasted with the available exact or numerical solutions. It is shown that the perturbation-iteration algorithm can be effectively used for solving boundary layer type problems.

  17. End Effects on the Linear Induction MHD Generator Calculated by Two-Sided Laplace Transform

    Energy Technology Data Exchange (ETDEWEB)

    Engeln, F.; Peschka, W. [Deutsche Versuchsanstalt fuer Luft- und Raumfahrt e.V., Institut fuer Energiewandlung und Elektrische Antriebe, Stuttgart, Federal Republic of Germany (Germany)

    1966-11-15

    In induction MHD systems special problems occur where the flow enters or leaves the magnetic field. These problems are generally described as end effects. Large gradients of the magnetic field are present at the inlet and also at the outlet of an MHD induction engine, these generating electric current systems in the fluid which may spoil the performance characteristics of the generator due to the interaction with the primary field of the engine. The two-dimensional induction MHD generator of finite length, using a polyphase winding system to obtain a travelling magnetic field, is treated as a boundary value problem by two-sided Laplace transform. For simplicity incompressibility is assumed. The two- dimensional boundary value problem of the induction engine is solved for - {infinity} Less-Than-Over-Equal-To x Less-Than-Over-Equal-To {infinity}. x is parallel to the flow direction of the linear MHD generator. In the region 0 Less-Than-Over-Equal-To x Less-Than-Over-Equal-To L the magnetic travelling wave is sinusoidal with a cyclical frequency {omega} and a phase-velocity v{sub s}. At x = 0 the conducting incompressible working fluid enters the field region and leaves it at the point-x = L. Two mathematical methods can be used to solve the boundary value problem, the Fourier transform or the two-sided Laplace transform. The latter offers the advantage of representing a complex analytical function in the image space. Moreover, it is possible to obtain the characteristics of the generator in the image space (e. g. field configuration, power flow function, etc.). That implies a large simplification of mathematical treatment. The solution in the original space then is given by asymptotic expansion of the known image function. (author)

  18. Acoustic boundary element method formulation with treatment of nearly singular integrands by element subdivision

    DEFF Research Database (Denmark)

    Cutanda Henríquez, Vicente; Juhl, Peter Møller

    2008-01-01

    It is well known that the Boundary Element Method (BEM) in its standard version cannot readily handle situations where the calculation point is very close to a surface. These problems are found: i) when two boundary surfaces are very close together, such as in narrow gaps and thin bodies, and ii)...

  19. Data completion problems solved as Nash games

    International Nuclear Information System (INIS)

    Habbal, A; Kallel, M

    2012-01-01

    The Cauchy problem for an elliptic operator is formulated as a two-player Nash game. Player (1) is given the known Dirichlet data, and uses as strategy variable the Neumann condition prescribed over the inaccessible part of the boundary. Player (2) is given the known Neumann data, and plays with the Dirichlet condition prescribed over the inaccessible boundary. The two players solve in parallel the associated Boundary Value Problems. Their respective objectives involve the gap between the non used Neumann/Dirichlet known data and the traces of the BVP's solutions over the accessible boundary, and are coupled through a difference term. We prove the existence of a unique Nash equilibrium, which turns out to be the reconstructed data when the Cauchy problem has a solution. We also prove that the completion algorithm is stable with respect to noise, and present two 3D experiments which illustrate the efficiency and stability of our algorithm.

  20. APPLICATION OF BOUNDARY INTEGRAL EQUATION METHOD FOR THERMOELASTICITY PROBLEMS

    Directory of Open Access Journals (Sweden)

    Vorona Yu.V.

    2015-12-01

    Full Text Available Boundary Integral Equation Method is used for solving analytically the problems of coupled thermoelastic spherical wave propagation. The resulting mathematical expressions coincide with the solutions obtained in a conventional manner.

  1. Parametrices and exact paralinearization of semi-linear boundary problems

    DEFF Research Database (Denmark)

    Johnsen, Jon

    2008-01-01

    The subject is parametrices for semi-linear problems, based on parametrices for linear boundary problems and on non-linearities that decompose into solution-dependent linear operators acting on the solutions. Non-linearities of product type are shown to admit this via exact paralinearization...... of homogeneous distributions, tensor products and halfspace extensions have been revised. Examples include the von Karman equation....

  2. Two-Capacitor Problem: A More Realistic View.

    Science.gov (United States)

    Powell, R. A.

    1979-01-01

    Discusses the two-capacitor problem by considering the self-inductance of the circuit used and by determining how well the usual series RC circuit approximates the two-capacitor problem when realistic values of L, C, and R are chosen. (GA)

  3. Integral Method of Boundary Characteristics: Neumann Condition

    Science.gov (United States)

    Kot, V. A.

    2018-05-01

    A new algorithm, based on systems of identical equalities with integral and differential boundary characteristics, is proposed for solving boundary-value problems on the heat conduction in bodies canonical in shape at a Neumann boundary condition. Results of a numerical analysis of the accuracy of solving heat-conduction problems with variable boundary conditions with the use of this algorithm are presented. The solutions obtained with it can be considered as exact because their errors comprise hundredths and ten-thousandths of a persent for a wide range of change in the parameters of a problem.

  4. Quantum Ising chains with boundary fields

    International Nuclear Information System (INIS)

    Campostrini, Massimo; Vicari, Ettore; Pelissetto, Andrea

    2015-01-01

    We present a detailed study of the finite one-dimensional quantum Ising chain in a transverse field in the presence of boundary magnetic fields coupled with the order-parameter spin operator. We consider two magnetic fields located at the boundaries of the chain that have the same strength and that are aligned in the same or in the opposite direction. We derive analytic expressions for the gap in all phases for large values of the chain length L, as a function of the boundary field strength. We also investigate the behaviour of the chain in the quantum ferromagnetic phase for oppositely aligned fields, focusing on the magnet-to-kink transition that occurs at a finite value of the magnetic field strength. At this transition we compute analytically the finite-size crossover functions for the gap, the magnetisation profile, the two-point correlation function, and the density of fermionic modes. As the magnet-to-kink transition is equivalent to the wetting transition in two-dimensional classical Ising models, our results provide new analytic predictions for the finite-size behaviour of Ising systems in a strip geometry at this transition. (paper)

  5. Inverse eigenvalue problems for Sturm-Liouville equations with spectral parameter linearly contained in one of the boundary conditions

    OpenAIRE

    Guliyev, Namig J.

    2008-01-01

    International audience; Inverse problems of recovering the coefficients of Sturm–Liouville problems with the eigenvalue parameter linearly contained in one of the boundary conditions are studied: 1) from the sequences of eigenvalues and norming constants; 2) from two spectra. Necessary and sufficient conditions for the solvability of these inverse problems are obtained.

  6. A review on application of MHD theory to plasma boundary problems in tokamaks

    International Nuclear Information System (INIS)

    Itoh, Kimitaka.

    1992-08-01

    A survey is made on the problems of the edge plasmas, to which the analyses based on the MHD theory have been successfully applied. Also discussed are the efforts to extend the model equation to more general (and important as well) problems such as H-mode physics. An overview is first made on the advantages of the MHD picture, and the necessary supplementary physics are examined. Next, one- and two-dimensional models of the spatial structure of the edge plasma is discussed. The results on the stationary structure, both analytical and numerical, are reviewed: Typical example as well as the scaling law are shown. The instabilities associated with edge plasma is next reviewed. The surface kink mode, ballooning mode, interchange mode, resistive interchange mode and thermal instability are discussed. Role of the geometry such as the location of the X-point is studied. Influences of the atomic processes, and those of the radial electric field are also discussed. The analysis of the H-mode transition physics is finally discussed. The boundary plasma is a nonlinear media which possesses the possibility for bifurcation in which the radial electric field plays a key role. The model of the ion viscosity is also studied. Transition physics is developed. Analysis on the self-generating oscillation is shown and the relation with ELMs is discussed. After reviewing these problems, several comments are made to what directions the study can be deepened. (author) 53 refs

  7. Localization of Point Sources for Poisson Equation using State Observers

    KAUST Repository

    Majeed, Muhammad Usman

    2016-08-09

    A method based On iterative observer design is presented to solve point source localization problem for Poisson equation with riven boundary data. The procedure involves solution of multiple boundary estimation sub problems using the available Dirichlet and Neumann data from different parts of the boundary. A weighted sum of these solution profiles of sub-problems localizes point sources inside the domain. Method to compute these weights is also provided. Numerical results are presented using finite differences in a rectangular domain. (C) 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

  8. Localization of Point Sources for Poisson Equation using State Observers

    KAUST Repository

    Majeed, Muhammad Usman; Laleg-Kirati, Taous-Meriem

    2016-01-01

    A method based On iterative observer design is presented to solve point source localization problem for Poisson equation with riven boundary data. The procedure involves solution of multiple boundary estimation sub problems using the available Dirichlet and Neumann data from different parts of the boundary. A weighted sum of these solution profiles of sub-problems localizes point sources inside the domain. Method to compute these weights is also provided. Numerical results are presented using finite differences in a rectangular domain. (C) 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

  9. New formulations on the finite element method for boundary value problems with internal/external boundary layers; Novas formulacoes de elementos finitos para problemas de valor de contorno com camadas limite interna/externa

    Energy Technology Data Exchange (ETDEWEB)

    Pereira, Luis Carlos Martins

    1998-06-15

    New Petrov-Galerkin formulations on the finite element methods for convection-diffusion problems with boundary layers are presented. Such formulations are based on a consistent new theory on discontinuous finite element methods. Existence and uniqueness of solutions for these problems in the new finite element spaces are demonstrated. Some numerical experiments shows how the new formulation operate and also their efficacy. (author)

  10. Reconsidering the boundary conditions for a dynamic, transient mode I crack problem

    KAUST Repository

    Leise, Tanya

    2008-11-01

    A careful examination of a dynamic mode I crack problem leads to the conclusion that the commonly used boundary conditions do not always hold in the case of an applied crack face loading, so that a modification is required to satisfy the equations. In particular, a transient compressive stress wave travels along the crack faces, moving outward from the loading region on the crack face. This does not occur in the quasistatic or steady state problems, and is a special feature of the transient dynamic problem that is important during the time interval immediately following the application of crack face loading. We demonstrate why the usual boundary conditions lead to a prediction of crack face interpenetration, and then examine how to modify the boundary condition for a semi-infinite crack with a cohesive zone. Numerical simulations illustrate the resulting approach.

  11. Numerical solution of the state-delayed optimal control problems by a fast and accurate finite difference θ-method

    Science.gov (United States)

    Hajipour, Mojtaba; Jajarmi, Amin

    2018-02-01

    Using the Pontryagin's maximum principle for a time-delayed optimal control problem results in a system of coupled two-point boundary-value problems (BVPs) involving both time-advance and time-delay arguments. The analytical solution of this advance-delay two-point BVP is extremely difficult, if not impossible. This paper provides a discrete general form of the numerical solution for the derived advance-delay system by applying a finite difference θ-method. This method is also implemented for the infinite-time horizon time-delayed optimal control problems by using a piecewise version of the θ-method. A matrix formulation and the error analysis of the suggested technique are provided. The new scheme is accurate, fast and very effective for the optimal control of linear and nonlinear time-delay systems. Various types of finite- and infinite-time horizon problems are included to demonstrate the accuracy, validity and applicability of the new technique.

  12. Accuracy of multi-point boundary crossing time analysis

    Directory of Open Access Journals (Sweden)

    J. Vogt

    2011-12-01

    Full Text Available Recent multi-spacecraft studies of solar wind discontinuity crossings using the timing (boundary plane triangulation method gave boundary parameter estimates that are significantly different from those of the well-established single-spacecraft minimum variance analysis (MVA technique. A large survey of directional discontinuities in Cluster data turned out to be particularly inconsistent in the sense that multi-point timing analyses did not identify any rotational discontinuities (RDs whereas the MVA results of the individual spacecraft suggested that RDs form the majority of events. To make multi-spacecraft studies of discontinuity crossings more conclusive, the present report addresses the accuracy of the timing approach to boundary parameter estimation. Our error analysis is based on the reciprocal vector formalism and takes into account uncertainties both in crossing times and in the spacecraft positions. A rigorous error estimation scheme is presented for the general case of correlated crossing time errors and arbitrary spacecraft configurations. Crossing time error covariances are determined through cross correlation analyses of the residuals. The principal influence of the spacecraft array geometry on the accuracy of the timing method is illustrated using error formulas for the simplified case of mutually uncorrelated and identical errors at different spacecraft. The full error analysis procedure is demonstrated for a solar wind discontinuity as observed by the Cluster FGM instrument.

  13. Numerical simulation of two-dimensional flows over a circular cylinder using the immersed boundary method

    International Nuclear Information System (INIS)

    Lima E Silva, A.L.F.; Silveira-Neto, A.; Damasceno, J.J.R.

    2003-01-01

    In this work, a virtual boundary method is applied to the numerical simulation of a uniform flow over a cylinder. The force source term, added to the two-dimensional Navier-Stokes equations, guarantees the imposition of the no-slip boundary condition over the body-fluid interface. These equations are discretized, using the finite differences method. The immersed boundary is represented with a finite number of Lagrangian points, distributed over the solid-fluid interface. A Cartesian grid is used to solve the fluid flow equations. The key idea is to propose a method to calculate the interfacial force without ad hoc constants that should usually be adjusted for the type of flow and the type of the numerical method, when this kind of model is used. In the present work, this force is calculated using the Navier-Stokes equations applied to the Lagrangian points and then distributed over the Eulerian grid. The main advantage of this approach is that it enables calculation of this force field, even if the interface is moving or deforming. It is unnecessary to locate the Eulerian grid points near this immersed boundary. The lift and drag coefficients and the Strouhal number, calculated for an immersed cylinder, are compared with previous experimental and numerical results, for different Reynolds numbers

  14. Optimal Wentzell Boundary Control of Parabolic Equations

    International Nuclear Information System (INIS)

    Luo, Yousong

    2017-01-01

    This paper deals with a class of optimal control problems governed by an initial-boundary value problem of a parabolic equation. The case of semi-linear boundary control is studied where the control is applied to the system via the Wentzell boundary condition. The differentiability of the state variable with respect to the control is established and hence a necessary condition is derived for the optimal solution in the case of both unconstrained and constrained problems. The condition is also sufficient for the unconstrained convex problems. A second order condition is also derived.

  15. Optimal Wentzell Boundary Control of Parabolic Equations

    Energy Technology Data Exchange (ETDEWEB)

    Luo, Yousong, E-mail: yousong.luo@rmit.edu.au [RMIT University, School of Mathematical and Geospatial Sciences (Australia)

    2017-04-15

    This paper deals with a class of optimal control problems governed by an initial-boundary value problem of a parabolic equation. The case of semi-linear boundary control is studied where the control is applied to the system via the Wentzell boundary condition. The differentiability of the state variable with respect to the control is established and hence a necessary condition is derived for the optimal solution in the case of both unconstrained and constrained problems. The condition is also sufficient for the unconstrained convex problems. A second order condition is also derived.

  16. A trust region interior point algorithm for optimal power flow problems

    Energy Technology Data Exchange (ETDEWEB)

    Wang Min [Hefei University of Technology (China). Dept. of Electrical Engineering and Automation; Liu Shengsong [Jiangsu Electric Power Dispatching and Telecommunication Company (China). Dept. of Automation

    2005-05-01

    This paper presents a new algorithm that uses the trust region interior point method to solve nonlinear optimal power flow (OPF) problems. The OPF problem is solved by a primal/dual interior point method with multiple centrality corrections as a sequence of linearized trust region sub-problems. It is the trust region that controls the linear step size and ensures the validity of the linear model. The convergence of the algorithm is improved through the modification of the trust region sub-problem. Numerical results of standard IEEE systems and two realistic networks ranging in size from 14 to 662 buses are presented. The computational results show that the proposed algorithm is very effective to optimal power flow applications, and favors the successive linear programming (SLP) method. Comparison with the predictor/corrector primal/dual interior point (PCPDIP) method is also made to demonstrate the superiority of the multiple centrality corrections technique. (author)

  17. A similarity hypothesis for the two-point correlation tensor in a temporally evolving plane wake

    Science.gov (United States)

    Ewing, D. W.; George, W. K.; Moser, R. D.; Rogers, M. M.

    1995-01-01

    The analysis demonstrated that the governing equations for the two-point velocity correlation tensor in the temporally evolving wake admit similarity solutions, which include the similarity solutions for the single-point moment as a special case. The resulting equations for the similarity solutions include two constants, beta and Re(sub sigma), that are ratios of three characteristic time scales of processes in the flow: a viscous time scale, a time scale characteristic of the spread rate of the flow, and a characteristic time scale of the mean strain rate. The values of these ratios depend on the initial conditions of the flow and are most likely measures of the coherent structures in the initial conditions. The occurrences of these constants in the governing equations for the similarity solutions indicates that these solutions, in general, will only be the same for two flows if these two constants are equal (and hence the coherent structures in the flows are related). The comparisons between the predictions of the similarity hypothesis and the data presented here and elsewhere indicate that the similarity solutions for the two-point correlation tensors provide a good approximation of the measures of those motions that are not significantly affected by the boundary conditions caused by the finite extent of real flows. Thus, the two-point similarity hypothesis provides a useful tool for both numerical and physical experimentalist that can be used to examine how the finite extent of real flows affect the evolution of the different scales of motion in the flow.

  18. Sample problem calculations related to two-phase flow transients in a PWR relief-piping network

    International Nuclear Information System (INIS)

    Shin, Y.W.; Wiedermann, A.H.

    1981-03-01

    Two sample problems related with the fast transients of water/steam flow in the relief line of a PWR pressurizer were calculated with a network-flow analysis computer code STAC (System Transient-Flow Analysis Code). The sample problems were supplied by EPRI and are designed to test computer codes or computational methods to determine whether they have the basic capability to handle the important flow features present in a typical relief line of a PWR pressurizer. It was found necessary to implement into the STAC code a number of additional boundary conditions in order to calculate the sample problems. This includes the dynamics of the fluid interface that is treated as a moving boundary. This report describes the methodologies adopted for handling the newly implemented boundary conditions and the computational results of the two sample problems. In order to demonstrate the accuracies achieved in the STAC code results, analytical solutions are also obtained and used as a basis for comparison

  19. Local non-similarity method through the Crocco's transformation in boundary layer problem

    International Nuclear Information System (INIS)

    Jardim, R.G.M.

    1981-04-01

    The coordinate transformation developed by L. Crocco to obtain the solution of the compressible fluid flows over isotermal flat plates is originally employed in the present work, with the purpose of adding its inherent advantage to the Non-Similarity Method idealized by E.M. Sparrow, in the solution of the incompressible non-similar boundary layers. The Crocco's transformation is applied to the conservation equation for forced convection, laminar, constant properties and two-dimensional flows over solids. Two non-similar problems arisen from freestream velocity distribution, the cylinder in crossflow and the Howarth's retarded flow, are solved with a view to illustrating the new procedure. In those solutions the effect of frictional heat is also considered. The results of hydrodynamic and thermal problems are compared with available published information and good agreement was observed. (Author) [pt

  20. An Issue of Boundary Value for Velocity and Training Overhead Using Cooperative MIMO Technique in Wireless Sensor Network

    Directory of Open Access Journals (Sweden)

    M. R. Islam

    2011-06-01

    Full Text Available A boundary value of velocity of data gathering node (DGN and a critical value for training overhead beyond which the cooperative communication in wireless sensor network will not be feasible is proposed in this paper. Multiple Input Multiple Outputs (MIMO cooperative communication is taken as an application. The performance in terms of energy efficiency and delay for a combination of two transmitting and two receiving antennas is analyzed. The results show that a set of critical value of velocity and training overhead pair is present for the long haul communication from the sensors to the data gathering node. Later a graphical relation between boundary value of training overhead and velocity is simulated. A mathematical relation between velocity and training overhead is also developed. The effects of several parameters on training overhead and velocity are analyzed.

  1. Material-Point Analysis of Large-Strain Problems

    DEFF Research Database (Denmark)

    Andersen, Søren

    The aim of this thesis is to apply and improve the material-point method for modelling of geotechnical problems. One of the geotechnical phenomena that is a subject of active research is the study of landslides. A large amount of research is focused on determining when slopes become unstable. Hence......, it is possible to predict if a certain slope is stable using commercial finite element or finite difference software such as PLAXIS, ABAQUS or FLAC. However, the dynamics during a landslide are less explored. The material-point method (MPM) is a novel numerical method aimed at analysing problems involving...... materials subjected to large strains in a dynamical time–space domain. This thesis explores the material-point method with the specific aim of improving the performance for geotechnical problems. Large-strain geotechnical problems such as landslides pose a major challenge to model numerically. Employing...

  2. Boundary conditions for free surface inlet and outlet problems

    KAUST Repository

    Taroni, M.; Breward, C. J. W.; Howell, P. D.; Oliver, J. M.

    2012-01-01

    We investigate and compare the boundary conditions that are to be applied to free-surface problems involving inlet and outlets of Newtonian fluid, typically found in coating processes. The flux of fluid is a priori known at an inlet, but unknown

  3. An iterative kernel based method for fourth order nonlinear equation with nonlinear boundary condition

    Science.gov (United States)

    Azarnavid, Babak; Parand, Kourosh; Abbasbandy, Saeid

    2018-06-01

    This article discusses an iterative reproducing kernel method with respect to its effectiveness and capability of solving a fourth-order boundary value problem with nonlinear boundary conditions modeling beams on elastic foundations. Since there is no method of obtaining reproducing kernel which satisfies nonlinear boundary conditions, the standard reproducing kernel methods cannot be used directly to solve boundary value problems with nonlinear boundary conditions as there is no knowledge about the existence and uniqueness of the solution. The aim of this paper is, therefore, to construct an iterative method by the use of a combination of reproducing kernel Hilbert space method and a shooting-like technique to solve the mentioned problems. Error estimation for reproducing kernel Hilbert space methods for nonlinear boundary value problems have yet to be discussed in the literature. In this paper, we present error estimation for the reproducing kernel method to solve nonlinear boundary value problems probably for the first time. Some numerical results are given out to demonstrate the applicability of the method.

  4. Combined conduction and radiation in a two-layer planar medium with flux boundary condition

    International Nuclear Information System (INIS)

    Ho, C.H.; Ozisik, M.N.

    1987-01-01

    The interaction of conduction and radiation is investigated under both transient and steady-state conditions for an absorbing, emitting, and isotropically scattering two-layer slab having opaque coverings at both boundaries. The slab is subjected to an externally applied constant heat flux at one boundary surface and dissipates heat by radiation into external ambients from both boundary surfaces. An analytic approach is applied to solve the radiation part of the problem, and a finite-difference scheme is used to solve the conduction part. The effects of the conduction-to-radiation parameter, the single scattering albedo, the optical thickness, and the surface emissivity on the temperature distribution are examined

  5. The traveling salesman problem with few inner points

    NARCIS (Netherlands)

    Deineko, V.G.; Hoffmann, M.; Okamoto, Y.; Woeginger, G.J.; Chwa, K.Y.; Munro, J.I.

    2004-01-01

    We study the traveling salesman problem (TSP) in the 2-dimensional Euclidean plane. The problem is NP-hard in general, but trivial if the points are in convex position. In this paper, we investigate the influence of the number of inner points (i.e., points in the interior of the convex hull) on the

  6. Classical and nonclassical symmetries analysis for initial value problems

    International Nuclear Information System (INIS)

    Zhang Zhiyong; Chen Yufu

    2010-01-01

    Classical and nonclassical symmetries are considered to reduce evolution equations with initial conditions in two independent variables. First of all, we rearrange the classical infinitesimal operators such that they leave the initial value problems invariant. Secondly, we give a sufficient condition for the nonclassical symmetry reductions of initial value problems. The generalized Kuramoto-Sivashinsky equation with dispersive effects is considered to examine the algorithms.

  7. Two-dimensional convection of an incompressible viscous fluid with the heat exchange on the free border

    Directory of Open Access Journals (Sweden)

    Svetlana S. Vlasova

    2016-09-01

    Full Text Available The exact stationary solution of the boundary-value problem that describes the convective motion of an incompressible viscous fluid in the two-dimensional layer with the square heating of a free surface in Stokes's approach is found. The linearization of the Oberbeck–Boussinesq equations allows one to describe the flow of fluid in extreme points of pressure and temperature. The condition under which the counter-current flows (two counter flows in the fluid can be observed, is introduced. If the stagnant point in the fluid exists, six non-closed whirlwinds can be observed.

  8. Classical solutions of mixed problems for quasilinear first order PFDEs on a cylindrical domain

    Directory of Open Access Journals (Sweden)

    Wojciech Czernous

    2014-01-01

    Full Text Available We abandon the setting of the domain as a Cartesian product of real intervals, customary for first order PFDEs (partial functional differential equations with initial boundary conditions. We give a new set of conditions on the possibly unbounded domain \\(\\Omega\\ with Lipschitz differentiable boundary. Well-posedness is then reliant on a variant of the normal vector condition. There is a neighbourhood of \\(\\partial\\Omega\\ with the property that if a characteristic trajectory has a point therein, then its every earlier point lies there as well. With local assumptions on coefficients and on the free term, we prove existence and Lipschitz dependence on data of classical solutions on \\((0,c\\times\\Omega\\ to the initial boundary value problem, for small \\(c\\. Regularity of solutions matches this domain, and the proof uses the Banach fixed-point theorem. Our general model of functional dependence covers problems with deviating arguments and integro-differential equations.

  9. Incremental localized boundary-domain integro-differential equations of elastic damage mechanics for inhomogeneous body

    OpenAIRE

    Mikhailov, SE

    2006-01-01

    Copyright @ 2006 Tech Science Press A quasi-static mixed boundary value problem of elastic damage mechanics for a continuously inhomogeneous body is considered. Using the two-operator Green-Betti formula and the fundamental solution of an auxiliary homogeneous linear elasticity with frozen initial, secant or tangent elastic coe±cients, a boundary-domain integro-differential formulation of the elasto-plastic problem with respect to the displacement rates and their gradients is derived. Usin...

  10. Exact Solution of the Two-Dimensional Problem on an Impact Ideal-Liquid Jet

    Science.gov (United States)

    Belik, V. D.

    2018-05-01

    The two-dimensional problem on the collision of a potential ideal-liquid jet, outflowing from a reservoir through a nozzle, with an infinite plane obstacle was considered for the case where the distance between the nozzle exit section and the obstacle is finite. An exact solution of this problem has been found using methods of the complex-variable function theory. Simple analytical expressions for the complex velocity of the liquid, its flow rate, and the force of action of the jet on the obstacle have been obtained. The velocity distributions of the liquid at the nozzle exit section, in the region of spreading of the jet, and at the obstacle have been constructed for different distances between the nozzle exit section and the obstacle. Analytical expressions for the thickness of the boundary layer and the Nusselt number at the point of stagnation of the jet have been obtained. A number of distributions of the local friction coefficient and the Nusselt number of the indicated jet are presented.

  11. Boundary-value problems in cosmological dynamics

    Science.gov (United States)

    Nusser, Adi

    2008-08-01

    The dynamics of cosmological gravitating system is governed by the Euler and the Poisson equations. Tiny fluctuations near the big bang singularity are amplified by gravitational instability into the observed structure today. Given the current distribution of galaxies and assuming initial homogeneity, dynamic reconstruction methods have been developed to derive the cosmic density and velocity fields back in time. The reconstruction method described here is based on a least action principle formulation of the dynamics of collisionless particles (representing galaxies). Two observational data sets will be considered. The first is the distribution of galaxies which is assumed to be an fair tracer of the mass density field of the dark matter. The second set is measurements of the peculiar velocities (deviations from pure Hubble flow) of galaxies. Given the first data set, the reconstruction method recovers the associated velocity field which can then be compared with the second data set. This comparison constrains the nature of the dark matter and the relation between mass and light in the Universe.

  12. Determination of free boundary problem of flow through porous media

    International Nuclear Information System (INIS)

    Tavares Junior, H.M.; Souza, A.J. de

    1989-01-01

    This paper deals with a free boundary problem of flow through porous media, which is solved by simplicial method conbined with mesh refinement. Variational method on fixed domain is utilized. (author)

  13. Stabilization of time domain acoustic boundary element method for the interior problem with impedance boundary conditions.

    Science.gov (United States)

    Jang, Hae-Won; Ih, Jeong-Guon

    2012-04-01

    The time domain boundary element method (BEM) is associated with numerical instability that typically stems from the time marching scheme. In this work, a formulation of time domain BEM is derived to deal with all types of boundary conditions adopting a multi-input, multi-output, infinite impulse response structure. The fitted frequency domain impedance data are converted into a time domain expression as a form of an infinite impulse response filter, which can also invoke a modeling error. In the calculation, the response at each time step is projected onto the wave vector space of natural radiation modes, which can be obtained from the eigensolutions of the single iterative matrix. To stabilize the computation, unstable oscillatory modes are nullified, and the same decay rate is used for two nonoscillatory modes. As a test example, a transient sound field within a partially lined, parallelepiped box is used, within which a point source is excited by an octave band impulse. In comparison with the results of the inverse Fourier transform of a frequency domain BEM, the average of relative difference norm in the stabilized time response is found to be 4.4%.

  14. A Boundary Element Solution to the Problem of Interacting AC Fields in Parallel Conductors

    Directory of Open Access Journals (Sweden)

    Einar M. Rønquist

    1984-04-01

    Full Text Available The ac fields in electrically insulated conductors will interact through the surrounding electromagnetic fields. The pertinent field equations reduce to the Helmholtz equation inside each conductor (interior problem, and to the Laplace equation outside the conductors (exterior problem. These equations are transformed to integral equations, with the magnetic vector potential and its normal derivative on the boundaries as unknowns. The integral equations are then approximated by sets of algebraic equations. The interior problem involves only unknowns on the boundary of each conductor, while the exterior problem couples unknowns from several conductors. The interior and the exterior problem are coupled through the field continuity conditions. The full set of equations is solved by standard Gaussian elimination. We also show how the total current and the dissipated power within each conductor can be expressed as boundary integrals. Finally, computational results for a sample problem are compared with a finite difference solution.

  15. Shortest path problem on a grid network with unordered intermediate points

    Science.gov (United States)

    Saw, Veekeong; Rahman, Amirah; Eng Ong, Wen

    2017-10-01

    We consider a shortest path problem with single cost factor on a grid network with unordered intermediate points. A two stage heuristic algorithm is proposed to find a feasible solution path within a reasonable amount of time. To evaluate the performance of the proposed algorithm, computational experiments are performed on grid maps of varying size and number of intermediate points. Preliminary results for the problem are reported. Numerical comparisons against brute forcing show that the proposed algorithm consistently yields solutions that are within 10% of the optimal solution and uses significantly less computation time.

  16. Elliptic boundary value problems

    CERN Document Server

    Maz'ya, V G; Plamenevskii, B A; Stupyali, L; Plamenevskii, B A

    1984-01-01

    The papers in this volume have been selected, translated, and edited from publications not otherwise translated into English under the auspices of the AMS-ASL-IMS Committee on Translations from Russian and Other Foreign Languages.

  17. Using the method of ideal point to solve dual-objective problem for production scheduling

    Directory of Open Access Journals (Sweden)

    Mariia Marko

    2016-07-01

    Full Text Available In practice, there are often problems, which must simultaneously optimize several criterias. This so-called multi-objective optimization problem. In the article we consider the use of the method ideal point to solve the two-objective optimization problem of production planning. The process of finding solution to the problem consists of a series of steps where using simplex method, we find the ideal point. After that for solving a scalar problems, we use the method of Lagrange multipliers

  18. ORIGINAL ARTICLE Fitted-Stable Finite Difference Method for ...

    African Journals Online (AJOL)

    Gemechis

    two point boundary value problems with the boundary layer at one end (left or right) ... scheme (SCD Method) and its value is obtained using the theory of singular ..... Eq. (15) at the point. N iih xxi. , ,2 ,1 ,0 ,.. = = = and taking the limit as. 0. →.

  19. First-order system least-squares for second-order elliptic problems with discontinuous coefficients: Further results

    Energy Technology Data Exchange (ETDEWEB)

    Bloechle, B.; Manteuffel, T.; McCormick, S.; Starke, G.

    1996-12-31

    Many physical phenomena are modeled as scalar second-order elliptic boundary value problems with discontinuous coefficients. The first-order system least-squares (FOSLS) methodology is an alternative to standard mixed finite element methods for such problems. The occurrence of singularities at interface corners and cross-points requires that care be taken when implementing the least-squares finite element method in the FOSLS context. We introduce two methods of handling the challenges resulting from singularities. The first method is based on a weighted least-squares functional and results in non-conforming finite elements. The second method is based on the use of singular basis functions and results in conforming finite elements. We also share numerical results comparing the two approaches.

  20. The interactions of radiation damage with grain boundaries

    International Nuclear Information System (INIS)

    King, A.H.

    1979-01-01

    This thesis reports a theoretical and experimental study of the fundamental effects giving rise to zones adjacent to grain boundaries which are denuded of irradiation-induced damage. The results, however, have significance in the wider field of point-defect absorption (and emission) by grain boundaries. Particular emphasis has been laid upon correlating the point-defect sink behaviour of grain boundaries with their structures and to this end, grain boundaries with periodically repeating structures have been chosen for study. The hypotheses that point-defect absorption is achieved by the climb of grain boundary dislocation spirals, loops and structural arrays have been investigated and firm evidence has been found to support the two latter mechanisms in specific cases. Loops, in particular, have been found to grow only on coherent twin boundary planes. Chapter two of the thesis investigates the crystallographic nature of the possible reactions of point-defects with periodic boundaries and demonstrates that effects such as grain boundary migration and grain translations may be associated with point-defect absorption. Chapter three presents a theoretical study of the effects of elastic interactions between point-defects and grain boundary dislocations and gives predictions of sink strength and bias of a grain boundary as a function of its structure. Chapter four consists of experimental examples of grain boundaries observed during and after irradiation. Chapter five discusses the results of chapters two, three and four considering their implications for the various hypotheses and presents the conclusions of the thesis and some suggestions for further work. (author)