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Sample records for solve nonlinear integro-differential

  1. A pertinent approach to solve nonlinear fuzzy integro-differential equations.

    Science.gov (United States)

    Narayanamoorthy, S; Sathiyapriya, S P

    2016-01-01

    Fuzzy integro-differential equations is one of the important parts of fuzzy analysis theory that holds theoretical as well as applicable values in analytical dynamics and so an appropriate computational algorithm to solve them is in essence. In this article, we use parametric forms of fuzzy numbers and suggest an applicable approach for solving nonlinear fuzzy integro-differential equations using homotopy perturbation method. A clear and detailed description of the proposed method is provided. Our main objective is to illustrate that the construction of appropriate convex homotopy in a proper way leads to highly accurate solutions with less computational work. The efficiency of the approximation technique is expressed via stability and convergence analysis so as to guarantee the efficiency and performance of the methodology. Numerical examples are demonstrated to verify the convergence and it reveals the validity of the presented numerical technique. Numerical results are tabulated and examined by comparing the obtained approximate solutions with the known exact solutions. Graphical representations of the exact and acquired approximate fuzzy solutions clarify the accuracy of the approach.

  2. A Numerical Algorithm for Solving a Four-Point Nonlinear Fractional Integro-Differential Equations

    OpenAIRE

    Gao, Er; Song, Songhe; Zhang, Xinjian

    2012-01-01

    We provide a new algorithm for a four-point nonlocal boundary value problem of nonlinear integro-differential equations of fractional order q∈(1,2] based on reproducing kernel space method. According to our work, the analytical solution of the equations is represented in the reproducing kernel space which we construct and so the n-term approximation. At the same time, the n-term approximation is proved to converge to the analytical solution. An illustrative example is also presented, which sh...

  3. A Numerical Algorithm for Solving a Four-Point Nonlinear Fractional Integro-Differential Equations

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    Er Gao

    2012-01-01

    Full Text Available We provide a new algorithm for a four-point nonlocal boundary value problem of nonlinear integro-differential equations of fractional order q∈(1,2] based on reproducing kernel space method. According to our work, the analytical solution of the equations is represented in the reproducing kernel space which we construct and so the n-term approximation. At the same time, the n-term approximation is proved to converge to the analytical solution. An illustrative example is also presented, which shows that the new algorithm is efficient and accurate.

  4. Stability analysis of Runge-Kutta methods for nonlinear neutral delay integro-differential equations

    Institute of Scientific and Technical Information of China (English)

    2007-01-01

    The sufficient conditions for the stability and asymptotic stability of Runge-Kutta methods for nonlinear neutral delay integro-differential equations are derived. A numerical test that confirms the theoretical results is given in the end.

  5. ADM For Solving Linear Second-Order Fredholm Integro-Differential Equations

    Science.gov (United States)

    Karim, Mohd F.; Mohamad, Mahathir; Saifullah Rusiman, Mohd; Che-Him, Norziha; Roslan, Rozaini; Khalid, Kamil

    2018-04-01

    In this paper, we apply Adomian Decomposition Method (ADM) as numerically analyse linear second-order Fredholm Integro-differential Equations. The approximate solutions of the problems are calculated by Maple package. Some numerical examples have been considered to illustrate the ADM for solving this equation. The results are compared with the existing exact solution. Thus, the Adomian decomposition method can be the best alternative method for solving linear second-order Fredholm Integro-Differential equation. It converges to the exact solution quickly and in the same time reduces computational work for solving the equation. The result obtained by ADM shows the ability and efficiency for solving these equations.

  6. Dielectric metasurfaces solve differential and integro-differential equations.

    Science.gov (United States)

    Abdollahramezani, Sajjad; Chizari, Ata; Dorche, Ali Eshaghian; Jamali, Mohammad Vahid; Salehi, Jawad A

    2017-04-01

    Leveraging subwavelength resonant nanostructures, plasmonic metasurfaces have recently attracted much attention as a breakthrough concept for engineering optical waves both spatially and spectrally. However, inherent ohmic losses concomitant with low coupling efficiencies pose fundamental impediments over their practical applications. Not only can all-dielectric metasurfaces tackle such substantial drawbacks, but also their CMOS-compatible configurations support both Mie resonances that are invariant to the incident angle. Here, we report on a transmittive metasurface comprising arrayed silicon nanodisks embedded in a homogeneous dielectric medium to manipulate phase and amplitude of incident light locally and almost independently. By taking advantage of the interplay between the electric/magnetic resonances and employing general concepts of spatial Fourier transformation, a highly efficient metadevice is proposed to perform mathematical operations including solution of ordinary differential and integro-differential equations with constant coefficients. Our findings further substantiate dielectric metasurfaces as promising candidates for miniaturized, two-dimensional, and planar optical analog computing systems that are much thinner than their conventional lens-based counterparts.

  7. Biorthogonal Systems Approximating the Solution of the Nonlinear Volterra Integro-Differential Equation

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    Berenguer MI

    2010-01-01

    Full Text Available This paper deals with obtaining a numerical method in order to approximate the solution of the nonlinear Volterra integro-differential equation. We define, following a fixed-point approach, a sequence of functions which approximate the solution of this type of equation, due to some properties of certain biorthogonal systems for the Banach spaces and .

  8. Fibonacci collocation method with a residual error Function to solve linear Volterra integro differential equations

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    Salih Yalcinbas

    2016-01-01

    Full Text Available In this paper, a new collocation method based on the Fibonacci polynomials is introduced to solve the high-order linear Volterra integro-differential equations under the conditions. Numerical examples are included to demonstrate the applicability and validity of the proposed method and comparisons are made with the existing results. In addition, an error estimation based on the residual functions is presented for this method. The approximate solutions are improved by using this error estimation.

  9. Matrix form of Legendre polynomials for solving linear integro-differential equations of high order

    Science.gov (United States)

    Kammuji, M.; Eshkuvatov, Z. K.; Yunus, Arif A. M.

    2017-04-01

    This paper presents an effective approximate solution of high order of Fredholm-Volterra integro-differential equations (FVIDEs) with boundary condition. Legendre truncated series is used as a basis functions to estimate the unknown function. Matrix operation of Legendre polynomials is used to transform FVIDEs with boundary conditions into matrix equation of Fredholm-Volterra type. Gauss Legendre quadrature formula and collocation method are applied to transfer the matrix equation into system of linear algebraic equations. The latter equation is solved by Gauss elimination method. The accuracy and validity of this method are discussed by solving two numerical examples and comparisons with wavelet and methods.

  10. Numerical Solution of Nonlinear Fredholm Integro-Differential Equations Using Spectral Homotopy Analysis Method

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    Z. Pashazadeh Atabakan

    2013-01-01

    Full Text Available Spectral homotopy analysis method (SHAM as a modification of homotopy analysis method (HAM is applied to obtain solution of high-order nonlinear Fredholm integro-differential problems. The existence and uniqueness of the solution and convergence of the proposed method are proved. Some examples are given to approve the efficiency and the accuracy of the proposed method. The SHAM results show that the proposed approach is quite reasonable when compared to homotopy analysis method, Lagrange interpolation solutions, and exact solutions.

  11. Effective quadrature formula in solving linear integro-differential equations of order two

    Science.gov (United States)

    Eshkuvatov, Z. K.; Kammuji, M.; Long, N. M. A. Nik; Yunus, Arif A. M.

    2017-08-01

    In this note, we solve general form of Fredholm-Volterra integro-differential equations (IDEs) of order 2 with boundary condition approximately and show that proposed method is effective and reliable. Initially, IDEs is reduced into integral equation of the third kind by using standard integration techniques and identity between multiple and single integrals then truncated Legendre series are used to estimate the unknown function. For the kernel integrals, we have applied Gauss-Legendre quadrature formula and collocation points are chosen as the roots of the Legendre polynomials. Finally, reduce the integral equations of the third kind into the system of algebraic equations and Gaussian elimination method is applied to get approximate solutions. Numerical examples and comparisons with other methods reveal that the proposed method is very effective and dominated others in many cases. General theory of existence of the solution is also discussed.

  12. Nonlinear Stability and Convergence of Two-Step Runge-Kutta Methods for Volterra Delay Integro-Differential Equations

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    Haiyan Yuan

    2013-01-01

    Full Text Available This paper introduces the stability and convergence of two-step Runge-Kutta methods with compound quadrature formula for solving nonlinear Volterra delay integro-differential equations. First, the definitions of (k,l-algebraically stable and asymptotically stable are introduced; then the asymptotical stability of a (k,l-algebraically stable two-step Runge-Kutta method with 0

  13. Method for solving the periodic problem for integro-differential equations

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    Snezhana G. Hristova

    1989-05-01

    Full Text Available In the paper a monotone-iterative method for approximate finding a couple of minimal and maximal quasisolutions of the periodic problem for a system of integro-differential equations of Volterra type is justified.

  14. Aumann Fuzzy Improper Integral and Its Application to Solve Fuzzy Integro-Differential Equations by Laplace Transform Method

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    Elhassan Eljaoui

    2018-01-01

    Full Text Available We introduce the Aumann fuzzy improper integral to define the convolution product of a fuzzy mapping and a crisp function in this paper. The Laplace convolution formula is proved in this case and used to solve fuzzy integro-differential equations with kernel of convolution type. Then, we report and correct an error in the article by Salahshour et al. dealing with the same topic.

  15. Existence and Analytic Approximation of Solutions of Duffing Type Nonlinear Integro-Differential Equation with Integral Boundary Conditions

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    Alsaedi Ahmed

    2009-01-01

    Full Text Available A generalized quasilinearization technique is developed to obtain a sequence of approximate solutions converging monotonically and quadratically to a unique solution of a boundary value problem involving Duffing type nonlinear integro-differential equation with integral boundary conditions. The convergence of order for the sequence of iterates is also established. It is found that the work presented in this paper not only produces new results but also yields several old results in certain limits.

  16. New continual analogs of two-dimensional Toda lattices related with nonlinear integro-differential equations

    International Nuclear Information System (INIS)

    Savel'ev, M.V.

    1988-01-01

    Continual ''extensions'' of two-dimensional Toda lattices are proposed. They are described by integro-differential equations, generally speaking, with singular kernels, depending on new (third) variable. The problem of their integrability on the corresponding class of the initial discrete system solutions is discussed. The latter takes place, in particular, for the kernel coinciding with the causal function

  17. Multi-soliton management by the integrable nonautonomous nonlinear integro-differential Schrödinger equation

    International Nuclear Information System (INIS)

    Zhang, Yu-Juan; Zhao, Dun; Luo, Hong-Gang

    2014-01-01

    We consider a wide class of integrable nonautonomous nonlinear integro-differential Schrödinger equation which contains the models for the soliton management in Bose–Einstein condensates, nonlinear optics, and inhomogeneous Heisenberg spin chain. With the help of the nonisospectral AKNS hierarchy, we obtain the N-fold Darboux transformation and the N-fold soliton-like solutions for the equation. The soliton management, especially the synchronized dispersive and nonlinear management in optical fibers is discussed. It is found that in the situation without external potential, the synchronized dispersive and nonlinear management can keep the integrability of the nonlinear Schrödinger equation; this suggests that in optical fibers, the synchronized dispersive and nonlinear management can control and maintain the propagation of a multi-soliton. - Highlights: • We consider a unified model for soliton management by an integrable integro-differential Schrödinger equation. • Using Lax pair, the N-fold Darboux transformation for the equation is presented. • The multi-soliton management is considered. • The synchronized dispersive and nonlinear management is suggested

  18. On a numerical method for solving integro-differential equations with variable coefficients with applications in finance

    Science.gov (United States)

    Kudryavtsev, O.; Rodochenko, V.

    2018-03-01

    We propose a new general numerical method aimed to solve integro-differential equations with variable coefficients. The problem under consideration arises in finance where in the context of pricing barrier options in a wide class of stochastic volatility models with jumps. To handle the effect of the correlation between the price and the variance, we use a suitable substitution for processes. Then we construct a Markov-chain approximation for the variation process on small time intervals and apply a maturity randomization technique. The result is a system of boundary problems for integro-differential equations with constant coefficients on the line in each vertex of the chain. We solve the arising problems using a numerical Wiener-Hopf factorization method. The approximate formulae for the factors are efficiently implemented by means of the Fast Fourier Transform. Finally, we use a recurrent procedure that moves backwards in time on the variance tree. We demonstrate the convergence of the method using Monte-Carlo simulations and compare our results with the results obtained by the Wiener-Hopf method with closed-form expressions of the factors.

  19. A direct method for numerical solution of a class of nonlinear Volterra integro-differential equations and its application to the nonlinear fission and fusion reactor kinetics

    International Nuclear Information System (INIS)

    Nakahara, Yasuaki; Ise, Takeharu; Kobayashi, Kensuke; Itoh, Yasuyuki

    1975-12-01

    A new method has been developed for numerical solution of a class of nonlinear Volterra integro-differential equations with quadratic nonlinearity. After dividing the domain of the variable into subintervals, piecewise approximations are applied in the subintervals. The equation is first integrated over a subinterval to obtain the piecewise equation, to which six approximate treatments are applied, i.e. fully explicit, fully implicit, Crank-Nicolson, linear interpolation, quadratic and cubic spline. The numerical solution at each time step is obtained directly as a positive root of the resulting algebraic quadratic equation. The point reactor kinetics with a ramp reactivity insertion, linear temperature feedback and delayed neutrons can be described by one of this type of nonlinear Volterra integro-differential equations. The algorithm is applied to the Argonne benchmark problem and a model problem for a fast reactor without delayed neutrons. The fully implicit method has been found to be unconditionally stable in the sense that it always gives the positive real roots. The cubic spline method is divergent, and the other four methods are intermediate in between. From the estimation of the stability, convergency, accuracy and CPU time, it is concluded that the Crank-Nicolson method is best, then the linear interpolation method comes closely next to it. Discussions are also made on the possibility of applying the algorithm to the fusion reactor kinetics in the form of a nonlinear partial differential equation. (auth.)

  20. Quarter-Sweep Iteration Concept on Conjugate Gradient Normal Residual Method via Second Order Quadrature - Finite Difference Schemes for Solving Fredholm Integro-Differential Equations

    International Nuclear Information System (INIS)

    Aruchunan, E.

    2015-01-01

    In this paper, we have examined the effectiveness of the quarter-sweep iteration concept on conjugate gradient normal residual (CGNR) iterative method by using composite Simpson's (CS) and finite difference (FD) discretization schemes in solving Fredholm integro-differential equations. For comparison purposes, Gauss- Seidel (GS) and the standard or full- and half-sweep CGNR methods namely FSCGNR and HSCGNR are also presented. To validate the efficacy of the proposed method, several analyses were carried out such as computational complexity and percentage reduction on the proposed and existing methods. (author)

  1. Analysis of stability for stochastic delay integro-differential equations.

    Science.gov (United States)

    Zhang, Yu; Li, Longsuo

    2018-01-01

    In this paper, we concern stability of numerical methods applied to stochastic delay integro-differential equations. For linear stochastic delay integro-differential equations, it is shown that the mean-square stability is derived by the split-step backward Euler method without any restriction on step-size, while the Euler-Maruyama method could reproduce the mean-square stability under a step-size constraint. We also confirm the mean-square stability of the split-step backward Euler method for nonlinear stochastic delay integro-differential equations. The numerical experiments further verify the theoretical results.

  2. Lipschitz Regularity of Solutions for Mixed Integro-Differential Equations

    OpenAIRE

    Barles, Guy; Chasseigne, Emmanuel; Ciomaga, Adina; Imbert, Cyril

    2011-01-01

    We establish new Hoelder and Lipschitz estimates for viscosity solutions of a large class of elliptic and parabolic nonlinear integro-differential equations, by the classical Ishii-Lions's method. We thus extend the Hoelder regularity results recently obtained by Barles, Chasseigne and Imbert (2011). In addition, we deal with a new class of nonlocal equations that we term mixed integro-differential equations. These equations are particularly interesting, as they are degenerate both in the loc...

  3. Integro-differential transport approaches

    International Nuclear Information System (INIS)

    Stepanek, J.; Arkuszewski, J.; Boffi, V.; Matausek, M.V.

    1981-01-01

    This chapter summarizes the work done in Italy, Poland, Switzerland and Yugoslavia in the field of integro-differential neutron transport theory. It reflects different viewpoints in the handling of the subject. Some of the methods are based only on the solution of the integro-differential equation, others use only the integral form of the transport equation. Use of the characteristic solution closely related to the integral equation (ARKUSZEWSKI et al.,(1979)) seems to be a rather effective way to accelerate the 2 dimensional discrete ordinates (Ssub(n)) transport methods and supress one of the main disadvantages, the ray effect. The advanced ''Surface Currents'' (MAEDER (1975)) and ''Surface Flux'' (STEPANEK (1979)) methods are based on the solution of both the integro-differential and integral form of the transport equation. As long as the spatial fluxes were considered to be flat in each region only the integral form of the transport equation was considered. The solution seems to be the best method of simple handling the higher order Legendre polynomials used to approximate spatial and angular flux distribution. The coupling of the Bsub(n) integral transport equations with the related Psub(n) equations removes the greatest disadvantage of the Psub(n) theory and closes the system of the Psub(n) equations (LIGOU, STEPANEK (1974))

  4. N-th order impulsive integro-differential equations in Banach spaces

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    Manfeng Hu

    2004-03-01

    Full Text Available We investigate the maximal and minimal solutions of initial value problem for N-th order nonlinear impulsive integro-differential equation in Banach space by establishing a comparison result and using the upper and lower solutions methods.

  5. New stability and boundedness results to Volterra integro-differential equations with delay

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    Cemil Tunç

    2016-04-01

    Full Text Available In this paper, we consider a certain non-linear Volterra integro-differential equations with delay. We study stability and boundedness of solutions. The technique of proof involves defining suitable Lyapunov functionals. Our results improve and extend the results obtained in literature.

  6. Triple positive  solutions of nth order impulsive integro-differential equations

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    Zeyong Qiu

    2011-07-01

    Full Text Available In this paper, we prove the existence of at least three positive solutions of boundary value problems for nth order nonlinear impulsive integro-differential equations of mixed type on infinite interval with infinite number of impulsive times. Our results are obtained by applying a new fixed point theorem introduced by Avery and Peterson.

  7. A remark on the stability and boundedness criteria in retarded Volterra integro-differential equations

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    Cemil Tunç

    2017-10-01

    Full Text Available In this article, the authors obtain some clear assumptions for the asymptotic stability (AS and boundedness (B of solutions of non-linear retarded Volterra integro-differential equations (VIDEs of first order by constructing a new Lyapunov functional (LF. The results obtained are new and differ from those found in the literature, and they also contain and improve a result found in the literature under more less restrictive conditions. We establish an example and give a discussion to indicate the applicability of the weaker conditions obtained. We also employ MATLAB-Simulink to display the behaviors of the orbits of the (VIDEs considered. Keywords: Nonlinear, Volterra integro-differential equations, First order, Asymptotic stability, Boundedness, Lyapunov functional, MSC: 34D05, 34K20, 45J05

  8. Continuous Multistep Methods for Volterra Integro-Differential

    African Journals Online (AJOL)

    Kamoh et al.

    DIFFERENTIAL EQUATIONS OF THE SECOND ORDER. 1Kamoh N.M. ... methods, Volterra integro-differential equation, Convergent, ...... Research of a Multistep Method Applied to Numerical Solution of. Volterra ... Congress on Engineering.

  9. Controllability of nonlocal second-order impulsive neutral stochastic functional integro-differential equations with delay and Poisson jumps

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    Diem Dang Huan

    2015-12-01

    Full Text Available The current paper is concerned with the controllability of nonlocal second-order impulsive neutral stochastic functional integro-differential equations with infinite delay and Poisson jumps in Hilbert spaces. Using the theory of a strongly continuous cosine family of bounded linear operators, stochastic analysis theory and with the help of the Banach fixed point theorem, we derive a new set of sufficient conditions for the controllability of nonlocal second-order impulsive neutral stochastic functional integro-differential equations with infinite delay and Poisson jumps. Finally, an application to the stochastic nonlinear wave equation with infinite delay and Poisson jumps is given.

  10. Integro-differential equation approach extended to larger nuclei

    International Nuclear Information System (INIS)

    Adam, R.M.; Sofianos, S.A.; Fiedeldey, H.; Fabre de la Ripelle, M.

    1992-01-01

    We extend the integro-differential equation approach (IDEA) from few-nucleon to closed-shell and closed-subshell nuclei and outline the analytical methods required for the calculation of the density functions, which enter into the integro-differential equations. These contain all the physics for a system of fermions associated with the Pauli principle. In order to test the accuracy of the IDEA comparisons are made of the binding energies of 4 He, 12 C and 16 O obtained with effective potentials using the hypercentral approximation (HCA) providing a variational solution without correlations, the IDEA which fully includes the two-body correlations, the S-states integro-differential equation (SIDE) valid for potentials operating only on pairs in the S-state and those calculated by several variational or perturbative methods in the literature. (author)

  11. Continuous multistep methods for volterra integro-differential ...

    African Journals Online (AJOL)

    A new class of numerical methods for Volterra integro-differential equations of the second order is developed. The methods are based on interpolation and collocation of the shifted Legendre polynomial as basis function with Trapezoidal quadrature rules. The convergence analysis revealed that the methods are consistent ...

  12. Singularly perturbed volterra integro-differential equations | Bijura ...

    African Journals Online (AJOL)

    Several investigations have been made on singularly perturbed integral equations. This paper aims at presenting an algorithm for the construction of asymptotic solutions and then provide a proof asymptotic correctness to singularly perturbed systems of Volterra integro-differential equations. Mathematics Subject

  13. Reproducing kernel method with Taylor expansion for linear Volterra integro-differential equations

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    Azizallah Alvandi

    2017-06-01

    Full Text Available This research aims of the present a new and single algorithm for linear integro-differential equations (LIDE. To apply the reproducing Hilbert kernel method, there is made an equivalent transformation by using Taylor series for solving LIDEs. Shown in series form is the analytical solution in the reproducing kernel space and the approximate solution $ u_{N} $ is constructed by truncating the series to $ N $ terms. It is easy to prove the convergence of $ u_{N} $ to the analytical solution. The numerical solutions from the proposed method indicate that this approach can be implemented easily which shows attractive features.

  14. Symmetry groups of integro-differential equations for linear thermoviscoelastic materials with memory

    Science.gov (United States)

    Zhou, L.-Q.; Meleshko, S. V.

    2017-07-01

    The group analysis method is applied to a system of integro-differential equations corresponding to a linear thermoviscoelastic model. A recently developed approach for calculating the symmetry groups of such equations is used. The general solution of the determining equations for the system is obtained. Using subalgebras of the admitted Lie algebra, two classes of partially invariant solutions of the considered system of integro-differential equations are studied.

  15. A bridge between hyperspherical and integro-differential approaches to the many-body bound states

    International Nuclear Information System (INIS)

    Fabre de la Ripelle, M.

    1986-01-01

    The solution of the Schroedinger equation can be obtained from the one of a system of coupled differential equations generated from the potential harmonic expansion of the bound-state wave function of a system of identical particles governed by two-body central interactions. It is shown that the system of coupled equations can be transformed into an equivalent integro-differential equation. For three bosons in S states this equation is identical to the Faddeev equation as written by Noyes. The integro-differential equations describing the triton for non-central realistic N-N forces are explicitly given. (Auth.)

  16. Shifted Legendre method with residual error estimation for delay linear Fredholm integro-differential equations

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    Şuayip Yüzbaşı

    2017-03-01

    Full Text Available In this paper, we suggest a matrix method for obtaining the approximate solutions of the delay linear Fredholm integro-differential equations with constant coefficients using the shifted Legendre polynomials. The problem is considered with mixed conditions. Using the required matrix operations, the delay linear Fredholm integro-differential equation is transformed into a matrix equation. Additionally, error analysis for the method is presented using the residual function. Illustrative examples are given to demonstrate the efficiency of the method. The results obtained in this study are compared with the known results.

  17. Asymptotic analysis and optimal control of an integro-differential system modelling healthy and cancer cells exposed to chemotherapy

    KAUST Repository

    Pouchol, Camille

    2017-10-27

    We consider a system of two coupled integro-differential equations modelling populations of healthy and cancer cells under chemotherapy. Both populations are structured by a phenotypic variable, representing their level of resistance to the treatment. We analyse the asymptotic behaviour of the model under constant infusion of drugs. By designing an appropriate Lyapunov function, we prove that both cell densities converge to Dirac masses. We then define an optimal control problem, by considering all possible infusion protocols and minimising the number of cancer cells over a prescribed time frame. We provide a quasi-optimal strategy and prove that it solves this problem for large final times. For this modelling framework, we illustrate our results with numerical simulations, and compare our optimal strategy with periodic treatment schedules.

  18. Bootstrap regularity for integro-differential operators and its application to nonlocal minimal surfaces

    OpenAIRE

    Barrera, Begoña Barrios; Figalli, Alessio; Valdinoci, Enrico

    2012-01-01

    We prove that $C^{1,\\alpha}$ $s$-minimal surfaces are automatically $C^\\infty$. For this, we develop a new bootstrap regularity theory for solutions of integro-differential equations of very general type, which we believe is of independent interest.

  19. Approximate solution of integro-differential equation of fractional (arbitrary order

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    Asma A. Elbeleze

    2016-01-01

    Full Text Available In the present paper, we study the integro-differential equations which are combination of differential and Fredholm–Volterra equations that have the fractional order with constant coefficients by the homotopy perturbation and the variational iteration. The fractional derivatives are described in Caputo sense. Some illustrative examples are presented.

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

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    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.

  1. On a non classical oblique derivative problem for parabolic singular integro-differential operators

    International Nuclear Information System (INIS)

    Nguyen Minh Chuong; Le Quang Trung

    1989-10-01

    In this paper an oblique derivative problem for parabolic singular integro-differential operators was studied. In this problem the direction of the derivative may be tangent to the boundary of the domain. By the large parameter method theorems of existence and uniqueness of solutions of the problem were obtained. (author). 10 refs

  2. Weighted asymptotic behavior of solutions to semilinear integro-differential equations in Banach spaces

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    Yan-Tao Bian

    2014-04-01

    Full Text Available In this article, we study weighted asymptotic behavior of solutions to the semilinear integro-differential equation $$ u'(t=Au(t+\\alpha\\int_{-\\infty}^{t}e^{-\\beta(t-s}Au(sds+f(t,u(t, \\quad t\\in \\mathbb{R}, $$ where $\\alpha, \\beta \\in \\mathbb{R}$, with $\\beta > 0, \\alpha \

  3. Existence of Mild Solutions for Impulsive Fractional Integro-Differential Inclusions with State-Dependent Delay

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    Selvaraj Suganya

    2017-01-01

    Full Text Available In this manuscript, we implement Bohnenblust–Karlin’s fixed point theorem to demonstrate the existence of mild solutions for a class of impulsive fractional integro-differential inclusions (IFIDI with state-dependent delay (SDD in Banach spaces. An example is provided to illustrate the obtained abstract results.

  4. A novel technique to solve nonlinear higher-index Hessenberg differential-algebraic equations by Adomian decomposition method.

    Science.gov (United States)

    Benhammouda, Brahim

    2016-01-01

    Since 1980, the Adomian decomposition method (ADM) has been extensively used as a simple powerful tool that applies directly to solve different kinds of nonlinear equations including functional, differential, integro-differential and algebraic equations. However, for differential-algebraic equations (DAEs) the ADM is applied only in four earlier works. There, the DAEs are first pre-processed by some transformations like index reductions before applying the ADM. The drawback of such transformations is that they can involve complex algorithms, can be computationally expensive and may lead to non-physical solutions. The purpose of this paper is to propose a novel technique that applies the ADM directly to solve a class of nonlinear higher-index Hessenberg DAEs systems efficiently. The main advantage of this technique is that; firstly it avoids complex transformations like index reductions and leads to a simple general algorithm. Secondly, it reduces the computational work by solving only linear algebraic systems with a constant coefficient matrix at each iteration, except for the first iteration where the algebraic system is nonlinear (if the DAE is nonlinear with respect to the algebraic variable). To demonstrate the effectiveness of the proposed technique, we apply it to a nonlinear index-three Hessenberg DAEs system with nonlinear algebraic constraints. This technique is straightforward and can be programmed in Maple or Mathematica to simulate real application problems.

  5. Abstract fractional integro-differential equations involving nonlocal initial conditions in α-norm

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    Wang Rong-Nian

    2011-01-01

    Full Text Available Abstract In the present paper, we deal with the Cauchy problems of abstract fractional integro-differential equations involving nonlocal initial conditions in α-norm, where the operator A in the linear part is the generator of a compact analytic semigroup. New criterions, ensuring the existence of mild solutions, are established. The results are obtained by using the theory of operator families associated with the function of Wright type and the semigroup generated by A, Krasnoselkii's fixed point theorem and Schauder's fixed point theorem. An application to a fractional partial integro-differential equation with nonlocal initial condition is also considered. Mathematics subject classification (2000 26A33, 34G10, 34G20

  6. 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...

  7. On choice of trial functions in integro-differential variational principles of transport theory

    International Nuclear Information System (INIS)

    Loyalka, S.K.; Cipolla, J.W. Jr.

    1988-01-01

    In several problems of particle transport, quantities of macroscopic interest can be related to stationary values of variational functionals based on general integro-differential equations and boundary conditions. Within the context of the jump (Milne's) problem, it is shown how highly accurate results can be obtained by using trial functions based on the eigenfunctions of the relevant integrodifferential equations. Such choices of trial functions should apply equally effectively to problems in curved geometries, both internal and external

  8. Some properties for integro-differential operator defined by a fractional formal.

    Science.gov (United States)

    Abdulnaby, Zainab E; Ibrahim, Rabha W; Kılıçman, Adem

    2016-01-01

    Recently, the study of the fractional formal (operators, polynomials and classes of special functions) has been increased. This study not only in mathematics but extended to another topics. In this effort, we investigate a generalized integro-differential operator [Formula: see text] defined by a fractional formal (fractional differential operator) and study some its geometric properties by employing it in new subclasses of analytic univalent functions.

  9. Existence results for fractional integro-differential inclusions with state-dependent delay

    Directory of Open Access Journals (Sweden)

    Siracusa Giovana

    2017-10-01

    Full Text Available In this paper we are concerned with a class of abstract fractional integro-differential inclusions with infinite state-dependent delay. Our approach is based on the existence of a resolvent operator for the homogeneous equation.We establish the existence of mild solutions using both contractive maps and condensing maps. Finally, an application to the theory of heat conduction in materials with memory is given.

  10. Analytical solution to DGLAP integro-differential equation in a simple toy-model with a fixed gauge coupling

    Energy Technology Data Exchange (ETDEWEB)

    Alvarez, Gustavo [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Concepcion Univ. (Chile). Dept. de Fisica; Cvetic, Gorazd [Univ. Tecnica Federico Santa Maria, Valparaiso (Chile). Dept. de Fisica; Kniehl, Bernd A. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Kondrashuk, Igor [Univ. del Bio-Bio, Chillan (Chile). Grupo de Matematica Aplicada; Univ. del Bio-Bio, Chillan (Chile). Grupo de Fisica de Altas Energias; Parra-Ferrada, Ivan [Talca Univ. (Chile). Inst. de Matematica y Fisica

    2016-11-15

    We consider a simple model for QCD dynamics in which DGLAP integro-differential equation may be solved analytically. This is a gauge model which possesses dominant evolution of gauge boson (gluon) distribution and in which the gauge coupling does not run. This may be N=4 supersymmetric gauge theory with softly broken supersymmetry, other finite supersymmetric gauge theory with lower level of supersymmetry, or topological Chern-Simons field theories. We maintain only one term in the splitting function of unintegrated gluon distribution and solve DGLAP analytically for this simplified splitting function. The solution is found by use of the Cauchy integral formula. The solution restricts form of the unintegrated gluon distribution as function of transfer momentum and of Bjorken x. Then we consider an almost realistic splitting function of unintegrated gluon distribution as an input to DGLAP equation and solve it by the same method which we have developed to solve DGLAP equation for the toy-model. We study a result obtained for the realistic gluon distribution and find a singular Bessel-like behaviour in the vicinity of the point x=0 and a smooth behaviour in the vicinity of the point x=1.

  11. A variational Integro-Differential Equation for three identical particles in an S-state

    International Nuclear Information System (INIS)

    Fabre de la Ripelle, M.; Braun, M.; Sofianos, S.A.

    1997-01-01

    Starting from the Schroedinger equation, a new Variational Integro-Differential Equation (VIDE) for three bosons in S-state is derived. The wave function has the simple structure of a sum of two-body amplitudes. It is shown that the new equation gives results which are three orders of magnitude better than the corresponding results obtained from a single Faddeev equation, where the pairs are in an S-state. The latter equation generates an exact solution only for S-state projected potentials. Moreover, the ghost contributions occurring in the Faddeev amplitudes for three bosons in an S-state do not exist in the new equation. (author)

  12. On an integro-differential model for pest control in a heterogeneous environment.

    Science.gov (United States)

    Rodríguez, Nancy

    2015-04-01

    Insect pests pose a major threat to a balanced ecology as it can threaten local species as well as spread human diseases; thus, making the study of pest control extremely important. In practice, the sterile insect release method (SIRM), where a sterile population is introduced into the wild population with the aim of significantly reducing the growth of the population, has been a popular technique used to control pest invasions. In this work we introduce an integro-differential equation to model the propagation of pests in a heterogeneous environment, where this environment is divided into three regions. In one region SIRM is not used making this environment conducive to propagation of the insects. A second region is the eradication zone where there is an intense release of sterile insects, leading to decay of the population in this region. In the final region we explore two scenarios. In the first case, there is a small release of sterile insects and we prove that if the eradication zone is sufficiently large the pests will not invade. In the second case, when SIRM is not used at all in this region we show that invasions always occur regardless of the size of the eradication zone. Finally, we consider the limiting equation of the integro-differential equation and prove that in this case there is a critical length of the eradication zone which separates propagation from obstruction. Moreover, we provide some upper and lower bound for the critical length.

  13. OPTIMAL ESTIMATES FOR THE SEMIDISCRETE GALERKIN METHOD APPLIED TO PARABOLIC INTEGRO-DIFFERENTIAL EQUATIONS WITH NONSMOOTH DATA

    KAUST Repository

    GOSWAMI, DEEPJYOTI; PANI, AMIYA K.; YADAV, SANGITA

    2014-01-01

    AWe propose and analyse an alternate approach to a priori error estimates for the semidiscrete Galerkin approximation to a time-dependent parabolic integro-differential equation with nonsmooth initial data. The method is based on energy arguments combined with repeated use of time integration, but without using parabolic-type duality techniques. An optimal L2-error estimate is derived for the semidiscrete approximation when the initial data is in L2. A superconvergence result is obtained and then used to prove a maximum norm estimate for parabolic integro-differential equations defined on a two-dimensional bounded domain. © 2014 Australian Mathematical Society.

  14. An hp-local Discontinuous Galerkin Method for Parabolic Integro-Differential Equations

    KAUST Repository

    Pani, Amiya K.

    2010-06-06

    In this article, a priori error bounds are derived for an hp-local discontinuous Galerkin (LDG) approximation to a parabolic integro-differential equation. It is shown that error estimates in L 2-norm of the gradient as well as of the potential are optimal in the discretizing parameter h and suboptimal in the degree of polynomial p. Due to the presence of the integral term, an introduction of an expanded mixed type Ritz-Volterra projection helps us to achieve optimal estimates. Further, it is observed that a negative norm estimate of the gradient plays a crucial role in our convergence analysis. As in the elliptic case, similar results on order of convergence are established for the semidiscrete method after suitably modifying the numerical fluxes. The optimality of these theoretical results is tested in a series of numerical experiments on two dimensional domains. © 2010 Springer Science+Business Media, LLC.

  15. An hp-local Discontinuous Galerkin Method for Parabolic Integro-Differential Equations

    KAUST Repository

    Pani, Amiya K.; Yadav, Sangita

    2010-01-01

    In this article, a priori error bounds are derived for an hp-local discontinuous Galerkin (LDG) approximation to a parabolic integro-differential equation. It is shown that error estimates in L 2-norm of the gradient as well as of the potential are optimal in the discretizing parameter h and suboptimal in the degree of polynomial p. Due to the presence of the integral term, an introduction of an expanded mixed type Ritz-Volterra projection helps us to achieve optimal estimates. Further, it is observed that a negative norm estimate of the gradient plays a crucial role in our convergence analysis. As in the elliptic case, similar results on order of convergence are established for the semidiscrete method after suitably modifying the numerical fluxes. The optimality of these theoretical results is tested in a series of numerical experiments on two dimensional domains. © 2010 Springer Science+Business Media, LLC.

  16. 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.

  17. Optimal Error Estimates of Two Mixed Finite Element Methods for Parabolic Integro-Differential Equations with Nonsmooth Initial Data

    KAUST Repository

    Goswami, Deepjyoti; Pani, Amiya K.; Yadav, Sangita

    2013-01-01

    In the first part of this article, a new mixed method is proposed and analyzed for parabolic integro-differential equations (PIDE) with nonsmooth initial data. Compared to the standard mixed method for PIDE, the present method does not bank on a

  18. Solving Nonlinear Coupled Differential Equations

    Science.gov (United States)

    Mitchell, L.; David, J.

    1986-01-01

    Harmonic balance method developed to obtain approximate steady-state solutions for nonlinear coupled ordinary differential equations. Method usable with transfer matrices commonly used to analyze shaft systems. Solution to nonlinear equation, with periodic forcing function represented as sum of series similar to Fourier series but with form of terms suggested by equation itself.

  19. Statistical mechanics of normal grain growth in one dimension: A partial integro-differential equation model

    International Nuclear Information System (INIS)

    Ng, Felix S.L.

    2016-01-01

    We develop a statistical-mechanical model of one-dimensional normal grain growth that does not require any drift-velocity parameterization for grain size, such as used in the continuity equation of traditional mean-field theories. The model tracks the population by considering grain sizes in neighbour pairs; the probability of a pair having neighbours of certain sizes is determined by the size-frequency distribution of all pairs. Accordingly, the evolution obeys a partial integro-differential equation (PIDE) over ‘grain size versus neighbour grain size’ space, so that the grain-size distribution is a projection of the PIDE's solution. This model, which is applicable before as well as after statistically self-similar grain growth has been reached, shows that the traditional continuity equation is invalid outside this state. During statistically self-similar growth, the PIDE correctly predicts the coarsening rate, invariant grain-size distribution and spatial grain size correlations observed in direct simulations. The PIDE is then reducible to the standard continuity equation, and we derive an explicit expression for the drift velocity. It should be possible to formulate similar parameterization-free models of normal grain growth in two and three dimensions.

  20. Composite spectral functions for solving Volterra's population model

    International Nuclear Information System (INIS)

    Ramezani, M.; Razzaghi, M.; Dehghan, M.

    2007-01-01

    An approximate method for solving Volterra's population model for population growth of a species in a closed system is proposed. Volterra's model is a nonlinear integro-differential equation, where the integral term represents the effect of toxin. The approach is based upon composite spectral functions approximations. The properties of composite spectral functions consisting of few terms of orthogonal functions are presented and are utilized to reduce the solution of the Volterra's model to the solution of a system of algebraic equations. The method is easy to implement and yields very accurate result

  1. Stability analysis of nonlinear integro-differential equations arising in age-dependent epidemic models

    International Nuclear Information System (INIS)

    El Doma, M.

    1995-05-01

    An age-structured epidemic model of an SI type that incorporate vertical transmission is investigated when the fertility and mortality rates depend on age. We determine the steady states and examine their stabilities. (author). 13 refs

  2. An analytical theory of a scattering of radio waves on meteoric ionization - II. Solution of the integro-differential equation in case of backscatter

    Science.gov (United States)

    Pecina, P.

    2016-12-01

    The integro-differential equation for the polarization vector P inside the meteor trail, representing the analytical solution of the set of Maxwell equations, is solved for the case of backscattering of radio waves on meteoric ionization. The transversal and longitudinal dimensions of a typical meteor trail are small in comparison to the distances to both transmitter and receiver and so the phase factor appearing in the kernel of the integral equation is large and rapidly changing. This allows us to use the method of stationary phase to obtain an approximate solution of the integral equation for the scattered field and for the corresponding generalized radar equation. The final solution is obtained by expanding it into the complete set of Bessel functions, which results in solving a system of linear algebraic equations for the coefficients of the expansion. The time behaviour of the meteor echoes is then obtained using the generalized radar equation. Examples are given for values of the electron density spanning a range from underdense meteor echoes to overdense meteor echoes. We show that the time behaviour of overdense meteor echoes using this method is very different from the one obtained using purely numerical solutions of the Maxwell equations. Our results are in much better agreement with the observations performed e.g. by the Ondřejov radar.

  3. Multiscale empirical interpolation for solving nonlinear PDEs

    KAUST Repository

    Calo, Victor M.

    2014-12-01

    In this paper, we propose a multiscale empirical interpolation method for solving nonlinear multiscale partial differential equations. The proposed method combines empirical interpolation techniques and local multiscale methods, such as the Generalized Multiscale Finite Element Method (GMsFEM). To solve nonlinear equations, the GMsFEM is used to represent the solution on a coarse grid with multiscale basis functions computed offline. Computing the GMsFEM solution involves calculating the system residuals and Jacobians on the fine grid. We use empirical interpolation concepts to evaluate these residuals and Jacobians of the multiscale system with a computational cost which is proportional to the size of the coarse-scale problem rather than the fully-resolved fine scale one. The empirical interpolation method uses basis functions which are built by sampling the nonlinear function we want to approximate a limited number of times. The coefficients needed for this approximation are computed in the offline stage by inverting an inexpensive linear system. The proposed multiscale empirical interpolation techniques: (1) divide computing the nonlinear function into coarse regions; (2) evaluate contributions of nonlinear functions in each coarse region taking advantage of a reduced-order representation of the solution; and (3) introduce multiscale proper-orthogonal-decomposition techniques to find appropriate interpolation vectors. We demonstrate the effectiveness of the proposed methods on several nonlinear multiscale PDEs that are solved with Newton\\'s methods and fully-implicit time marching schemes. Our numerical results show that the proposed methods provide a robust framework for solving nonlinear multiscale PDEs on a coarse grid with bounded error and significant computational cost reduction.

  4. The method of normal forms for singularly perturbed systems of Fredholm integro-differential equations with rapidly varying kernels

    Energy Technology Data Exchange (ETDEWEB)

    Bobodzhanov, A A; Safonov, V F [National Research University " Moscow Power Engineering Institute" , Moscow (Russian Federation)

    2013-07-31

    The paper deals with extending the Lomov regularization method to classes of singularly perturbed Fredholm-type integro-differential systems, which have not so far been studied. In these the limiting operator is discretely noninvertible. Such systems are commonly known as problems with unstable spectrum. Separating out the essential singularities in the solutions to these problems presents great difficulties. The principal one is to give an adequate description of the singularities induced by 'instability points' of the spectrum. A methodology for separating singularities by using normal forms is developed. It is applied to the above type of systems and is substantiated in these systems. Bibliography: 10 titles.

  5. Application of Reproducing Kernel Method for Solving Nonlinear Fredholm-Volterra Integrodifferential Equations

    Directory of Open Access Journals (Sweden)

    Omar Abu Arqub

    2012-01-01

    Full Text Available This paper investigates the numerical solution of nonlinear Fredholm-Volterra integro-differential equations using reproducing kernel Hilbert space method. The solution ( is represented in the form of series in the reproducing kernel space. In the mean time, the n-term approximate solution ( is obtained and it is proved to converge to the exact solution (. Furthermore, the proposed method has an advantage that it is possible to pick any point in the interval of integration and as well the approximate solution and its derivative will be applicable. Numerical examples are included to demonstrate the accuracy and applicability of the presented technique. The results reveal that the method is very effective and simple.

  6. Optimal Error Estimates of Two Mixed Finite Element Methods for Parabolic Integro-Differential Equations with Nonsmooth Initial Data

    KAUST Repository

    Goswami, Deepjyoti

    2013-05-01

    In the first part of this article, a new mixed method is proposed and analyzed for parabolic integro-differential equations (PIDE) with nonsmooth initial data. Compared to the standard mixed method for PIDE, the present method does not bank on a reformulation using a resolvent operator. Based on energy arguments combined with a repeated use of an integral operator and without using parabolic type duality technique, optimal L2 L2-error estimates are derived for semidiscrete approximations, when the initial condition is in L2 L2. Due to the presence of the integral term, it is, further, observed that a negative norm estimate plays a crucial role in our error analysis. Moreover, the proposed analysis follows the spirit of the proof techniques used in deriving optimal error estimates for finite element approximations to PIDE with smooth data and therefore, it unifies both the theories, i.e., one for smooth data and other for nonsmooth data. Finally, we extend the proposed analysis to the standard mixed method for PIDE with rough initial data and provide an optimal error estimate in L2, L 2, which improves upon the results available in the literature. © 2013 Springer Science+Business Media New York.

  7. Applicability of angular flux discontinuity factor preserving region-wise leakage for integro-differential transport equation

    International Nuclear Information System (INIS)

    Sakamoto, Tatsuya; Endo, Tomohiro; Yamamoto, Akio

    2014-01-01

    In the current core analysis, spatial homogenization is utilized to reduce the computational time. The discontinuity factor (DF) is one of the effective correction factors to reduce spatial homogenization error. The DF in diffusion equation is widely used; on the other hand the DF in transport equation has not been put to practical use although several efforts have been carried out. In this paper, the angular flux discontinuity factor (AFDF) as the DF for the integro-differential transport equation (e.g., the discrete-ordinate method, the method of characteristics) is theoretically described and its applicability is discussed. The AFDF is used to preserve the region-wise neutron leakage at each spatial mesh and defined as a ratio of heterogeneous and homogeneous angular fluxes at the homogenized region surface. In a homogeneous calculation with the AFDF, the angular flux is discontinuous at the region surface. In this paper the applicability of the AFDF to fuel pin cell homogenization is verified for one-dimensional slab geometry. As a result of this verification, it is confirmed that the AFDF has the capability to reduce the spatial homogenization error of fuel pin cell homogenization. (author)

  8. Rapid Fourier space solution of linear partial integro-differential equations in toroidal magnetic confinement geometries

    International Nuclear Information System (INIS)

    McMillan, B.F.; Jolliet, S.; Tran, T.M.; Villard, L.; Bottino, A.; Angelino, P.

    2010-01-01

    Fluctuating quantities in magnetic confinement geometries often inherit a strong anisotropy along the field lines. One technique for describing these structures is the use of a certain set of Fourier components on the tori of nested flux surfaces. We describe an implementation of this approach for solving partial differential equations, like Poisson's equation, where a different set of Fourier components may be chosen on each surface according to the changing safety factor profile. Allowing the resolved components to change to follow the anisotropy significantly reduces the total number of degrees of freedom in the description. This can permit large gains in computational performance. We describe, in particular, how this approach can be applied to rapidly solve the gyrokinetic Poisson equation in a particle code, ORB5 (Jolliet et al. (2007) [5]), with a regular (non-field-aligned) mesh. (authors)

  9. Solution of stochastic nonlinear PDEs using Wiener-Hermite expansion of high orders

    KAUST Repository

    El Beltagy, Mohamed

    2016-01-06

    In this work, the Wiener-Hermite Expansion (WHE) is used to solve stochastic nonlinear PDEs excited with noise. The generation of the equivalent set of deterministic integro-differential equations is automated and hence allows for high order terms of WHE. The automation difficulties are discussed, solved and implemented to output the final system to be solved. A numerical Pikard-like algorithm is suggested to solve the resulting deterministic system. The automated WHE is applied to the 1D diffusion equation and to the heat equation. The results are compared with previous solutions obtained with WHEP (WHE with perturbation) technique. The solution obtained using the suggested WHE technique is shown to be the limit of the WHEP solutions with infinite number of corrections. The automation is extended easily to account for white-noise of higher dimension and for general nonlinear PDEs.

  10. Solution of stochastic nonlinear PDEs using Wiener-Hermite expansion of high orders

    KAUST Repository

    El Beltagy, Mohamed

    2016-01-01

    In this work, the Wiener-Hermite Expansion (WHE) is used to solve stochastic nonlinear PDEs excited with noise. The generation of the equivalent set of deterministic integro-differential equations is automated and hence allows for high order terms of WHE. The automation difficulties are discussed, solved and implemented to output the final system to be solved. A numerical Pikard-like algorithm is suggested to solve the resulting deterministic system. The automated WHE is applied to the 1D diffusion equation and to the heat equation. The results are compared with previous solutions obtained with WHEP (WHE with perturbation) technique. The solution obtained using the suggested WHE technique is shown to be the limit of the WHEP solutions with infinite number of corrections. The automation is extended easily to account for white-noise of higher dimension and for general nonlinear PDEs.

  11. Convergence of hybrid methods for solving non-linear partial ...

    African Journals Online (AJOL)

    This paper is concerned with the numerical solution and convergence analysis of non-linear partial differential equations using a hybrid method. The solution technique involves discretizing the non-linear system of PDE to obtain a corresponding non-linear system of algebraic difference equations to be solved at each time ...

  12. 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 ...

  13. elative controllability of nonlinear neutral Volterra Integrodiferential ...

    African Journals Online (AJOL)

    In this paper we established sufficient conditions for the relative controllability of the nonlinear neutral volterra integro-differential systems with distributed delays in the control. The results were established using the Schauder's fixed point theorem which is an extension of known results. Journal of the Nigerian Association of ...

  14. Solving Nonlinear Partial Differential Equations with Maple and Mathematica

    CERN Document Server

    Shingareva, Inna K

    2011-01-01

    The emphasis of the book is given in how to construct different types of solutions (exact, approximate analytical, numerical, graphical) of numerous nonlinear PDEs correctly, easily, and quickly. The reader can learn a wide variety of techniques and solve numerous nonlinear PDEs included and many other differential equations, simplifying and transforming the equations and solutions, arbitrary functions and parameters, presented in the book). Numerous comparisons and relationships between various types of solutions, different methods and approaches are provided, the results obtained in Maple an

  15. Reproducing Kernel Method for Solving Nonlinear Differential-Difference Equations

    Directory of Open Access Journals (Sweden)

    Reza Mokhtari

    2012-01-01

    Full Text Available On the basis of reproducing kernel Hilbert spaces theory, an iterative algorithm for solving some nonlinear differential-difference equations (NDDEs is presented. The analytical solution is shown in a series form in a reproducing kernel space, and the approximate solution , is constructed by truncating the series to terms. The convergence of , to the analytical solution is also proved. Results obtained by the proposed method imply that it can be considered as a simple and accurate method for solving such differential-difference problems.

  16. New Efficient Fourth Order Method for Solving Nonlinear Equations

    Directory of Open Access Journals (Sweden)

    Farooq Ahmad

    2013-12-01

    Full Text Available In a paper [Appl. Math. Comput., 188 (2 (2007 1587--1591], authors have suggested and analyzed a method for solving nonlinear equations. In the present work, we modified this method by using the finite difference scheme, which has a quintic convergence. We have compared this modified Halley method with some other iterative of fifth-orders convergence methods, which shows that this new method having convergence of fourth order, is efficient.

  17. Improved algorithm for solving nonlinear parabolized stability equations

    Science.gov (United States)

    Zhao, Lei; Zhang, Cun-bo; Liu, Jian-xin; Luo, Ji-sheng

    2016-08-01

    Due to its high computational efficiency and ability to consider nonparallel and nonlinear effects, nonlinear parabolized stability equations (NPSE) approach has been widely used to study the stability and transition mechanisms. However, it often diverges in hypersonic boundary layers when the amplitude of disturbance reaches a certain level. In this study, an improved algorithm for solving NPSE is developed. In this algorithm, the mean flow distortion is included into the linear operator instead of into the nonlinear forcing terms in NPSE. An under-relaxation factor for computing the nonlinear terms is introduced during the iteration process to guarantee the robustness of the algorithm. Two case studies, the nonlinear development of stationary crossflow vortices and the fundamental resonance of the second mode disturbance in hypersonic boundary layers, are presented to validate the proposed algorithm for NPSE. Results from direct numerical simulation (DNS) are regarded as the baseline for comparison. Good agreement can be found between the proposed algorithm and DNS, which indicates the great potential of the proposed method on studying the crossflow and streamwise instability in hypersonic boundary layers. Project supported by the National Natural Science Foundation of China (Grant Nos. 11332007 and 11402167).

  18. Improved algorithm for solving nonlinear parabolized stability equations

    International Nuclear Information System (INIS)

    Zhao Lei; Zhang Cun-bo; Liu Jian-xin; Luo Ji-sheng

    2016-01-01

    Due to its high computational efficiency and ability to consider nonparallel and nonlinear effects, nonlinear parabolized stability equations (NPSE) approach has been widely used to study the stability and transition mechanisms. However, it often diverges in hypersonic boundary layers when the amplitude of disturbance reaches a certain level. In this study, an improved algorithm for solving NPSE is developed. In this algorithm, the mean flow distortion is included into the linear operator instead of into the nonlinear forcing terms in NPSE. An under-relaxation factor for computing the nonlinear terms is introduced during the iteration process to guarantee the robustness of the algorithm. Two case studies, the nonlinear development of stationary crossflow vortices and the fundamental resonance of the second mode disturbance in hypersonic boundary layers, are presented to validate the proposed algorithm for NPSE. Results from direct numerical simulation (DNS) are regarded as the baseline for comparison. Good agreement can be found between the proposed algorithm and DNS, which indicates the great potential of the proposed method on studying the crossflow and streamwise instability in hypersonic boundary layers. (paper)

  19. Taylor's series method for solving the nonlinear point kinetics equations

    International Nuclear Information System (INIS)

    Nahla, Abdallah A.

    2011-01-01

    Highlights: → Taylor's series method for nonlinear point kinetics equations is applied. → The general order of derivatives are derived for this system. → Stability of Taylor's series method is studied. → Taylor's series method is A-stable for negative reactivity. → Taylor's series method is an accurate computational technique. - Abstract: Taylor's series method for solving the point reactor kinetics equations with multi-group of delayed neutrons in the presence of Newtonian temperature feedback reactivity is applied and programmed by FORTRAN. This system is the couples of the stiff nonlinear ordinary differential equations. This numerical method is based on the different order derivatives of the neutron density, the precursor concentrations of i-group of delayed neutrons and the reactivity. The r th order of derivatives are derived. The stability of Taylor's series method is discussed. Three sets of applications: step, ramp and temperature feedback reactivities are computed. Taylor's series method is an accurate computational technique and stable for negative step, negative ramp and temperature feedback reactivities. This method is useful than the traditional methods for solving the nonlinear point kinetics equations.

  20. SOLVING NONLINEAR KLEIN-GORDON EQUATION WITH A QUADRATIC NONLINEAR TERM USING HOMOTOPY ANALYSIS METHOD

    Directory of Open Access Journals (Sweden)

    H. Jafari

    2010-07-01

    Full Text Available In this paper, nonlinear Klein-Gordon equation with quadratic term is solved by means of an analytic technique, namely the Homotopy analysis method (HAM.Comparisons are made between the Adomian decomposition method (ADM, the exact solution and homotopy analysis method. The results reveal that the proposed method is very effective and simple.

  1. Solving nonlinear evolution equation system using two different methods

    Science.gov (United States)

    Kaplan, Melike; Bekir, Ahmet; Ozer, Mehmet N.

    2015-12-01

    This paper deals with constructing more general exact solutions of the coupled Higgs equation by using the (G0/G, 1/G)-expansion and (1/G0)-expansion methods. The obtained solutions are expressed by three types of functions: hyperbolic, trigonometric and rational functions with free parameters. It has been shown that the suggested methods are productive and will be used to solve nonlinear partial differential equations in applied mathematics and engineering. Throughout the paper, all the calculations are made with the aid of the Maple software.

  2. Various Newton-type iterative methods for solving nonlinear equations

    Directory of Open Access Journals (Sweden)

    Manoj Kumar

    2013-10-01

    Full Text Available The aim of the present paper is to introduce and investigate new ninth and seventh order convergent Newton-type iterative methods for solving nonlinear equations. The ninth order convergent Newton-type iterative method is made derivative free to obtain seventh-order convergent Newton-type iterative method. These new with and without derivative methods have efficiency indices 1.5518 and 1.6266, respectively. The error equations are used to establish the order of convergence of these proposed iterative methods. Finally, various numerical comparisons are implemented by MATLAB to demonstrate the performance of the developed methods.

  3. The H-N method for solving linear transport equation: theory and application

    International Nuclear Information System (INIS)

    Kaskas, A.; Gulecyuz, M.C.; Tezcan, C.

    2002-01-01

    The system of singular integral equation which is obtained from the integro-differential form of the linear transport equation as a result of Placzec lemma is solved. Application are given using the exit distributions and the infinite medium Green's function. The same theoretical results are also obtained with the use of the singular eigenfunction of the method of elementary solutions

  4. Superconvergence of Finite Element Approximations to Parabolic and Hyperbolic Integro-Differential Equations%抛物型和双曲型积分-微分方程有限元逼近的超收敛性质

    Institute of Scientific and Technical Information of China (English)

    张铁; 李长军

    2001-01-01

    The object of this paper is to investigate the superconvergence properties of finite element approximations to parabolic and hyperbolic integro-differential equations. The quasi projection technique introduced earlier by Douglas et al. is developed to derive the O(h2r) order knot superconvergence in the case of a single space variable, and to show the optimal order negative norm estimates in the case of several space variables.

  5. Development and Retrospective Clinical Assessment of a Patient-Specific Closed-Form Integro-Differential Equation Model of Plasma Dilution.

    Science.gov (United States)

    Atlas, Glen; Li, John K-J; Amin, Shawn; Hahn, Robert G

    2017-01-01

    A closed-form integro-differential equation (IDE) model of plasma dilution (PD) has been derived which represents both the intravenous (IV) infusion of crystalloid and the postinfusion period. Specifically, PD is mathematically represented using a combination of constant ratio, differential, and integral components. Furthermore, this model has successfully been applied to preexisting data, from a prior human study, in which crystalloid was infused for a period of 30 minutes at the beginning of thyroid surgery. Using Euler's formula and a Laplace transform solution to the IDE, patients could be divided into two distinct groups based on their response to PD during the infusion period. Explicitly, Group 1 patients had an infusion-based PD response which was modeled using an exponentially decaying hyperbolic sine function, whereas Group 2 patients had an infusion-based PD response which was modeled using an exponentially decaying trigonometric sine function. Both Group 1 and Group 2 patients had postinfusion PD responses which were modeled using the same combination of hyperbolic sine and hyperbolic cosine functions. Statistically significant differences, between Groups 1 and 2, were noted with respect to the area under their PD curves during both the infusion and postinfusion periods. Specifically, Group 2 patients exhibited a response to PD which was most likely consistent with a preoperative hypovolemia. Overall, this IDE model of PD appears to be highly "adaptable" and successfully fits clinically-obtained human data on a patient-specific basis, during both the infusion and postinfusion periods. In addition, patient-specific IDE modeling of PD may be a useful adjunct in perioperative fluid management and in assessing clinical volume kinetics, of crystalloid solutions, in real time.

  6. On choosing a nonlinear initial iterate for solving the 2-D 3-T heat conduction equations

    International Nuclear Information System (INIS)

    An Hengbin; Mo Zeyao; Xu Xiaowen; Liu Xu

    2009-01-01

    The 2-D 3-T heat conduction equations can be used to approximately describe the energy broadcast in materials and the energy swapping between electron and photon or ion. To solve the equations, a fully implicit finite volume scheme is often used as the discretization method. Because the energy diffusion and swapping coefficients have a strongly nonlinear dependence on the temperature, and some physical parameters are discontinuous across the interfaces between the materials, it is a challenge to solve the discretized nonlinear algebraic equations. Particularly, as time advances, the temperature varies so greatly in the front of energy that it is difficult to choose an effective initial iterate when the nonlinear algebraic equations are solved by an iterative method. In this paper, a method of choosing a nonlinear initial iterate is proposed for iterative solving this kind of nonlinear algebraic equations. Numerical results show the proposed initial iterate can improve the computational efficiency, and also the convergence behavior of the nonlinear iteration.

  7. Solving eigenvalue response matrix equations with nonlinear techniques

    International Nuclear Information System (INIS)

    Roberts, Jeremy A.; Forget, Benoit

    2014-01-01

    Highlights: • High performance solvers were applied within ERMM for the first time. • Accelerated fixed-point methods were developed that reduce computational times by 2–3. • A nonlinear, Newton-based ERMM led to similar improvement and more robustness. • A 3-D, SN-based ERMM shows how ERMM can apply fine-mesh methods to full-core analysis. - Abstract: This paper presents new algorithms for use in the eigenvalue response matrix method (ERMM) for reactor eigenvalue problems. ERMM spatially decomposes a domain into independent nodes linked via boundary conditions approximated as truncated orthogonal expansions, the coefficients of which are response functions. In its simplest form, ERMM consists of a two-level eigenproblem: an outer Picard iteration updates the k-eigenvalue via balance, while the inner λ-eigenproblem imposes neutron balance between nodes. Efficient methods are developed for solving the inner λ-eigenvalue problem within the outer Picard iteration. Based on results from several diffusion and transport benchmark models, it was found that the Krylov–Schur method applied to the λ-eigenvalue problem reduces Picard solver times (excluding response generation) by a factor of 2–5. Furthermore, alternative methods, including Picard acceleration schemes, Steffensen’s method, and Newton’s method, are developed in this paper. These approaches often yield faster k-convergence and a need for fewer k-dependent response function evaluations, which is important because response generation is often the primary cost for problems using responses computed online (i.e., not from a precomputed database). Accelerated Picard iteration was found to reduce total computational times by 2–3 compared to the unaccelerated case for problems dominated by response generation. In addition, Newton’s method was found to provide nearly the same performance with improved robustness

  8. Auxiliary equation method for solving nonlinear partial differential equations

    International Nuclear Information System (INIS)

    Sirendaoreji,; Jiong, Sun

    2003-01-01

    By using the solutions of an auxiliary ordinary differential equation, a direct algebraic method is described to construct several kinds of exact travelling wave solutions for some nonlinear partial differential equations. By this method some physically important nonlinear equations are investigated and new exact travelling wave solutions are explicitly obtained with the aid of symbolic computation

  9. Integral transform method for solving time fractional systems and fractional heat equation

    Directory of Open Access Journals (Sweden)

    Arman Aghili

    2014-01-01

    Full Text Available In the present paper, time fractional partial differential equation is considered, where the fractional derivative is defined in the Caputo sense. Laplace transform method has been applied to obtain an exact solution. The authors solved certain homogeneous and nonhomogeneous time fractional heat equations using integral transform. Transform method is a powerful tool for solving fractional singular Integro - differential equations and PDEs. The result reveals that the transform method is very convenient and effective.

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

    Indian Academy of Sciences (India)

    2013-12-01

    Dec 1, 2013 ... 1School of Mathematics and Applied Statistics, University of Wollongong, Wollongong,. NSW 2522 ... the nonlinear phenomena as well as their further applications in the real-life situations, it is ... concentration gradient. Thus ...

  11. Numerical treatments for solving nonlinear mixed integral equation

    Directory of Open Access Journals (Sweden)

    M.A. Abdou

    2016-12-01

    Full Text Available We consider a mixed type of nonlinear integral equation (MNLIE of the second kind in the space C[0,T]×L2(Ω,T<1. The Volterra integral terms (VITs are considered in time with continuous kernels, while the Fredholm integral term (FIT is considered in position with singular general kernel. Using the quadratic method and separation of variables method, we obtain a nonlinear system of Fredholm integral equations (NLSFIEs with singular kernel. A Toeplitz matrix method, in each case, is then used to obtain a nonlinear algebraic system. Numerical results are calculated when the kernels take a logarithmic form or Carleman function. Moreover, the error estimates, in each case, are then computed.

  12. Projection-iteration methods for solving nonlinear operator equations

    International Nuclear Information System (INIS)

    Nguyen Minh Chuong; Tran thi Lan Anh; Tran Quoc Binh

    1989-09-01

    In this paper, the authors investigate a nonlinear operator equation in uniformly convex Banach spaces as in metric spaces by using stationary and nonstationary generalized projection-iteration methods. Convergence theorems in the strong and weak sense were established. (author). 7 refs

  13. Application of the trial equation method for solving some nonlinear ...

    Indian Academy of Sciences (India)

    Therefore, our aim is just to find the function F. Liu has obtained a number of exact solutions to many nonlinear differential equations when F(u) is a polynomial or a rational function. ... In this study, we apply the trial equation method to seek exact solutions of the ... twice and setting the integration constant to zero, we have.

  14. Sufficient Descent Conjugate Gradient Methods for Solving Convex Constrained Nonlinear Monotone Equations

    Directory of Open Access Journals (Sweden)

    San-Yang Liu

    2014-01-01

    Full Text Available Two unified frameworks of some sufficient descent conjugate gradient methods are considered. Combined with the hyperplane projection method of Solodov and Svaiter, they are extended to solve convex constrained nonlinear monotone equations. Their global convergence is proven under some mild conditions. Numerical results illustrate that these methods are efficient and can be applied to solve large-scale nonsmooth equations.

  15. A New Numerical Technique for Solving Systems Of Nonlinear Fractional Partial Differential Equations

    Directory of Open Access Journals (Sweden)

    Mountassir Hamdi Cherif

    2017-11-01

    Full Text Available In this paper, we apply an efficient method called the Aboodh decomposition method to solve systems of nonlinear fractional partial differential equations. This method is a combined form of Aboodh transform with Adomian decomposition method. The theoretical analysis of this investigated for systems of nonlinear fractional partial differential equations is calculated in the explicit form of a power series with easily computable terms. Some examples are given to shows that this method is very efficient and accurate. This method can be applied to solve others nonlinear systems problems.

  16. Nonlinear evolution equations and solving algebraic systems: the importance of computer algebra

    International Nuclear Information System (INIS)

    Gerdt, V.P.; Kostov, N.A.

    1989-01-01

    In the present paper we study the application of computer algebra to solve the nonlinear polynomial systems which arise in investigation of nonlinear evolution equations. We consider several systems which are obtained in classification of integrable nonlinear evolution equations with uniform rank. Other polynomial systems are related with the finding of algebraic curves for finite-gap elliptic potentials of Lame type and generalizations. All systems under consideration are solved using the method based on construction of the Groebner basis for corresponding polynomial ideals. The computations have been carried out using computer algebra systems. 20 refs

  17. Eddy current modeling in linear and nonlinear multifilamentary composite materials

    Science.gov (United States)

    Menana, Hocine; Farhat, Mohamad; Hinaje, Melika; Berger, Kevin; Douine, Bruno; Lévêque, Jean

    2018-04-01

    In this work, a numerical model is developed for a rapid computation of eddy currents in composite materials, adaptable for both carbon fiber reinforced polymers (CFRPs) for NDT applications and multifilamentary high temperature superconductive (HTS) tapes for AC loss evaluation. The proposed model is based on an integro-differential formulation in terms of the electric vector potential in the frequency domain. The high anisotropy and the nonlinearity of the considered materials are easily handled in the frequency domain.

  18. An Efficient Numerical Approach for Solving Nonlinear Coupled Hyperbolic Partial Differential Equations with Nonlocal Conditions

    Directory of Open Access Journals (Sweden)

    A. H. Bhrawy

    2014-01-01

    Full Text Available One of the most important advantages of collocation method is the possibility of dealing with nonlinear partial differential equations (PDEs as well as PDEs with variable coefficients. A numerical solution based on a Jacobi collocation method is extended to solve nonlinear coupled hyperbolic PDEs with variable coefficients subject to initial-boundary nonlocal conservation conditions. This approach, based on Jacobi polynomials and Gauss-Lobatto quadrature integration, reduces solving the nonlinear coupled hyperbolic PDEs with variable coefficients to a system of nonlinear ordinary differential equation which is far easier to solve. In fact, we deal with initial-boundary coupled hyperbolic PDEs with variable coefficients as well as initial-nonlocal conditions. Using triangular, soliton, and exponential-triangular solutions as exact solutions, the obtained results show that the proposed numerical algorithm is efficient and very accurate.

  19. Stability analysis of solutions to nonlinear stiff Volterra functional differential equations in Banach spaces

    Institute of Scientific and Technical Information of China (English)

    LI Shoufu

    2005-01-01

    A series of stability, contractivity and asymptotic stability results of the solutions to nonlinear stiff Volterra functional differential equations (VFDEs) in Banach spaces is obtained, which provides the unified theoretical foundation for the stability analysis of solutions to nonlinear stiff problems in ordinary differential equations(ODEs), delay differential equations(DDEs), integro-differential equations(IDEs) and VFDEs of other type which appear in practice.

  20. Solving Large Scale Nonlinear Eigenvalue Problem in Next-Generation Accelerator Design

    Energy Technology Data Exchange (ETDEWEB)

    Liao, Ben-Shan; Bai, Zhaojun; /UC, Davis; Lee, Lie-Quan; Ko, Kwok; /SLAC

    2006-09-28

    A number of numerical methods, including inverse iteration, method of successive linear problem and nonlinear Arnoldi algorithm, are studied in this paper to solve a large scale nonlinear eigenvalue problem arising from finite element analysis of resonant frequencies and external Q{sub e} values of a waveguide loaded cavity in the next-generation accelerator design. They present a nonlinear Rayleigh-Ritz iterative projection algorithm, NRRIT in short and demonstrate that it is the most promising approach for a model scale cavity design. The NRRIT algorithm is an extension of the nonlinear Arnoldi algorithm due to Voss. Computational challenges of solving such a nonlinear eigenvalue problem for a full scale cavity design are outlined.

  1. Computer programs for solving systems of nonlinear equations

    International Nuclear Information System (INIS)

    Asaoka, Takumi

    1978-03-01

    Computer programs to find a solution, usually the one closest to some guess, of a system of simultaneous nonlinear equations are provided for real functions of the real arguments. These are based on quasi-Newton methods or projection methods, which are briefly reviewed in the present report. Benchmark tests were performed on these subroutines to grasp their characteristics. As the program not requiring analytical forms of the derivatives of the Jacobian matrix, we have dealt with NS01A of Powell, NS03A of Reid for a system with the sparse Jacobian and NONLIN of Brown. Of these three subroutines of quasi-Newton methods, NONLIN is shown to be the most useful because of its stable algorithm and short computation time. On the other hand, as the subroutine for which the derivatives of the Jacobian are to be supplied analytically, we have tested INTECH of a quasi-Newton method based on the Boggs' algorithm, PROJA of Georg and Keller based on the projection method and an option of NS03A. The results have shown that INTECH, treating variables which appear only linearly in the functions separately, takes the shortest computation time, on the whole, while the projection method requires further research to find an optimal algorithm. (auth.)

  2. Multivariate Padé Approximation for Solving Nonlinear Partial Differential Equations of Fractional Order

    Directory of Open Access Journals (Sweden)

    Veyis Turut

    2013-01-01

    Full Text Available Two tecHniques were implemented, the Adomian decomposition method (ADM and multivariate Padé approximation (MPA, for solving nonlinear partial differential equations of fractional order. The fractional derivatives are described in Caputo sense. First, the fractional differential equation has been solved and converted to power series by Adomian decomposition method (ADM, then power series solution of fractional differential equation was put into multivariate Padé series. Finally, numerical results were compared and presented in tables and figures.

  3. The Convergence Study of the Homotopy Analysis Method for Solving Nonlinear Volterra-Fredholm Integrodifferential Equations

    Directory of Open Access Journals (Sweden)

    Behzad Ghanbari

    2014-01-01

    Full Text Available We aim to study the convergence of the homotopy analysis method (HAM in short for solving special nonlinear Volterra-Fredholm integrodifferential equations. The sufficient condition for the convergence of the method is briefly addressed. Some illustrative examples are also presented to demonstrate the validity and applicability of the technique. Comparison of the obtained results HAM with exact solution shows that the method is reliable and capable of providing analytic treatment for solving such equations.

  4. Solving Nonlinear Fractional Differential Equation by Generalized Mittag-Leffler Function Method

    Science.gov (United States)

    Arafa, A. A. M.; Rida, S. Z.; Mohammadein, A. A.; Ali, H. M.

    2013-06-01

    In this paper, we use Mittag—Leffler function method for solving some nonlinear fractional differential equations. A new solution is constructed in power series. The fractional derivatives are described by Caputo's sense. To illustrate the reliability of the method, some examples are provided.

  5. 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.

  6. 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...

  7. Iterative Adaptive Dynamic Programming for Solving Unknown Nonlinear Zero-Sum Game Based on Online Data.

    Science.gov (United States)

    Zhu, Yuanheng; Zhao, Dongbin; Li, Xiangjun

    2017-03-01

    H ∞ control is a powerful method to solve the disturbance attenuation problems that occur in some control systems. The design of such controllers relies on solving the zero-sum game (ZSG). But in practical applications, the exact dynamics is mostly unknown. Identification of dynamics also produces errors that are detrimental to the control performance. To overcome this problem, an iterative adaptive dynamic programming algorithm is proposed in this paper to solve the continuous-time, unknown nonlinear ZSG with only online data. A model-free approach to the Hamilton-Jacobi-Isaacs equation is developed based on the policy iteration method. Control and disturbance policies and value are approximated by neural networks (NNs) under the critic-actor-disturber structure. The NN weights are solved by the least-squares method. According to the theoretical analysis, our algorithm is equivalent to a Gauss-Newton method solving an optimization problem, and it converges uniformly to the optimal solution. The online data can also be used repeatedly, which is highly efficient. Simulation results demonstrate its feasibility to solve the unknown nonlinear ZSG. When compared with other algorithms, it saves a significant amount of online measurement time.

  8. Derivative free Davidon-Fletcher-Powell (DFP) for solving symmetric systems of nonlinear equations

    Science.gov (United States)

    Mamat, M.; Dauda, M. K.; Mohamed, M. A. bin; Waziri, M. Y.; Mohamad, F. S.; Abdullah, H.

    2018-03-01

    Research from the work of engineers, economist, modelling, industry, computing, and scientist are mostly nonlinear equations in nature. Numerical solution to such systems is widely applied in those areas of mathematics. Over the years, there has been significant theoretical study to develop methods for solving such systems, despite these efforts, unfortunately the methods developed do have deficiency. In a contribution to solve systems of the form F(x) = 0, x ∈ Rn , a derivative free method via the classical Davidon-Fletcher-Powell (DFP) update is presented. This is achieved by simply approximating the inverse Hessian matrix with {Q}k+1-1 to θkI. The modified method satisfied the descent condition and possess local superlinear convergence properties. Interestingly, without computing any derivative, the proposed method never fail to converge throughout the numerical experiments. The output is based on number of iterations and CPU time, different initial starting points were used on a solve 40 benchmark test problems. With the aid of the squared norm merit function and derivative-free line search technique, the approach yield a method of solving symmetric systems of nonlinear equations that is capable of significantly reducing the CPU time and number of iteration, as compared to its counterparts. A comparison between the proposed method and classical DFP update were made and found that the proposed methodis the top performer and outperformed the existing method in almost all the cases. In terms of number of iterations, out of the 40 problems solved, the proposed method solved 38 successfully, (95%) while classical DFP solved 2 problems (i.e. 05%). In terms of CPU time, the proposed method solved 29 out of the 40 problems given, (i.e.72.5%) successfully whereas classical DFP solves 11 (27.5%). The method is valid in terms of derivation, reliable in terms of number of iterations and accurate in terms of CPU time. Thus, suitable and achived the objective.

  9. Direct method of solving finite difference nonlinear equations for multicomponent diffusion in a gas centrifuge

    International Nuclear Information System (INIS)

    Potemki, Valeri G.; Borisevich, Valentine D.; Yupatov, Sergei V.

    1996-01-01

    This paper describes the the next evolution step in development of the direct method for solving systems of Nonlinear Algebraic Equations (SNAE). These equations arise from the finite difference approximation of original nonlinear partial differential equations (PDE). This method has been extended on the SNAE with three variables. The solving SNAE bases on Reiterating General Singular Value Decomposition of rectangular matrix pencils (RGSVD-algorithm). In contrast to the computer algebra algorithm in integer arithmetic based on the reduction to the Groebner's basis that algorithm is working in floating point arithmetic and realizes the reduction to the Kronecker's form. The possibilities of the method are illustrated on the example of solving the one-dimensional diffusion equation for 3-component model isotope mixture in a ga centrifuge. The implicit scheme for the finite difference equations without simplifying the nonlinear properties of the original equations is realized. The technique offered provides convergence to the solution for the single run. The Toolbox SNAE is developed in the framework of the high performance numeric computation and visualization software MATLAB. It includes more than 30 modules in MATLAB language for solving SNAE with two and three variables. (author)

  10. A Time Marching Scheme for Solving Volume Integral Equations on Nonlinear Scatterers

    KAUST Repository

    Bagci, Hakan

    2015-01-01

    Transient electromagnetic field interactions on inhomogeneous penetrable scatterers can be analyzed by solving time domain volume integral equations (TDVIEs). TDVIEs are oftentimes solved using marchingon-in-time (MOT) schemes. Unlike finite difference and finite element schemes, MOT-TDVIE solvers require discretization of only the scatterers, do not call for artificial absorbing boundary conditions, and are more robust to numerical phase dispersion. On the other hand, their computational cost is high, they suffer from late-time instabilities, and their implicit nature makes incorporation of nonlinear constitutive relations more difficult. Development of plane-wave time-domain (PWTD) and FFT-based schemes has significantly reduced the computational cost of the MOT-TDVIE solvers. Additionally, latetime instability problem has been alleviated for all practical purposes with the development of accurate integration schemes and specially designed temporal basis functions. Addressing the third challenge is the topic of this presentation. I will talk about an explicit MOT scheme developed for solving the TDVIE on scatterers with nonlinear material properties. The proposed scheme separately discretizes the TDVIE and the nonlinear constitutive relation between electric field intensity and flux density. The unknown field intensity and flux density are expanded using half and full Schaubert-Wilton-Glisson (SWG) basis functions in space and polynomial temporal interpolators in time. The resulting coupled system of the discretized TDVIE and constitutive relation is integrated in time using an explicit P E(CE) m scheme to yield the unknown expansion coefficients. Explicitness of time marching allows for straightforward incorporation of the nonlinearity as a function evaluation on the right hand side of the coupled system of equations. Consequently, the resulting MOT scheme does not call for a Newton-like nonlinear solver. Numerical examples, which demonstrate the applicability

  11. A Time Marching Scheme for Solving Volume Integral Equations on Nonlinear Scatterers

    KAUST Repository

    Bagci, Hakan

    2015-01-07

    Transient electromagnetic field interactions on inhomogeneous penetrable scatterers can be analyzed by solving time domain volume integral equations (TDVIEs). TDVIEs are oftentimes solved using marchingon-in-time (MOT) schemes. Unlike finite difference and finite element schemes, MOT-TDVIE solvers require discretization of only the scatterers, do not call for artificial absorbing boundary conditions, and are more robust to numerical phase dispersion. On the other hand, their computational cost is high, they suffer from late-time instabilities, and their implicit nature makes incorporation of nonlinear constitutive relations more difficult. Development of plane-wave time-domain (PWTD) and FFT-based schemes has significantly reduced the computational cost of the MOT-TDVIE solvers. Additionally, latetime instability problem has been alleviated for all practical purposes with the development of accurate integration schemes and specially designed temporal basis functions. Addressing the third challenge is the topic of this presentation. I will talk about an explicit MOT scheme developed for solving the TDVIE on scatterers with nonlinear material properties. The proposed scheme separately discretizes the TDVIE and the nonlinear constitutive relation between electric field intensity and flux density. The unknown field intensity and flux density are expanded using half and full Schaubert-Wilton-Glisson (SWG) basis functions in space and polynomial temporal interpolators in time. The resulting coupled system of the discretized TDVIE and constitutive relation is integrated in time using an explicit P E(CE) m scheme to yield the unknown expansion coefficients. Explicitness of time marching allows for straightforward incorporation of the nonlinearity as a function evaluation on the right hand side of the coupled system of equations. Consequently, the resulting MOT scheme does not call for a Newton-like nonlinear solver. Numerical examples, which demonstrate the applicability

  12. Pseudo-transient Continuation Based Variable Relaxation Solve in Nonlinear Magnetohydrodynamic Simulations

    Energy Technology Data Exchange (ETDEWEB)

    Jin Chen

    2009-12-07

    Efficient and robust Variable Relaxation Solver, based on pseudo-transient continuation, is developed to solve nonlinear anisotropic thermal conduction arising from fusion plasma simulations. By adding first and/or second order artificial time derivatives to the system, this type of method advances the resulting time-dependent nonlinear PDEs to steady state, which is the solution to be sought. In this process, only the stiffness matrix itself is involved so that the numerical complexity and errors can be greatly reduced. In fact, this work is an extension of integrating efficient linear elliptic solvers for fusion simulation on Cray XIE. Two schemes are derived in this work, first and second order Variable Relaxations. Four factors are observed to be critical for efficiency and preservation of solution's symmetric structure arising from periodic boundary condition: refining meshes in different coordinate directions, initializing nonlinear process, varying time steps in both temporal and spatial directions, and accurately generating nonlinear stiffness matrix. First finer mesh scale should be taken in strong transport direction; Next the system is carefully initialized by the solution with linear conductivity; Third, time step and relaxation factor are vertex-based varied and optimized at each time step; Finally, the nonlinear stiffness matrix is updated by just scaling corresponding linear one with the vector generated from nonlinear thermal conductivity.

  13. Pseudo-transient Continuation Based Variable Relaxation Solve in Nonlinear Magnetohydrodynamic Simulations

    International Nuclear Information System (INIS)

    Chen, Jin

    2009-01-01

    Efficient and robust Variable Relaxation Solver, based on pseudo-transient continuation, is developed to solve nonlinear anisotropic thermal conduction arising from fusion plasma simulations. By adding first and/or second order artificial time derivatives to the system, this type of method advances the resulting time-dependent nonlinear PDEs to steady state, which is the solution to be sought. In this process, only the stiffness matrix itself is involved so that the numerical complexity and errors can be greatly reduced. In fact, this work is an extension of integrating efficient linear elliptic solvers for fusion simulation on Cray XIE. Two schemes are derived in this work, first and second order Variable Relaxations. Four factors are observed to be critical for efficiency and preservation of solution's symmetric structure arising from periodic boundary condition: refining meshes in different coordinate directions, initializing nonlinear process, varying time steps in both temporal and spatial directions, and accurately generating nonlinear stiffness matrix. First finer mesh scale should be taken in strong transport direction; Next the system is carefully initialized by the solution with linear conductivity; Third, time step and relaxation factor are vertex-based varied and optimized at each time step; Finally, the nonlinear stiffness matrix is updated by just scaling corresponding linear one with the vector generated from nonlinear thermal conductivity.

  14. Solving nonlinear, High-order partial differential equations using a high-performance isogeometric analysis framework

    KAUST Repository

    Cortes, Adriano Mauricio; Vignal, Philippe; Sarmiento, Adel; Garcí a, Daniel O.; Collier, Nathan; Dalcin, Lisandro; Calo, Victor M.

    2014-01-01

    In this paper we present PetIGA, a high-performance implementation of Isogeometric Analysis built on top of PETSc. We show its use in solving nonlinear and time-dependent problems, such as phase-field models, by taking advantage of the high-continuity of the basis functions granted by the isogeometric framework. In this work, we focus on the Cahn-Hilliard equation and the phase-field crystal equation.

  15. A semi-analytical approach for solving of nonlinear systems of functional differential equations with delay

    Science.gov (United States)

    Rebenda, Josef; Šmarda, Zdeněk

    2017-07-01

    In the paper, we propose a correct and efficient semi-analytical approach to solve initial value problem for systems of functional differential equations with delay. The idea is to combine the method of steps and differential transformation method (DTM). In the latter, formulas for proportional arguments and nonlinear terms are used. An example of using this technique for a system with constant and proportional delays is presented.

  16. Iterative Methods for Solving Nonlinear Parabolic Problem in Pension Saving Management

    Science.gov (United States)

    Koleva, M. N.

    2011-11-01

    In this work we consider a nonlinear parabolic equation, obtained from Riccati like transformation of the Hamilton-Jacobi-Bellman equation, arising in pension saving management. We discuss two numerical iterative methods for solving the model problem—fully implicit Picard method and mixed Picard-Newton method, which preserves the parabolic characteristics of the differential problem. Numerical experiments for comparison the accuracy and effectiveness of the algorithms are discussed. Finally, observations are given.

  17. On Newton-Kantorovich Method for Solving the Nonlinear Operator Equation

    Directory of Open Access Journals (Sweden)

    Hameed Husam Hameed

    2015-01-01

    Full Text Available We develop the Newton-Kantorovich method to solve the system of 2×2 nonlinear Volterra integral equations where the unknown function is in logarithmic form. A new majorant function is introduced which leads to the increment of the convergence interval. The existence and uniqueness of approximate solution are proved and a numerical example is provided to show the validation of the method.

  18. An explicit MOT scheme for solving the TD-EFVIE on nonlinear and dispersive scatterers

    KAUST Repository

    Sayed, Sadeed Bin; Ulku, H. Arda; Bagci, Hakan

    2017-01-01

    An explicit marching-on-in-time (MOT) scheme for solving the time domain electric field volume integral equation (TD-EFVIE) on nonlinear and dispersive scatterers is described. The unknown electric field intensity, electric flux density, and polarization densities representing Kerr nonlinearity along with Lorentz dispersion relation, all of which are induced inside the scatterer upon excitation, are expanded using half and full Schaubert-Wilton-Glisson functions in space. The TD-EFVIE and the constitutive relations between polarization, field, and flux terms are cast in the form of a first-order ordinary differential equation. The resulting matrix system is integrated in time using a predictor-corrector scheme to obtain the time dependent unknown expansion coefficients. The resulting MOT scheme is explicit and accounts for nonlinearity by simple function evaluations.

  19. An explicit MOT scheme for solving the TD-EFVIE on nonlinear and dispersive scatterers

    KAUST Repository

    Sayed, Sadeed Bin

    2017-10-25

    An explicit marching-on-in-time (MOT) scheme for solving the time domain electric field volume integral equation (TD-EFVIE) on nonlinear and dispersive scatterers is described. The unknown electric field intensity, electric flux density, and polarization densities representing Kerr nonlinearity along with Lorentz dispersion relation, all of which are induced inside the scatterer upon excitation, are expanded using half and full Schaubert-Wilton-Glisson functions in space. The TD-EFVIE and the constitutive relations between polarization, field, and flux terms are cast in the form of a first-order ordinary differential equation. The resulting matrix system is integrated in time using a predictor-corrector scheme to obtain the time dependent unknown expansion coefficients. The resulting MOT scheme is explicit and accounts for nonlinearity by simple function evaluations.

  20. On multilevel RBF collocation to solve nonlinear PDEs arising from endogenous stochastic volatility models

    Science.gov (United States)

    Bastani, Ali Foroush; Dastgerdi, Maryam Vahid; Mighani, Abolfazl

    2018-06-01

    The main aim of this paper is the analytical and numerical study of a time-dependent second-order nonlinear partial differential equation (PDE) arising from the endogenous stochastic volatility model, introduced in [Bensoussan, A., Crouhy, M. and Galai, D., Stochastic equity volatility related to the leverage effect (I): equity volatility behavior. Applied Mathematical Finance, 1, 63-85, 1994]. As the first step, we derive a consistent set of initial and boundary conditions to complement the PDE, when the firm is financed by equity and debt. In the sequel, we propose a Newton-based iteration scheme for nonlinear parabolic PDEs which is an extension of a method for solving elliptic partial differential equations introduced in [Fasshauer, G. E., Newton iteration with multiquadrics for the solution of nonlinear PDEs. Computers and Mathematics with Applications, 43, 423-438, 2002]. The scheme is based on multilevel collocation using radial basis functions (RBFs) to solve the resulting locally linearized elliptic PDEs obtained at each level of the Newton iteration. We show the effectiveness of the resulting framework by solving a prototypical example from the field and compare the results with those obtained from three different techniques: (1) a finite difference discretization; (2) a naive RBF collocation and (3) a benchmark approximation, introduced for the first time in this paper. The numerical results confirm the robustness, higher convergence rate and good stability properties of the proposed scheme compared to other alternatives. We also comment on some possible research directions in this field.

  1. TENSOLVE: A software package for solving systems of nonlinear equations and nonlinear least squares problems using tensor methods

    Energy Technology Data Exchange (ETDEWEB)

    Bouaricha, A. [Argonne National Lab., IL (United States). Mathematics and Computer Science Div.; Schnabel, R.B. [Colorado Univ., Boulder, CO (United States). Dept. of Computer Science

    1996-12-31

    This paper describes a modular software package for solving systems of nonlinear equations and nonlinear least squares problems, using a new class of methods called tensor methods. It is intended for small to medium-sized problems, say with up to 100 equations and unknowns, in cases where it is reasonable to calculate the Jacobian matrix or approximate it by finite differences at each iteration. The software allows the user to select between a tensor method and a standard method based upon a linear model. The tensor method models F({ital x}) by a quadratic model, where the second-order term is chosen so that the model is hardly more expensive to form, store, or solve than the standard linear model. Moreover, the software provides two different global strategies, a line search and a two- dimensional trust region approach. Test results indicate that, in general, tensor methods are significantly more efficient and robust than standard methods on small and medium-sized problems in iterations and function evaluations.

  2. Modified multiple time scale method for solving strongly nonlinear damped forced vibration systems

    Science.gov (United States)

    Razzak, M. A.; Alam, M. Z.; Sharif, M. N.

    2018-03-01

    In this paper, modified multiple time scale (MTS) method is employed to solve strongly nonlinear forced vibration systems. The first-order approximation is only considered in order to avoid complexicity. The formulations and the determination of the solution procedure are very easy and straightforward. The classical multiple time scale (MS) and multiple scales Lindstedt-Poincare method (MSLP) do not give desire result for the strongly damped forced vibration systems with strong damping effects. The main aim of this paper is to remove these limitations. Two examples are considered to illustrate the effectiveness and convenience of the present procedure. The approximate external frequencies and the corresponding approximate solutions are determined by the present method. The results give good coincidence with corresponding numerical solution (considered to be exact) and also provide better result than other existing results. For weak nonlinearities with weak damping effect, the absolute relative error measures (first-order approximate external frequency) in this paper is only 0.07% when amplitude A = 1.5 , while the relative error gives MSLP method is surprisingly 28.81%. Furthermore, for strong nonlinearities with strong damping effect, the absolute relative error found in this article is only 0.02%, whereas the relative error obtained by MSLP method is 24.18%. Therefore, the present method is not only valid for weakly nonlinear damped forced systems, but also gives better result for strongly nonlinear systems with both small and strong damping effect.

  3. A multiple-scale power series method for solving nonlinear ordinary differential equations

    Directory of Open Access Journals (Sweden)

    Chein-Shan Liu

    2016-02-01

    Full Text Available The power series solution is a cheap and effective method to solve nonlinear problems, like the Duffing-van der Pol oscillator, the Volterra population model and the nonlinear boundary value problems. A novel power series method by considering the multiple scales $R_k$ in the power term $(t/R_k^k$ is developed, which are derived explicitly to reduce the ill-conditioned behavior in the data interpolation. In the method a huge value times a tiny value is avoided, such that we can decrease the numerical instability and which is the main reason to cause the failure of the conventional power series method. The multiple scales derived from an integral can be used in the power series expansion, which provide very accurate numerical solutions of the problems considered in this paper.

  4. A MODIFIED DECOMPOSITION METHOD FOR SOLVING NONLINEAR PROBLEM OF FLOW IN CONVERGING- DIVERGING CHANNEL

    Directory of Open Access Journals (Sweden)

    MOHAMED KEZZAR

    2015-08-01

    Full Text Available In this research, an efficient technique of computation considered as a modified decomposition method was proposed and then successfully applied for solving the nonlinear problem of the two dimensional flow of an incompressible viscous fluid between nonparallel plane walls. In fact this method gives the nonlinear term Nu and the solution of the studied problem as a power series. The proposed iterative procedure gives on the one hand a computationally efficient formulation with an acceleration of convergence rate and on the other hand finds the solution without any discretization, linearization or restrictive assumptions. The comparison of our results with those of numerical treatment and other earlier works shows clearly the higher accuracy and efficiency of the used Modified Decomposition Method.

  5. A New Method to Solve Numeric Solution of Nonlinear Dynamic System

    Directory of Open Access Journals (Sweden)

    Min Hu

    2016-01-01

    Full Text Available It is well known that the cubic spline function has advantages of simple forms, good convergence, approximation, and second-order smoothness. A particular class of cubic spline function is constructed and an effective method to solve the numerical solution of nonlinear dynamic system is proposed based on the cubic spline function. Compared with existing methods, this method not only has high approximation precision, but also avoids the Runge phenomenon. The error analysis of several methods is given via two numeric examples, which turned out that the proposed method is a much more feasible tool applied to the engineering practice.

  6. Global Convergence of Schubert’s Method for Solving Sparse Nonlinear Equations

    Directory of Open Access Journals (Sweden)

    Huiping Cao

    2014-01-01

    Full Text Available Schubert’s method is an extension of Broyden’s method for solving sparse nonlinear equations, which can preserve the zero-nonzero structure defined by the sparse Jacobian matrix and can retain many good properties of Broyden’s method. In particular, Schubert’s method has been proved to be locally and q-superlinearly convergent. In this paper, we globalize Schubert’s method by using a nonmonotone line search. Under appropriate conditions, we show that the proposed algorithm converges globally and superlinearly. Some preliminary numerical experiments are presented, which demonstrate that our algorithm is effective for large-scale problems.

  7. Intuitionistic Fuzzy Goal Programming Technique for Solving Non-Linear Multi-objective Structural Problem

    Directory of Open Access Journals (Sweden)

    Samir Dey

    2015-07-01

    Full Text Available This paper proposes a new multi-objective intuitionistic fuzzy goal programming approach to solve a multi-objective nonlinear programming problem in context of a structural design. Here we describe some basic properties of intuitionistic fuzzy optimization. We have considered a multi-objective structural optimization problem with several mutually conflicting objectives. The design objective is to minimize weight of the structure and minimize the vertical deflection at loading point of a statistically loaded three-bar planar truss subjected to stress constraints on each of the truss members. This approach is used to solve the above structural optimization model based on arithmetic mean and compare with the solution by intuitionistic fuzzy goal programming approach. A numerical solution is given to illustrate our approach.

  8. Improved Quasi-Newton method via PSB update for solving systems of nonlinear equations

    Science.gov (United States)

    Mamat, Mustafa; Dauda, M. K.; Waziri, M. Y.; Ahmad, Fadhilah; Mohamad, Fatma Susilawati

    2016-10-01

    The Newton method has some shortcomings which includes computation of the Jacobian matrix which may be difficult or even impossible to compute and solving the Newton system in every iteration. Also, the common setback with some quasi-Newton methods is that they need to compute and store an n × n matrix at each iteration, this is computationally costly for large scale problems. To overcome such drawbacks, an improved Method for solving systems of nonlinear equations via PSB (Powell-Symmetric-Broyden) update is proposed. In the proposed method, the approximate Jacobian inverse Hk of PSB is updated and its efficiency has improved thereby require low memory storage, hence the main aim of this paper. The preliminary numerical results show that the proposed method is practically efficient when applied on some benchmark problems.

  9. Matrix Methods for Solving Hartree-Fock Equations in Atomic Structure Calculations and Line Broadening

    Directory of Open Access Journals (Sweden)

    Thomas Gomez

    2018-04-01

    Full Text Available Atomic structure of N-electron atoms is often determined by solving the Hartree-Fock equations, which are a set of integro-differential equations. The integral part of the Hartree-Fock equations treats electron exchange, but the Hartree-Fock equations are not often treated as an integro-differential equation. The exchange term is often approximated as an inhomogeneous or an effective potential so that the Hartree-Fock equations become a set of ordinary differential equations (which can be solved using the usual shooting methods. Because the Hartree-Fock equations are an iterative-refinement method, the inhomogeneous term relies on the previous guess of the wavefunction. In addition, there are numerical complications associated with solving inhomogeneous differential equations. This work uses matrix methods to solve the Hartree-Fock equations as an integro-differential equation. It is well known that a derivative operator can be expressed as a matrix made of finite-difference coefficients; energy eigenvalues and eigenvectors can be obtained by using linear-algebra packages. The integral (exchange part of the Hartree-Fock equation can be approximated as a sum and written as a matrix. The Hartree-Fock equations can be solved as a matrix that is the sum of the differential and integral matrices. We compare calculations using this method against experiment and standard atomic structure calculations. This matrix method can also be used to solve for free-electron wavefunctions, thus improving how the atoms and free electrons interact. This technique is important for spectral line broadening in two ways: it improves the atomic structure calculations, and it improves the motion of the plasma electrons that collide with the atom.

  10. Method of mechanical quadratures for solving singular integral equations of various types

    Science.gov (United States)

    Sahakyan, A. V.; Amirjanyan, H. A.

    2018-04-01

    The method of mechanical quadratures is proposed as a common approach intended for solving the integral equations defined on finite intervals and containing Cauchy-type singular integrals. This method can be used to solve singular integral equations of the first and second kind, equations with generalized kernel, weakly singular equations, and integro-differential equations. The quadrature rules for several different integrals represented through the same coefficients are presented. This allows one to reduce the integral equations containing integrals of different types to a system of linear algebraic equations.

  11. 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.

  12. Programmable Solution for Solving Non-linearity Characteristics of Smart Sensor Applications

    Directory of Open Access Journals (Sweden)

    S. Khan

    2007-10-01

    Full Text Available This paper presents a simple but programmable technique to solve the problem of non-linear characteristics of sensors used in more sensitive applications. The nonlinearity of the output response becomes a very sensitive issue in cases where a proportional increase in the physical quantity fails to bring about a proportional increase in the signal measured. The nonlinearity is addressed by using the interpolation method on the characteristics of a given sensor, approximating it to a set of tangent lines, the tangent points of which are recognized in the code of the processor by IF-THEN code. The method suggested here eliminates the use of external circuits for interfacing, and eases the programming burden on the processor at the cost of proportionally reduced memory requirements. The mathematically worked out results are compared with the simulation and experimental results for an IR sensor selected for the purpose and used for level measurement. This work will be of paramount importance and significance in applications where the controlled signal is required to follow the input signal precisely particularly in sensitive robotic applications.

  13. Solving nonlinear nonstationary problem of heat-conductivity by finite element method

    Directory of Open Access Journals (Sweden)

    Антон Янович Карвацький

    2016-11-01

    Full Text Available Methodology and effective solving algorithm of non-linear dynamic problems of thermal and electric conductivity with significant temperature dependence of thermal and physical properties are given on the basis of finite element method (FEM and Newton linearization method. Discrete equations system FEM was obtained with the use of Galerkin method, where the main function is the finite element form function. The methodology based on successive solving problems of thermal and electrical conductivity has been examined in the work in order to minimize the requirements for calculating resources (RAM. in particular. Having used Mathcad software original programming code was developed to solve the given problem. After investigation of the received results, comparative analyses of accurate solution data and results of numerical solutions, obtained with the use of Matlab programming products, was held. The geometry of one fourth part of the finite sized cylinder was used to test the given numerical model. The discretization of the calculation part was fulfilled using the open programming software for automated Gmsh nets with tetrahedral units, while ParaView, which is an open programming code as well, was used to visualize the calculation results. It was found out that the maximum value violation of potential and temperature determination doesn`t exceed 0,2-0,83% in the given work according to the problem conditions

  14. A New Approach and Solution Technique to Solve Time Fractional Nonlinear Reaction-Diffusion Equations

    Directory of Open Access Journals (Sweden)

    Inci Cilingir Sungu

    2015-01-01

    Full Text Available A new application of the hybrid generalized differential transform and finite difference method is proposed by solving time fractional nonlinear reaction-diffusion equations. This method is a combination of the multi-time-stepping temporal generalized differential transform and the spatial finite difference methods. The procedure first converts the time-evolutionary equations into Poisson equations which are then solved using the central difference method. The temporal differential transform method as used in the paper takes care of stability and the finite difference method on the resulting equation results in a system of diagonally dominant linear algebraic equations. The Gauss-Seidel iterative procedure then used to solve the linear system thus has assured convergence. To have optimized convergence rate, numerical experiments were done by using a combination of factors involving multi-time-stepping, spatial step size, and degree of the polynomial fit in time. It is shown that the hybrid technique is reliable, accurate, and easy to apply.

  15. Nonlinearly Activated Neural Network for Solving Time-Varying Complex Sylvester Equation.

    Science.gov (United States)

    Li, Shuai; Li, Yangming

    2013-10-28

    The Sylvester equation is often encountered in mathematics and control theory. For the general time-invariant Sylvester equation problem, which is defined in the domain of complex numbers, the Bartels-Stewart algorithm and its extensions are effective and widely used with an O(n³) time complexity. When applied to solving the time-varying Sylvester equation, the computation burden increases intensively with the decrease of sampling period and cannot satisfy continuous realtime calculation requirements. For the special case of the general Sylvester equation problem defined in the domain of real numbers, gradient-based recurrent neural networks are able to solve the time-varying Sylvester equation in real time, but there always exists an estimation error while a recently proposed recurrent neural network by Zhang et al [this type of neural network is called Zhang neural network (ZNN)] converges to the solution ideally. The advancements in complex-valued neural networks cast light to extend the existing real-valued ZNN for solving the time-varying real-valued Sylvester equation to its counterpart in the domain of complex numbers. In this paper, a complex-valued ZNN for solving the complex-valued Sylvester equation problem is investigated and the global convergence of the neural network is proven with the proposed nonlinear complex-valued activation functions. Moreover, a special type of activation function with a core function, called sign-bi-power function, is proven to enable the ZNN to converge in finite time, which further enhances its advantage in online processing. In this case, the upper bound of the convergence time is also derived analytically. Simulations are performed to evaluate and compare the performance of the neural network with different parameters and activation functions. Both theoretical analysis and numerical simulations validate the effectiveness of the proposed method.

  16. Inexact Newton–Landweber iteration for solving nonlinear inverse problems in Banach spaces

    International Nuclear Information System (INIS)

    Jin, Qinian

    2012-01-01

    By making use of duality mappings, we formulate an inexact Newton–Landweber iteration method for solving nonlinear inverse problems in Banach spaces. The method consists of two components: an outer Newton iteration and an inner scheme providing the increments by applying the Landweber iteration in Banach spaces to the local linearized equations. It has the advantage of reducing computational work by computing more cheap steps in each inner scheme. We first prove a convergence result for the exact data case. When the data are given approximately, we terminate the method by a discrepancy principle and obtain a weak convergence result. Finally, we test the method by reporting some numerical simulations concerning the sparsity recovery and the noisy data containing outliers. (paper)

  17. A novel algebraic procedure for solving non-linear evolution equations of higher order

    International Nuclear Information System (INIS)

    Huber, Alfred

    2007-01-01

    We report here a systematic approach that can easily be used for solving non-linear partial differential equations (nPDE), especially of higher order. We restrict the analysis to the so called evolution equations describing any wave propagation. The proposed new algebraic approach leads us to traveling wave solutions and moreover, new class of solution can be obtained. The crucial step of our method is the basic assumption that the solutions satisfy an ordinary differential equation (ODE) of first order that can be easily integrated. The validity and reliability of the method is tested by its application to some non-linear evolution equations. The important aspect of this paper however is the fact that we are able to calculate distinctive class of solutions which cannot be found in the current literature. In other words, using this new algebraic method the solution manifold is augmented to new class of solution functions. Simultaneously we would like to stress the necessity of such sophisticated methods since a general theory of nPDE does not exist. Otherwise, for practical use the algebraic construction of new class of solutions is of fundamental interest

  18. The spectral transform as a tool for solving nonlinear discrete evolution equations

    International Nuclear Information System (INIS)

    Levi, D.

    1979-01-01

    In this contribution we study nonlinear differential difference equations which became important to the description of an increasing number of problems in natural science. Difference equations arise for instance in the study of electrical networks, in statistical problems, in queueing problems, in ecological problems, as computer models for differential equations and as models for wave excitation in plasma or vibrations of particles in an anharmonic lattice. We shall first review the passages necessary to solve linear discrete evolution equations by the discrete Fourier transfrom, then, starting from the Zakharov-Shabat discretized eigenvalue, problem, we shall introduce the spectral transform. In the following part we obtain the correlation between the evolution of the potentials and scattering data through the Wronskian technique, giving at the same time many other properties as, for example, the Baecklund transformations. Finally we recover some of the important equations belonging to this class of nonlinear discrete evolution equations and extend the method to equations with n-dependent coefficients. (HJ)

  19. Performance prediction of gas turbines by solving a system of non-linear equations

    Energy Technology Data Exchange (ETDEWEB)

    Kaikko, J

    1998-09-01

    This study presents a novel method for implementing the performance prediction of gas turbines from the component models. It is based on solving the non-linear set of equations that corresponds to the process equations, and the mass and energy balances for the engine. General models have been presented for determining the steady state operation of single components. Single and multiple shad arrangements have been examined with consideration also being given to heat regeneration and intercooling. Emphasis has been placed upon axial gas turbines of an industrial scale. Applying the models requires no information of the structural dimensions of the gas turbines. On comparison with the commonly applied component matching procedures, this method incorporates several advantages. The application of the models for providing results is facilitated as less attention needs to be paid to calculation sequences and routines. Solving the set of equations is based on zeroing co-ordinate functions that are directly derived from the modelling equations. Therefore, controlling the accuracy of the results is easy. This method gives more freedom for the selection of the modelling parameters since, unlike for the matching procedures, exchanging these criteria does not itself affect the algorithms. Implicit relationships between the variables are of no significance, thus increasing the freedom for the modelling equations as well. The mathematical models developed in this thesis will provide facilities to optimise the operation of any major gas turbine configuration with respect to the desired process parameters. The computational methods used in this study may also be adapted to any other modelling problems arising in industry. (orig.) 36 refs.

  20. Method for solving the problem of nonlinear heating a cylindrical body with unknown initial temperature

    Science.gov (United States)

    Yaparova, N.

    2017-10-01

    We consider the problem of heating a cylindrical body with an internal thermal source when the main characteristics of the material such as specific heat, thermal conductivity and material density depend on the temperature at each point of the body. We can control the surface temperature and the heat flow from the surface inside the cylinder, but it is impossible to measure the temperature on axis and the initial temperature in the entire body. This problem is associated with the temperature measurement challenge and appears in non-destructive testing, in thermal monitoring of heat treatment and technical diagnostics of operating equipment. The mathematical model of heating is represented as nonlinear parabolic PDE with the unknown initial condition. In this problem, both the Dirichlet and Neumann boundary conditions are given and it is required to calculate the temperature values at the internal points of the body. To solve this problem, we propose the numerical method based on using of finite-difference equations and a regularization technique. The computational scheme involves solving the problem at each spatial step. As a result, we obtain the temperature function at each internal point of the cylinder beginning from the surface down to the axis. The application of the regularization technique ensures the stability of the scheme and allows us to significantly simplify the computational procedure. We investigate the stability of the computational scheme and prove the dependence of the stability on the discretization steps and error level of the measurement results. To obtain the experimental temperature error estimates, computational experiments were carried out. The computational results are consistent with the theoretical error estimates and confirm the efficiency and reliability of the proposed computational scheme.

  1. Linear differential equations to solve nonlinear mechanical problems: A novel approach

    OpenAIRE

    Nair, C. Radhakrishnan

    2004-01-01

    Often a non-linear mechanical problem is formulated as a non-linear differential equation. A new method is introduced to find out new solutions of non-linear differential equations if one of the solutions of a given non-linear differential equation is known. Using the known solution of the non-linear differential equation, linear differential equations are set up. The solutions of these linear differential equations are found using standard techniques. Then the solutions of the linear differe...

  2. An analytical method for solving exact solutions of the nonlinear Bogoyavlenskii equation and the nonlinear diffusive predator–prey system

    Directory of Open Access Journals (Sweden)

    Md. Nur Alam

    2016-06-01

    Full Text Available In this article, we apply the exp(-Φ(ξ-expansion method to construct many families of exact solutions of nonlinear evolution equations (NLEEs via the nonlinear diffusive predator–prey system and the Bogoyavlenskii equations. These equations can be transformed to nonlinear ordinary differential equations. As a result, some new exact solutions are obtained through the hyperbolic function, the trigonometric function, the exponential functions and the rational forms. If the parameters take specific values, then the solitary waves are derived from the traveling waves. Also, we draw 2D and 3D graphics of exact solutions for the special diffusive predator–prey system and the Bogoyavlenskii equations by the help of programming language Maple.

  3. Constructing Frozen Jacobian Iterative Methods for Solving Systems of Nonlinear Equations, Associated with ODEs and PDEs Using the Homotopy Method

    Directory of Open Access Journals (Sweden)

    Uswah Qasim

    2016-03-01

    Full Text Available A homotopy method is presented for the construction of frozen Jacobian iterative methods. The frozen Jacobian iterative methods are attractive because the inversion of the Jacobian is performed in terms of LUfactorization only once, for a single instance of the iterative method. We embedded parameters in the iterative methods with the help of the homotopy method: the values of the parameters are determined in such a way that a better convergence rate is achieved. The proposed homotopy technique is general and has the ability to construct different families of iterative methods, for solving weakly nonlinear systems of equations. Further iterative methods are also proposed for solving general systems of nonlinear equations.

  4. Nonlinearities Distribution Homotopy Perturbation Method Applied to Solve Nonlinear Problems: Thomas-Fermi Equation as a Case Study

    Directory of Open Access Journals (Sweden)

    U. Filobello-Nino

    2015-01-01

    Full Text Available We propose an approximate solution of T-F equation, obtained by using the nonlinearities distribution homotopy perturbation method (NDHPM. Besides, we show a table of comparison, between this proposed approximate solution and a numerical of T-F, by establishing the accuracy of the results.

  5. Fourth order Douglas implicit scheme for solving three dimension reaction diffusion equation with non-linear source term

    Directory of Open Access Journals (Sweden)

    Shahid Hasnain

    2017-07-01

    Full Text Available This research paper represents a numerical approximation to non-linear three dimension reaction diffusion equation with non-linear source term from population genetics. Since various initial and boundary value problems exist in three dimension reaction diffusion phenomena, which are studied numerically by different numerical methods, here we use finite difference schemes (Alternating Direction Implicit and Fourth Order Douglas Implicit to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with analytical results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. Numerical results showed that Fourth Order Douglas Implicit scheme is very efficient and reliable for solving 3-D non-linear reaction diffusion equation.

  6. Fourth order Douglas implicit scheme for solving three dimension reaction diffusion equation with non-linear source term

    Science.gov (United States)

    Hasnain, Shahid; Saqib, Muhammad; Mashat, Daoud Suleiman

    2017-07-01

    This research paper represents a numerical approximation to non-linear three dimension reaction diffusion equation with non-linear source term from population genetics. Since various initial and boundary value problems exist in three dimension reaction diffusion phenomena, which are studied numerically by different numerical methods, here we use finite difference schemes (Alternating Direction Implicit and Fourth Order Douglas Implicit) to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with analytical results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. Numerical results showed that Fourth Order Douglas Implicit scheme is very efficient and reliable for solving 3-D non-linear reaction diffusion equation.

  7. Applications of IBSOM and ETEM for solving the nonlinear chains of atoms with long-range interactions

    Science.gov (United States)

    Foroutan, Mohammadreza; Zamanpour, Isa; Manafian, Jalil

    2017-10-01

    This paper presents a number of new solutions obtained for solving a complex nonlinear equation describing dynamics of nonlinear chains of atoms via the improved Bernoulli sub-ODE method (IBSOM) and the extended trial equation method (ETEM). The proposed solutions are kink solitons, anti-kink solitons, soliton solutions, hyperbolic solutions, trigonometric solutions, and bellshaped soliton solutions. Then our new results are compared with the well-known results. The methods used here are very simple and succinct and can be also applied to other nonlinear models. The balance number of these methods is not constant contrary to other methods. The proposed methods also allow us to establish many new types of exact solutions. By utilizing the Maple software package, we show that all obtained solutions satisfy the conditions of the studied model. More importantly, the solutions found in this work can have significant applications in Hamilton's equations and generalized momentum where solitons are used for long-range interactions.

  8. Memetic Algorithms to Solve a Global Nonlinear Optimization Problem. A Review

    Directory of Open Access Journals (Sweden)

    M. K. Sakharov

    2015-01-01

    Full Text Available In recent decades, evolutionary algorithms have proven themselves as the powerful optimization techniques of search engine. Their popularity is due to the fact that they are easy to implement and can be used in all areas, since they are based on the idea of universal evolution. For example, in the problems of a large number of local optima, the traditional optimization methods, usually, fail in finding the global optimum. To solve such problems using a variety of stochastic methods, in particular, the so-called population-based algorithms, which are a kind of evolutionary methods. The main disadvantage of this class of methods is their slow convergence to the exact solution in the neighborhood of the global optimum, as these methods incapable to use the local information about the landscape of the function. This often limits their use in largescale real-world problems where the computation time is a critical factor.One of the promising directions in the field of modern evolutionary computation are memetic algorithms, which can be regarded as a combination of population search of the global optimum and local procedures for verifying solutions, which gives a synergistic effect. In the context of memetic algorithms, the meme is an implementation of the local optimization method to refine solution in the search.The concept of memetic algorithms provides ample opportunities for the development of various modifications of these algorithms, which can vary the frequency of the local search, the conditions of its end, and so on. The practically significant memetic algorithm modifications involve the simultaneous use of different memes. Such algorithms are called multi-memetic.The paper gives statement of the global problem of nonlinear unconstrained optimization, describes the most promising areas of AI modifications, including hybridization and metaoptimization. The main content of the work is the classification and review of existing varieties of

  9. Modern nonlinear equations

    CERN Document Server

    Saaty, Thomas L

    1981-01-01

    Covers major types of classical equations: operator, functional, difference, integro-differential, and more. Suitable for graduate students as well as scientists, technologists, and mathematicians. "A welcome contribution." - Math Reviews. 1964 edition.

  10. An overview of adaptive model theory: solving the problems of redundancy, resources, and nonlinear interactions in human movement control.

    Science.gov (United States)

    Neilson, Peter D; Neilson, Megan D

    2005-09-01

    Adaptive model theory (AMT) is a computational theory that addresses the difficult control problem posed by the musculoskeletal system in interaction with the environment. It proposes that the nervous system creates motor maps and task-dependent synergies to solve the problems of redundancy and limited central resources. These lead to the adaptive formation of task-dependent feedback/feedforward controllers able to generate stable, noninteractive control and render nonlinear interactions unobservable in sensory-motor relationships. AMT offers a unified account of how the nervous system might achieve these solutions by forming internal models. This is presented as the design of a simulator consisting of neural adaptive filters based on cerebellar circuitry. It incorporates a new network module that adaptively models (in real time) nonlinear relationships between inputs with changing and uncertain spectral and amplitude probability density functions as is the case for sensory and motor signals.

  11. Solving non-linear Horn clauses using a linear Horn clause solver

    DEFF Research Database (Denmark)

    Kafle, Bishoksan; Gallagher, John Patrick; Ganty, Pierre

    2016-01-01

    In this paper we show that checking satisfiability of a set of non-linear Horn clauses (also called a non-linear Horn clause program) can be achieved using a solver for linear Horn clauses. We achieve this by interleaving a program transformation with a satisfiability checker for linear Horn...... clauses (also called a solver for linear Horn clauses). The program transformation is based on the notion of tree dimension, which we apply to a set of non-linear clauses, yielding a set whose derivation trees have bounded dimension. Such a set of clauses can be linearised. The main algorithm...... dimension. We constructed a prototype implementation of this approach and performed some experiments on a set of verification problems, which shows some promise....

  12. An ansatz for solving nonlinear partial differential equations in mathematical physics.

    Science.gov (United States)

    Akbar, M Ali; Ali, Norhashidah Hj Mohd

    2016-01-01

    In this article, we introduce an ansatz involving exact traveling wave solutions to nonlinear partial differential equations. To obtain wave solutions using direct method, the choice of an appropriate ansatz is of great importance. We apply this ansatz to examine new and further general traveling wave solutions to the (1+1)-dimensional modified Benjamin-Bona-Mahony equation. Abundant traveling wave solutions are derived including solitons, singular solitons, periodic solutions and general solitary wave solutions. The solutions emphasize the nobility of this ansatz in providing distinct solutions to various tangible phenomena in nonlinear science and engineering. The ansatz could be more efficient tool to deal with higher dimensional nonlinear evolution equations which frequently arise in many real world physical problems.

  13. Direct application of Padé approximant for solving nonlinear differential equations.

    Science.gov (United States)

    Vazquez-Leal, Hector; Benhammouda, Brahim; Filobello-Nino, Uriel; Sarmiento-Reyes, Arturo; Jimenez-Fernandez, Victor Manuel; Garcia-Gervacio, Jose Luis; Huerta-Chua, Jesus; Morales-Mendoza, Luis Javier; Gonzalez-Lee, Mario

    2014-01-01

    This work presents a direct procedure to apply Padé method to find approximate solutions for nonlinear differential equations. Moreover, we present some cases study showing the strength of the method to generate highly accurate rational approximate solutions compared to other semi-analytical methods. The type of tested nonlinear equations are: a highly nonlinear boundary value problem, a differential-algebraic oscillator problem, and an asymptotic problem. The high accurate handy approximations obtained by the direct application of Padé method shows the high potential if the proposed scheme to approximate a wide variety of problems. What is more, the direct application of the Padé approximant aids to avoid the previous application of an approximative method like Taylor series method, homotopy perturbation method, Adomian Decomposition method, homotopy analysis method, variational iteration method, among others, as tools to obtain a power series solutions to post-treat with the Padé approximant. 34L30.

  14. Two-dimensional differential transform method for solving linear and non-linear Schroedinger equations

    International Nuclear Information System (INIS)

    Ravi Kanth, A.S.V.; Aruna, K.

    2009-01-01

    In this paper, we propose a reliable algorithm to develop exact and approximate solutions for the linear and nonlinear Schroedinger equations. The approach rest mainly on two-dimensional differential transform method which is one of the approximate methods. The method can easily be applied to many linear and nonlinear problems and is capable of reducing the size of computational work. Exact solutions can also be achieved by the known forms of the series solutions. Several illustrative examples are given to demonstrate the effectiveness of the present method.

  15. Neural network based online simultaneous policy update algorithm for solving the HJI equation in nonlinear H∞ control.

    Science.gov (United States)

    Wu, Huai-Ning; Luo, Biao

    2012-12-01

    It is well known that the nonlinear H∞ state feedback control problem relies on the solution of the Hamilton-Jacobi-Isaacs (HJI) equation, which is a nonlinear partial differential equation that has proven to be impossible to solve analytically. In this paper, a neural network (NN)-based online simultaneous policy update algorithm (SPUA) is developed to solve the HJI equation, in which knowledge of internal system dynamics is not required. First, we propose an online SPUA which can be viewed as a reinforcement learning technique for two players to learn their optimal actions in an unknown environment. The proposed online SPUA updates control and disturbance policies simultaneously; thus, only one iterative loop is needed. Second, the convergence of the online SPUA is established by proving that it is mathematically equivalent to Newton's method for finding a fixed point in a Banach space. Third, we develop an actor-critic structure for the implementation of the online SPUA, in which only one critic NN is needed for approximating the cost function, and a least-square method is given for estimating the NN weight parameters. Finally, simulation studies are provided to demonstrate the effectiveness of the proposed algorithm.

  16. Efficient Solving of Large Non-linear Arithmetic Constraint Systems with Complex Boolean Structure

    Czech Academy of Sciences Publication Activity Database

    Fränzle, M.; Herde, C.; Teige, T.; Ratschan, Stefan; Schubert, T.

    2007-01-01

    Roč. 1, - (2007), s. 209-236 ISSN 1574-0617 Grant - others:AVACS(DE) SFB/TR 14 Institutional research plan: CEZ:AV0Z10300504 Keywords : interval-based arithmetic constraint solving * SAT modulo theories Subject RIV: BA - General Mathematics

  17. New Quasi-Newton Method for Solving Systems of Nonlinear Equations

    Czech Academy of Sciences Publication Activity Database

    Lukšan, Ladislav; Vlček, Jan

    2017-01-01

    Roč. 62, č. 2 (2017), s. 121-134 ISSN 0862-7940 R&D Projects: GA ČR GA13-06684S Institutional support: RVO:67985807 Keywords : nonlinear equations * systems of equations * trust-region methods * quasi-Newton methods * adjoint Broyden methods * numerical algorithms * numerical experiments Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 0.618, year: 2016 http://hdl.handle.net/10338.dmlcz/146699

  18. Solving Boundary Value Problem for a Nonlinear Stationary Controllable System with Synthesizing Control

    Directory of Open Access Journals (Sweden)

    Alexander N. Kvitko

    2017-01-01

    Full Text Available An algorithm for constructing a control function that transfers a wide class of stationary nonlinear systems of ordinary differential equations from an initial state to a final state under certain control restrictions is proposed. The algorithm is designed to be convenient for numerical implementation. A constructive criterion of the desired transfer possibility is presented. The problem of an interorbital flight is considered as a test example and it is simulated numerically with the presented method.

  19. Nonlinear Projective-Iteration Methods for Solving Transport Problems on Regular and Unstructured Grids

    International Nuclear Information System (INIS)

    Dmitriy Y. Anistratov; Adrian Constantinescu; Loren Roberts; William Wieselquist

    2007-01-01

    This is a project in the field of fundamental research on numerical methods for solving the particle transport equation. Numerous practical problems require to use unstructured meshes, for example, detailed nuclear reactor assembly-level calculations, large-scale reactor core calculations, radiative hydrodynamics problems, where the mesh is determined by hydrodynamic processes, and well-logging problems in which the media structure has very complicated geometry. Currently this is an area of very active research in numerical transport theory. main issues in developing numerical methods for solving the transport equation are the accuracy of the numerical solution and effectiveness of iteration procedure. The problem in case of unstructured grids is that it is very difficult to derive an iteration algorithm that will be unconditionally stable

  20. An Efficient Higher-Order Quasilinearization Method for Solving Nonlinear BVPs

    Directory of Open Access Journals (Sweden)

    Eman S. Alaidarous

    2013-01-01

    Full Text Available In this research paper, we present higher-order quasilinearization methods for the boundary value problems as well as coupled boundary value problems. The construction of higher-order convergent methods depends on a decomposition method which is different from Adomain decomposition method (Motsa and Sibanda, 2013. The reported method is very general and can be extended to desired order of convergence for highly nonlinear differential equations and also computationally superior to proposed iterative method based on Adomain decomposition because our proposed iterative scheme avoids the calculations of Adomain polynomials and achieves the same computational order of convergence as authors have claimed in Motsa and Sibanda, 2013. In order to check the validity and computational performance, the constructed iterative schemes are also successfully applied to bifurcation problems to calculate the values of critical parameters. The numerical performance is also tested for one-dimension Bratu and Frank-Kamenetzkii equations.

  1. solveME: fast and reliable solution of nonlinear ME models

    DEFF Research Database (Denmark)

    Yang, Laurence; Ma, Ding; Ebrahim, Ali

    2016-01-01

    Background: Genome-scale models of metabolism and macromolecular expression (ME) significantly expand the scope and predictive capabilities of constraint-based modeling. ME models present considerable computational challenges: they are much (>30 times) larger than corresponding metabolic reconstr......Background: Genome-scale models of metabolism and macromolecular expression (ME) significantly expand the scope and predictive capabilities of constraint-based modeling. ME models present considerable computational challenges: they are much (>30 times) larger than corresponding metabolic...... reconstructions (M models), are multiscale, and growth maximization is a nonlinear programming (NLP) problem, mainly due to macromolecule dilution constraints. Results: Here, we address these computational challenges. We develop a fast and numerically reliable solution method for growth maximization in ME models...

  2. A nonlinear boundary integral equations method for the solving of quasistatic elastic contact problem with Coulomb friction

    Directory of Open Access Journals (Sweden)

    Yurii M. Streliaiev

    2016-06-01

    Full Text Available Three-dimensional quasistatic contact problem of two linearly elastic bodies' interaction with Coulomb friction taken into account is considered. The boundary conditions of the problem have been simplified by the modification of the Coulomb's law of friction. This modification is based on the introducing of a delay in normal contact tractions that bound tangent contact tractions in the Coulomb's law of friction expressions. At this statement the problem is reduced to a sequence of similar systems of nonlinear integral equations describing bodies' interaction at each step of loading. A method for an approximate solution of the integral equations system corresponded to each step of loading is applied. This method consists of system regularization, discretization of regularized system and iterative process application for solving the discretized system. A numerical solution of a contact problem of an elastic sphere with an elastic half-space interaction under increasing and subsequently decreasing normal compressive force has been obtained.

  3. Non-linear algorithms solved with the help of the GIBIANE macro-language

    International Nuclear Information System (INIS)

    Ebersolt, L.; Combescure, A.; Millard, A.; Verpeaux, P.

    1987-01-01

    Non linear finite element problems are often solved with the help of iteratives procedures. In the finite element program CASTEM 2000, the syntax of the dataset permits the user to derive his own algorithm and tune it to his problem. These basic ideas, simple to imagine, needed a proper frame to be materialized in a general purpose finite element program, and three concepts emerged: Operators, the Gibiane macro-language. In the two first paragraphs, we will detail these concepts, in the third paragraph, we will describe the different possibilities of the program, in the fourth paragraph, we will show, by combining operators in a proper order, how to obtain the desired algorithm. (orig./GL)

  4. Microscopic tunneling theory of long Josephson junctions

    DEFF Research Database (Denmark)

    Grønbech-Jensen, N.; Hattel, Søren A.; Samuelsen, Mogens Rugholm

    1992-01-01

    We present a numerical scheme for solving a nonlinear partial integro-differential equation with nonlocal time dependence. The equation describes the dynamics in a long Josephson junction modeled by use of the microscopic theory for tunneling between superconductors. We demonstrate that the detai......We present a numerical scheme for solving a nonlinear partial integro-differential equation with nonlocal time dependence. The equation describes the dynamics in a long Josephson junction modeled by use of the microscopic theory for tunneling between superconductors. We demonstrate...

  5. On an adaptive time stepping strategy for solving nonlinear diffusion equations

    International Nuclear Information System (INIS)

    Chen, K.; Baines, M.J.; Sweby, P.K.

    1993-01-01

    A new time step selection procedure is proposed for solving non- linear diffusion equations. It has been implemented in the ASWR finite element code of Lorenz and Svoboda [10] for 2D semiconductor process modelling diffusion equations. The strategy is based on equi-distributing the local truncation errors of the numerical scheme. The use of B-splines for interpolation (as well as for the trial space) results in a banded and diagonally dominant matrix. The approximate inverse of such a matrix can be provided to a high degree of accuracy by another banded matrix, which in turn can be used to work out the approximate finite difference scheme corresponding to the ASWR finite element method, and further to calculate estimates of the local truncation errors of the numerical scheme. Numerical experiments on six full simulation problems arising in semiconductor process modelling have been carried out. Results show that our proposed strategy is more efficient and better conserves the total mass. 18 refs., 6 figs., 2 tabs

  6. Nonlinear wave propagation through a ferromagnet with damping in ...

    Indian Academy of Sciences (India)

    magnetic waves in a ferromagnet can be reduced to an integro-differential equation. Keywords. Solitons; integro-differential equations; reductive perturbation method. PACS Nos 41.20 Jb; 05.45 Yv; 03.50 De; 78.20 Ls. 1. Introduction. The phenomenon of propagation of electromagnetic waves in ferromagnets are not only.

  7. On the conditions for the onset of nonlinear chirping structures in NSTX

    Science.gov (United States)

    Duarte, Vinicius; Podesta, Mario; Berk, Herbert; Gorelenkov, Nikolai

    2015-11-01

    The nonlinear dynamics of phase space structures is a topic of interest in tokamak physics in connection with fast ion loss mechanisms. The onset of phase-space holes and clumps has been theoretically shown to be associated with an explosive solution of an integro-differential, nonlocal cubic equation that governs the early mode amplitude evolution in the weakly nonlinear regime. The existence and stability of the solutions of the cubic equation have been theoretically studied as a function of Fokker-Planck coefficients for the idealized case of a single resonant point of a localized mode. From realistic computations of NSTX mode structures and resonant surfaces, we calculate effective pitch angle scattering and slowing-down (drag) collisional coefficients and analyze NSTX discharges for different cases with respect to chirping experimental observation. Those results are confronted to the theory that predicts the parameters region that allow for chirping to take place.

  8. New extended (G'/G)-expansion method to solve nonlinear evolution equation: the (3 + 1)-dimensional potential-YTSF equation.

    Science.gov (United States)

    Roshid, Harun-Or-; Akbar, M Ali; Alam, Md Nur; Hoque, Md Fazlul; Rahman, Nizhum

    2014-01-01

    In this article, a new extended (G'/G) -expansion method has been proposed for constructing more general exact traveling wave solutions of nonlinear evolution equations with the aid of symbolic computation. In order to illustrate the validity and effectiveness of the method, we pick the (3 + 1)-dimensional potential-YTSF equation. As a result, abundant new and more general exact solutions have been achieved of this equation. It has been shown that the proposed method provides a powerful mathematical tool for solving nonlinear wave equations in applied mathematics, engineering and mathematical physics.

  9. The use of symbolic computation in radiative, energy, and neutron transport calculations. Final report

    International Nuclear Information System (INIS)

    Frankel, J.I.

    1997-01-01

    This investigation used sysmbolic manipulation in developing analytical methods and general computational strategies for solving both linear and nonlinear, regular and singular integral and integro-differential equations which appear in radiative and mixed-mode energy transport. Contained in this report are seven papers which present the technical results as individual modules

  10. An analytical method for solving exact solutions of a nonlinear evolution equation describing the dynamics of ionic currents along microtubules

    Directory of Open Access Journals (Sweden)

    Md. Nur Alam

    2017-11-01

    Full Text Available In this article, a variety of solitary wave solutions are observed for microtubules (MTs. We approach the problem by treating the solutions as nonlinear RLC transmission lines and then find exact solutions of Nonlinear Evolution Equations (NLEEs involving parameters of special interest in nanobiosciences and biophysics. We determine hyperbolic, trigonometric, rational and exponential function solutions and obtain soliton-like pulse solutions for these equations. A comparative study against other methods demonstrates the validity of the technique that we developed and demonstrates that our method provides additional solutions. Finally, using suitable parameter values, we plot 2D and 3D graphics of the exact solutions that we observed using our method. Keywords: Analytical method, Exact solutions, Nonlinear evolution equations (NLEEs of microtubules, Nonlinear RLC transmission lines

  11. Quaternion Approach to Solve Coupled Nonlinear Schrödinger Equation and Crosstalk of Quarter-Phase-Shift-Key Signals in Polarization Multiplexing Systems

    International Nuclear Information System (INIS)

    Liu Lan-Lan; Wu Chong-Qing; Wang Jian; Gao Kai-Qiang; Shang Chao

    2015-01-01

    The quaternion approach to solve the coupled nonlinear Schrödinger equations (CNSEs) in fibers is proposed, converting the CNSEs to a single variable equation by using a conception of eigen-quaternion of coupled quaternion. The crosstalk of quarter-phase-shift-key signals caused by fiber nonlinearity in polarization multiplexing systems with 100 Gbps bit-rate is investigated and simulated. The results demonstrate that the crosstalk is like a rotated ghosting of input constellation. For the 50 km conventional fiber link, when the total power is less than 4 mW, the crosstalk effect can be neglected; when the power is larger than 20 mW, the crosstalk is very obvious. In addition, the crosstalk can not be detected according to the output eye diagram and state of polarization in Poincaré sphere in the trunk fiber, making it difficult for the monitoring of optical trunk link. (paper)

  12. Nonlinear physics of shear Alfvén waves

    International Nuclear Information System (INIS)

    Zonca, Fulvio; Chen, Liu

    2014-01-01

    Shear Alfvén waves (SAW) play fundamental roles in thermonuclear plasmas of fusion interest, since they are readily excited by energetic particles in the MeV range as well as by the thermal plasma components. Thus, understanding fluctuation induced transport in burning plasmas requires understanding nonlinear SAW physics. There exist two possible routes to nonlinear SAW physics: (i) wave-wave interactions and the resultant spectral energy transfer; (ii) nonlinear wave-particle interactions of SAW instabilities with energetic particles. Within the first route, it is advantageous to understand and describe nonlinear processes in term of proximity of the system to the Alfvénic state, where wave-wave interactions are minimized due to the cancellation of Reynolds and Maxwell stresses. Here, various wave-wave nonlinear dynamics are elucidated in terms of how they break the Alfvénic state. In particular, we discuss the qualitative and quantitative modification of the SAW parametric decay process due to finite ion compressibility and finite ion Larmor radius. We also show that toroidal geometry plays a crucial role in the nonlinear excitation of zonal structures by Alfvén eigenmodes. Within the second route, the coherent nonlinear dynamics of structures in the energetic particle phase space, by which secular resonant particle transport can occur on meso- and macro-scales, must be addressed and understood. These 'nonlinear equilibria' or 'phase-space zonal structures' dynamically evolve on characteristic (fluctuation induced) turbulent transport time scales, which are generally of the same order of the nonlinear time scale of the underlying fluctuations. In this work, we introduce the general structure of nonlinear Schrödinger equations with complex integro-differential nonlinear terms, which govern these physical processes. To elucidate all these aspects, theoretical analyses are presented together with numerical simulation results

  13. Nonlinear physics of shear Alfvén waves

    Science.gov (United States)

    Zonca, Fulvio; Chen, Liu

    2014-02-01

    Shear Alfvén waves (SAW) play fundamental roles in thermonuclear plasmas of fusion interest, since they are readily excited by energetic particles in the MeV range as well as by the thermal plasma components. Thus, understanding fluctuation induced transport in burning plasmas requires understanding nonlinear SAW physics. There exist two possible routes to nonlinear SAW physics: (i) wave-wave interactions and the resultant spectral energy transfer; (ii) nonlinear wave-particle interactions of SAW instabilities with energetic particles. Within the first route, it is advantageous to understand and describe nonlinear processes in term of proximity of the system to the Alfvénic state, where wave-wave interactions are minimized due to the cancellation of Reynolds and Maxwell stresses. Here, various wave-wave nonlinear dynamics are elucidated in terms of how they break the Alfvénic state. In particular, we discuss the qualitative and quantitative modification of the SAW parametric decay process due to finite ion compressibility and finite ion Larmor radius. We also show that toroidal geometry plays a crucial role in the nonlinear excitation of zonal structures by Alfvén eigenmodes. Within the second route, the coherent nonlinear dynamics of structures in the energetic particle phase space, by which secular resonant particle transport can occur on meso- and macro-scales, must be addressed and understood. These "nonlinear equilibria" or "phase-space zonal structures" dynamically evolve on characteristic (fluctuation induced) turbulent transport time scales, which are generally of the same order of the nonlinear time scale of the underlying fluctuations. In this work, we introduce the general structure of nonlinear Schrödinger equations with complex integro-differential nonlinear terms, which govern these physical processes. To elucidate all these aspects, theoretical analyses are presented together with numerical simulation results.

  14. Solving a Local Boundary Value Problem for a Nonlinear Nonstationary System in the Class of Feedback Controls

    Science.gov (United States)

    Kvitko, A. N.

    2018-01-01

    An algorithm convenient for numerical implementation is proposed for constructing differentiable control functions that transfer a wide class of nonlinear nonstationary systems of ordinary differential equations from an initial state to a given point of the phase space. Constructive sufficient conditions imposed on the right-hand side of the controlled system are obtained under which this transfer is possible. The control of a robotic manipulator is considered, and its numerical simulation is performed.

  15. A non-linear branch and cut method for solving discrete minimum compliance problems to global optimality

    DEFF Research Database (Denmark)

    Stolpe, Mathias; Bendsøe, Martin P.

    2007-01-01

    This paper present some initial results pertaining to a search for globally optimal solutions to a challenging benchmark example proposed by Zhou and Rozvany. This means that we are dealing with global optimization of the classical single load minimum compliance topology design problem with a fixed...... finite element discretization and with discrete design variables. Global optimality is achieved by the implementation of some specially constructed convergent nonlinear branch and cut methods, based on the use of natural relaxations and by applying strengthening constraints (linear valid inequalities...

  16. A non-linear branch and cut method for solving discrete minimum compliance problems to global optimality

    DEFF Research Database (Denmark)

    Stolpe, Mathias; Bendsøe, Martin P.

    2007-01-01

    This paper present some initial results pertaining to a search for globally optimal solutions to a challenging benchmark example proposed by Zhou and Rozvany. This means that we are dealing with global optimization of the classical single load minimum compliance topology design problem with a fixed...... finite element discretization and with discrete design variables. Global optimality is achieved by the implementation of some specially constructed convergent nonlinear branch and cut methods, based on the use of natural relaxations and by applying strengthening constraints (linear valid inequalities......) and cuts....

  17. Utilizing a Coupled Nonlinear Schrödinger Model to Solve the Linear Modal Problem for Stratified Flows

    Science.gov (United States)

    Liu, Tianyang; Chan, Hiu Ning; Grimshaw, Roger; Chow, Kwok Wing

    2017-11-01

    The spatial structure of small disturbances in stratified flows without background shear, usually named the `Taylor-Goldstein equation', is studied by employing the Boussinesq approximation (variation in density ignored except in the buoyancy). Analytical solutions are derived for special wavenumbers when the Brunt-Väisälä frequency is quadratic in hyperbolic secant, by comparison with coupled systems of nonlinear Schrödinger equations intensively studied in the literature. Cases of coupled Schrödinger equations with four, five and six components are utilized as concrete examples. Dispersion curves for arbitrary wavenumbers are obtained numerically. The computations of the group velocity, second harmonic, induced mean flow, and the second derivative of the angular frequency can all be facilitated by these exact linear eigenfunctions of the Taylor-Goldstein equation in terms of hyperbolic function, leading to a cubic Schrödinger equation for the evolution of a wavepacket. The occurrence of internal rogue waves can be predicted if the dispersion and cubic nonlinearity terms of the Schrödinger equations are of the same sign. Partial financial support has been provided by the Research Grants Council contract HKU 17200815.

  18. A high-order relaxation method with projective integration for solving nonlinear systems of hyperbolic conservation laws

    Science.gov (United States)

    Lafitte, Pauline; Melis, Ward; Samaey, Giovanni

    2017-07-01

    We present a general, high-order, fully explicit relaxation scheme which can be applied to any system of nonlinear hyperbolic conservation laws in multiple dimensions. The scheme consists of two steps. In a first (relaxation) step, the nonlinear hyperbolic conservation law is approximated by a kinetic equation with stiff BGK source term. Then, this kinetic equation is integrated in time using a projective integration method. After taking a few small (inner) steps with a simple, explicit method (such as direct forward Euler) to damp out the stiff components of the solution, the time derivative is estimated and used in an (outer) Runge-Kutta method of arbitrary order. We show that, with an appropriate choice of inner step size, the time step restriction on the outer time step is similar to the CFL condition for the hyperbolic conservation law. Moreover, the number of inner time steps is also independent of the stiffness of the BGK source term. We discuss stability and consistency, and illustrate with numerical results (linear advection, Burgers' equation and the shallow water and Euler equations) in one and two spatial dimensions.

  19. The nonlinear dynamics of family problem solving in adolescence: the predictive validity of a peaceful resolution attractor.

    Science.gov (United States)

    Dishion, Thomas J; Forgatch, Marion; Van Ryzin, Mark; Winter, Charlotte

    2012-07-01

    In this study we examined the videotaped family interactions of a community sample of adolescents and their parents. Youths were assessed in early to late adolescence on their levels of antisocial behavior. At age 16-17, youths and their parents were videotaped interacting while completing a variety of tasks, including family problem solving. The interactions were coded and compared for three developmental patterns of antisocial behavior: early onset, persistent; adolescence onset; and typically developing. The mean duration of conflict bouts was the only interaction pattern that discriminated the 3 groups. In the prediction of future antisocial behavior, parent and youth reports of transition entropy and conflict resolution interacted to account for antisocial behavior at age 18-19. Families with low entropy and peaceful resolutions predicted low levels of youth antisocial behavior at age 18-19. These findings suggest the need to study both attractors and repellers to understand family dynamics associated with health and social and emotional development.

  20. Nonlinear interaction between a pair of oblique modes in a supersonic mixing layer: Long-wave limit

    Science.gov (United States)

    Balsa, Thomas F.; Gartside, James

    1995-01-01

    The nonlinear interaction between a pair of symmetric, oblique, and spatial instability modes is studied in the long-wave limit using asymptotic methods. The base flow is taken to be a supersonic mixing layer whose Mach number is such that the corresponding vortex sheet is marginally stable according to Miles' criterion. It is shown that the amplitude of the mode obeys a nonlinear integro-differential equation. Numerical solutions of this equation show that, when the obliqueness angle is less than pi/4, the effect of the nonlinearity is to enhance the growth rate of the instability. The solution terminates in a singularity at a finite streamwise location. This result is reminiscent of that obtained in the vicinity of the neutral point by other authors in several different types of flows. On the other hand, when the obliqueness angle is more than pi/4, the streamwise development of the amplitude is characterized by a series of modulations. This arises from the fact that the nonlinear term in the amplitude equation may be either stabilizing or destabilizing, depending on the value of the streamwise coordinate. However, even in this case the amplitude of the disturbance increases, though not as rapidly as in the case for which the angle is less than pi/4. Quite generally then, the nonlinear interaction between two oblique modes in a supersonic mixing layer enhances the growth of the disturbance.

  1. Angular finite volume method for solving the multigroup transport equation with piecewise average scattering cross sections

    Energy Technology Data Exchange (ETDEWEB)

    Calloo, A.; Vidal, J.F.; Le Tellier, R.; Rimpault, G., E-mail: ansar.calloo@cea.fr, E-mail: jean-francois.vidal@cea.fr, E-mail: romain.le-tellier@cea.fr, E-mail: gerald.rimpault@cea.fr [CEA, DEN, DER/SPRC/LEPh, Saint-Paul-lez-Durance (France)

    2011-07-01

    This paper deals with the solving of the multigroup integro-differential form of the transport equation for fine energy group structure. In that case, multigroup transfer cross sections display strongly peaked shape for light scatterers and the current Legendre polynomial expansion is not well-suited to represent them. Furthermore, even if considering an exact scattering cross sections representation, the scattering source in the discrete ordinates method (also known as the Sn method) being calculated by sampling the angular flux at given directions, may be wrongly computed due to lack of angular support for the angular flux. Hence, following the work of Gerts and Matthews, an angular finite volume solver has been developed for 2D Cartesian geometries. It integrates the multigroup transport equation over discrete volume elements obtained by meshing the unit sphere with a product grid over the polar and azimuthal coordinates and by considering the integrated flux per solid angle element. The convergence of this method has been compared to the S{sub n} method for a highly anisotropic benchmark. Besides, piecewise-average scattering cross sections have been produced for non-bound Hydrogen atoms using a free gas model for thermal neutrons. LWR lattice calculations comparing Legendre representations of the Hydrogen scattering multigroup cross section at various orders and piecewise-average cross sections for this same atom are carried out (while keeping a Legendre representation for all other isotopes). (author)

  2. Angular finite volume method for solving the multigroup transport equation with piecewise average scattering cross sections

    International Nuclear Information System (INIS)

    Calloo, A.; Vidal, J.F.; Le Tellier, R.; Rimpault, G.

    2011-01-01

    This paper deals with the solving of the multigroup integro-differential form of the transport equation for fine energy group structure. In that case, multigroup transfer cross sections display strongly peaked shape for light scatterers and the current Legendre polynomial expansion is not well-suited to represent them. Furthermore, even if considering an exact scattering cross sections representation, the scattering source in the discrete ordinates method (also known as the Sn method) being calculated by sampling the angular flux at given directions, may be wrongly computed due to lack of angular support for the angular flux. Hence, following the work of Gerts and Matthews, an angular finite volume solver has been developed for 2D Cartesian geometries. It integrates the multigroup transport equation over discrete volume elements obtained by meshing the unit sphere with a product grid over the polar and azimuthal coordinates and by considering the integrated flux per solid angle element. The convergence of this method has been compared to the S_n method for a highly anisotropic benchmark. Besides, piecewise-average scattering cross sections have been produced for non-bound Hydrogen atoms using a free gas model for thermal neutrons. LWR lattice calculations comparing Legendre representations of the Hydrogen scattering multigroup cross section at various orders and piecewise-average cross sections for this same atom are carried out (while keeping a Legendre representation for all other isotopes). (author)

  3. The lie-algebraic structures and integrability of differential and differential-difference nonlinear dynamical systems

    International Nuclear Information System (INIS)

    Prykarpatsky, A.K.; Blackmore, D.L.; Bogolubov, N.N. Jr.

    2007-05-01

    The infinite-dimensional operator Lie algebras of the related integrable nonlocal differential-difference dynamical systems are treated as their hidden symmetries. As a result of their dimerization the Lax type representations for both local differential-difference equations and nonlocal ones are obtained. An alternative approach to the Lie-algebraic interpretation of the integrable local differential-difference systems is also proposed. The Hamiltonian representation for a hierarchy of Lax type equations on a dual space to the centrally extended Lie algebra of integro-differential operators with matrix-valued coefficients coupled with suitable eigenfunctions and adjoint eigenfunctions evolutions of associated spectral problems is obtained by means of a specially constructed Baecklund transformation. The Hamiltonian description for the corresponding set of additional symmetry hierarchies is represented. The relation of these hierarchies with Lax type integrable (3+1)-dimensional nonlinear dynamical systems and their triple Lax type linearizations is analyzed. The Lie-algebraic structures, related with centrally extended current operator Lie algebras are discussed with respect to constructing new nonlinear integrable dynamical systems on functional manifolds and super-manifolds. Special Poisson structures and related with them factorized integrable operator dynamical systems having interesting applications in modern mathematical physics, quantum computing mathematics and other fields are constructed. The previous purely computational results are explained within the approach developed. (author)

  4. Transport methods: general. 7. Formulation of a Fourier-Boltzmann Transformation to Solve the Three-Dimensional Transport Equation

    International Nuclear Information System (INIS)

    Stancic, V.

    2001-01-01

    This paper presents some elements of a new approach to solve analytically the linearized three-dimensional (3-D) transport equation of neutral particles. Since this task is of such special importance, we present some results of a paper that is still in progress. The most important is that using this transformation, an integro-differential equation with an analytical solution is obtained. For this purpose, a simplest 3-D equation is being considered which describes the transport process in an infinite medium. Until now, this equation has been analytically considered either using the Laplace transform with respect to time parameter t or applying the Fourier transform over the space coordinate. Both of them reduce the number of differential terms in the equation; however, evaluation of the inverse transformation is complicated. In this paper, we introduce for the first time a Fourier transform induced by the Boltzmann operator. For this, we use a complete set of 3-D eigenfunctions of the Boltzmann transport operator defined in a similar way as those that have been already used in 3-D transport theory as a basic set to transform the transport equation. This set consists of a continuous part and a discrete one with spectral measure. The density distribution equation shows the known form asymptotic behavior. Several applications are to be performed using this equation and compared to the benchmark one. Such an analysis certainly would be out of the available space

  5. Symmetric and arbitrarily high-order Birkhoff-Hermite time integrators and their long-time behaviour for solving nonlinear Klein-Gordon equations

    Science.gov (United States)

    Liu, Changying; Iserles, Arieh; Wu, Xinyuan

    2018-03-01

    The Klein-Gordon equation with nonlinear potential occurs in a wide range of application areas in science and engineering. Its computation represents a major challenge. The main theme of this paper is the construction of symmetric and arbitrarily high-order time integrators for the nonlinear Klein-Gordon equation by integrating Birkhoff-Hermite interpolation polynomials. To this end, under the assumption of periodic boundary conditions, we begin with the formulation of the nonlinear Klein-Gordon equation as an abstract second-order ordinary differential equation (ODE) and its operator-variation-of-constants formula. We then derive a symmetric and arbitrarily high-order Birkhoff-Hermite time integration formula for the nonlinear abstract ODE. Accordingly, the stability, convergence and long-time behaviour are rigorously analysed once the spatial differential operator is approximated by an appropriate positive semi-definite matrix, subject to suitable temporal and spatial smoothness. A remarkable characteristic of this new approach is that the requirement of temporal smoothness is reduced compared with the traditional numerical methods for PDEs in the literature. Numerical results demonstrate the advantage and efficiency of our time integrators in comparison with the existing numerical approaches.

  6. The breakdown of the weakly-nonlinear regime for kinetic instabilities

    Science.gov (United States)

    Sanz-Orozco, David; Berk, Herbert; Wang, Ge

    2017-10-01

    The evolution of marginally-unstable waves that interact resonantly with populations of energetic particles is governed by a well-known cubic integro-differential equation for the mode amplitude. One of the outcomes predicted by the equation is the so-called ``explosive'' regime, where the amplitude grows indefinitely, eventually taking the equation outside of its domain of validity. Beyond this point, only full Vlasov simulations will accurately describe the evolution of the mode amplitude. In this work, we study the breakdown of the cubic equation in detail. We find that, while the cubic equation is still valid, the distribution function of the energetic particles locally flattens or ``folds'' in phase space. This feature is unexpected in view of the assumptions of the theory that are given in. We also derive fifth-order terms in the wave equation, which not only give us a more accurate description of the marginally-unstable modes, but they also allow us to predict the breakdown of the cubic equation. Our findings allow us to better understand the transition between weakly-nonlinear modes and the long-term chirping modes that ultimately emerge.

  7. Birth-jump processes and application to forest fire spotting.

    Science.gov (United States)

    Hillen, T; Greese, B; Martin, J; de Vries, G

    2015-01-01

    Birth-jump models are designed to describe population models for which growth and spatial spread cannot be decoupled. A birth-jump model is a nonlinear integro-differential equation. We present two different derivations of this equation, one based on a random walk approach and the other based on a two-compartmental reaction-diffusion model. In the case that the redistribution kernels are highly concentrated, we show that the integro-differential equation can be approximated by a reaction-diffusion equation, in which the proliferation rate contributes to both the diffusion term and the reaction term. We completely solve the corresponding critical domain size problem and the minimal wave speed problem. Birth-jump models can be applied in many areas in mathematical biology. We highlight an application of our results in the context of forest fire spread through spotting. We show that spotting increases the invasion speed of a forest fire front.

  8. Spectral finite element methods for solving fractional differential equations with applications in anomalous transport

    Energy Technology Data Exchange (ETDEWEB)

    Carella, Alfredo Raul

    2012-09-15

    Quantifying species transport rates is a main concern in chemical and petrochemical industries. In particular, the design and operation of many large-scale industrial chemical processes is as much dependent on diffusion as it is on reaction rates. However, the existing diffusion models sometimes fail to predict experimentally observed behaviors and their accuracy is usually insufficient for process optimization purposes. Fractional diffusion models offer multiple possibilities for generalizing Flick's law in a consistent manner in order to account for history dependence and nonlocal effects. These models have not been extensively applied to the study of real systems, mainly due to their computational cost and mathematical complexity. A least squares spectral formulation was developed for solving fractional differential equations. The proposed method was proven particularly well-suited for dealing with the numerical difficulties inherent to fractional differential operators. The practical implementation was explained in detail in order to enhance reproducibility, and directions were specified for extending it to multiple dimensions and arbitrarily shaped domains. A numerical framework based on the least-squares spectral element method was developed for studying and comparing anomalous diffusion models in pellets. This simulation tool is capable of solving arbitrary integro-differential equations and can be effortlessly adapted to various problems in any number of dimensions. Simulations of the flow around a cylindrical particle were achieved by extending the functionality of the developed framework. A test case was analyzed by coupling the boundary condition yielded by the fluid model with two families of anomalous diffusion models: hyperbolic diffusion and fractional diffusion. Qualitative guidelines for determining the suitability of diffusion models can be formulated by complementing experimental data with the results obtained from this approach.(Author)

  9. Pole solutions for flame front propagation

    CERN Document Server

    Kupervasser, Oleg

    2015-01-01

    This book deals with solving mathematically the unsteady flame propagation equations. New original mathematical methods for solving complex non-linear equations and investigating their properties are presented. Pole solutions for flame front propagation are developed. Premixed flames and filtration combustion have remarkable properties: the complex nonlinear integro-differential equations for these problems have exact analytical solutions described by the motion of poles in a complex plane. Instead of complex equations, a finite set of ordinary differential equations is applied. These solutions help to investigate analytically and numerically properties of the flame front propagation equations.

  10. Nonlinear optimization

    CERN Document Server

    Ruszczynski, Andrzej

    2011-01-01

    Optimization is one of the most important areas of modern applied mathematics, with applications in fields from engineering and economics to finance, statistics, management science, and medicine. While many books have addressed its various aspects, Nonlinear Optimization is the first comprehensive treatment that will allow graduate students and researchers to understand its modern ideas, principles, and methods within a reasonable time, but without sacrificing mathematical precision. Andrzej Ruszczynski, a leading expert in the optimization of nonlinear stochastic systems, integrates the theory and the methods of nonlinear optimization in a unified, clear, and mathematically rigorous fashion, with detailed and easy-to-follow proofs illustrated by numerous examples and figures. The book covers convex analysis, the theory of optimality conditions, duality theory, and numerical methods for solving unconstrained and constrained optimization problems. It addresses not only classical material but also modern top...

  11. Nodal approximations of varying order by energy group for solving the diffusion equation

    International Nuclear Information System (INIS)

    Broda, J.T.

    1992-02-01

    The neutron flux across the nuclear reactor core is of interest to reactor designers and others. The diffusion equation, an integro-differential equation in space and energy, is commonly used to determine the flux level. However, the solution of a simplified version of this equation when automated is very time consuming. Since the flux level changes with time, in general, this calculation must be made repeatedly. Therefore solution techniques that speed the calculation while maintaining accuracy are desirable. One factor that contributes to the solution time is the spatial flux shape approximation used. It is common practice to use the same order flux shape approximation in each energy group even though this method may not be the most efficient. The one-dimensional, two-energy group diffusion equation was solved, for the node average flux and core k-effective, using two sets of spatial shape approximations for each of three reactor types. A fourth-order approximation in both energy groups forms the first set of approximations used. The second set used combines a second-order approximation with a fourth-order approximation in energy group two. Comparison of the results from the two approximation sets show that the use of a different order spatial flux shape approximation results in considerable loss in accuracy for the pressurized water reactor modeled. However, the loss in accuracy is small for the heavy water and graphite reactors modeled. The use of different order approximations in each energy group produces mixed results. Further investigation into the accuracy and computing time is required before any quantitative advantage of the use of the second-order approximation in energy group one and the fourth-order approximation in energy group two can be determined

  12. Some stability and boundedness criteria for a class of Volterra integro-differential systems

    Directory of Open Access Journals (Sweden)

    Jito Vanualailai

    2002-01-01

    Full Text Available Using Lyapunov and Lyapunov-like functionals, we study the stability and boundedness of the solutions of a system of Volterra integrodifferential equations. Our results, also extending some of the more well-known criteria, give new sufficient conditions for stability of the zero solution of the nonperturbed system, and prove that the same conditions for the perturbed system yield boundedness when the perturbation is $L^2$.

  13. Thermoacoustic tomography for an integro-differential wave equation modeling attenuation

    Science.gov (United States)

    Acosta, Sebastián; Palacios, Benjamín

    2018-02-01

    In this article we study the inverse problem of thermoacoustic tomography (TAT) on a medium with attenuation represented by a time-convolution (or memory) term, and whose consideration is motivated by the modeling of ultrasound waves in heterogeneous tissue via fractional derivatives with spatially dependent parameters. Under the assumption of being able to measure data on the whole boundary, we prove uniqueness and stability, and propose a convergent reconstruction method for a class of smooth variable sound speeds. By a suitable modification of the time reversal technique, we obtain a Neumann series reconstruction formula.

  14. Deterministic factor analysis: methods of integro-differentiation of non-integral order

    Directory of Open Access Journals (Sweden)

    Valentina V. Tarasova

    2016-12-01

    Full Text Available Objective to summarize the methods of deterministic factor economic analysis namely the differential calculus and the integral method. nbsp Methods mathematical methods for integrodifferentiation of nonintegral order the theory of derivatives and integrals of fractional nonintegral order. Results the basic concepts are formulated and the new methods are developed that take into account the memory and nonlocality effects in the quantitative description of the influence of individual factors on the change in the effective economic indicator. Two methods are proposed for integrodifferentiation of nonintegral order for the deterministic factor analysis of economic processes with memory and nonlocality. It is shown that the method of integrodifferentiation of nonintegral order can give more accurate results compared with standard methods method of differentiation using the first order derivatives and the integral method using the integration of the first order for a wide class of functions describing effective economic indicators. Scientific novelty the new methods of deterministic factor analysis are proposed the method of differential calculus of nonintegral order and the integral method of nonintegral order. Practical significance the basic concepts and formulas of the article can be used in scientific and analytical activity for factor analysis of economic processes. The proposed method for integrodifferentiation of nonintegral order extends the capabilities of the determined factorial economic analysis. The new quantitative method of deterministic factor analysis may become the beginning of quantitative studies of economic agents behavior with memory hereditarity and spatial nonlocality. The proposed methods of deterministic factor analysis can be used in the study of economic processes which follow the exponential law in which the indicators endogenous variables are power functions of the factors exogenous variables including the processes described by the Cobb ndash Douglas production function since these methods allow to more accurately describe the total influence of the factors in comparison with the standard method. The proposed methods can be used in the study of economic processes described by equations with a powerlaw nonlocality in factor space and in state space.

  15. Qualitative analysis of an integro-differential equation model of periodic chemotherapy

    KAUST Repository

    Jain, Harsh Vardhan; Byrne, Helen M.

    2012-01-01

    An existing model of tumor growth that accounts for cell cycle arrest and cell death induced by chemotherapy is extended to simulate the response to treatment of a tumor growing in vivo. The tumor is assumed to undergo logistic growth in the absence

  16. Singular Cauchy Initial Value Problem for Certain Classes of Integro-Differential Equations

    Directory of Open Access Journals (Sweden)

    Zdeněk Šmarda

    2010-01-01

    Full Text Available The existence and uniqueness of solutions and asymptotic estimate of solution formulas are studied for the following initial value problem: g(ty′(t=ay(t[1+f(t,y(t,∫0+tK(t,s,y(t,y(sds], y(0+=0, t∈(0,t0], where a>0 is a constant and t0>0. An approach which combines topological method of T. Ważewski and Schauder's fixed point theorem is used.

  17. Singular Cauchy Initial Value Problem for Certain Classes of Integro-Differential Equations

    Directory of Open Access Journals (Sweden)

    Šmarda Zdeněk

    2010-01-01

    Full Text Available The existence and uniqueness of solutions and asymptotic estimate of solution formulas are studied for the following initial value problem: , , , where is a constant and . An approach which combines topological method of T. Ważewski and Schauder's fixed point theorem is used.

  18. Integro-differential equation analysis and radioisotope imaging systems. Research proposal

    International Nuclear Information System (INIS)

    Hart, H.

    1976-01-01

    Design modifications of a five-probe focusing collimator coincidence radioisotope scanning system are described. Clinical applications of the system were tested in phantoms using radioisotopes with short biological half-lives, including 75 Se, 192 Ir, 43 K, 130 I, and 82 Br. Data processing methods are also described

  19. Asymptotic and spectral analysis of the gyrokinetic-waterbag integro-differential operator in toroidal geometry

    Energy Technology Data Exchange (ETDEWEB)

    Besse, Nicolas, E-mail: Nicolas.Besse@oca.eu [Laboratoire J.-L. Lagrange, UMR CNRS/OCA/UCA 7293, Université Côte d’Azur, Observatoire de la Côte d’Azur, Bd de l’Observatoire CS 34229, 06304 Nice Cedex 4 (France); Institut Jean Lamour, UMR CNRS/UL 7198, Université de Lorraine, BP 70239 54506 Vandoeuvre-lès-Nancy Cedex (France); Coulette, David, E-mail: David.Coulette@ipcms.unistra.fr [Institut Jean Lamour, UMR CNRS/UL 7198, Université de Lorraine, BP 70239 54506 Vandoeuvre-lès-Nancy Cedex (France); Institut de Physique et Chimie des Matériaux de Strasbourg, UMR CNRS/US 7504, Université de Strasbourg, 23 Rue du Loess, 67034 Strasbourg (France)

    2016-08-15

    Achieving plasmas with good stability and confinement properties is a key research goal for magnetic fusion devices. The underlying equations are the Vlasov–Poisson and Vlasov–Maxwell (VPM) equations in three space variables, three velocity variables, and one time variable. Even in those somewhat academic cases where global equilibrium solutions are known, studying their stability requires the analysis of the spectral properties of the linearized operator, a daunting task. We have identified a model, for which not only equilibrium solutions can be constructed, but many of their stability properties are amenable to rigorous analysis. It uses a class of solution to the VPM equations (or to their gyrokinetic approximations) known as waterbag solutions which, in particular, are piecewise constant in phase-space. It also uses, not only the gyrokinetic approximation of fast cyclotronic motion around magnetic field lines, but also an asymptotic approximation regarding the magnetic-field-induced anisotropy: the spatial variation along the field lines is taken much slower than across them. Together, these assumptions result in a drastic reduction in the dimensionality of the linearized problem, which becomes a set of two nested one-dimensional problems: an integral equation in the poloidal variable, followed by a one-dimensional complex Schrödinger equation in the radial variable. We show here that the operator associated to the poloidal variable is meromorphic in the eigenparameter, the pulsation frequency. We also prove that, for all but a countable set of real pulsation frequencies, the operator is compact and thus behaves mostly as a finite-dimensional one. The numerical algorithms based on such ideas have been implemented in a companion paper [D. Coulette and N. Besse, “Numerical resolution of the global eigenvalue problem for gyrokinetic-waterbag model in toroidal geometry” (submitted)] and were found to be surprisingly close to those for the original gyrokinetic-Vlasov equations. The purpose of the present paper is to make these new ideas accessible to two readerships: applied mathematicians and plasma physicists.

  20. The Form of the Solutions of the Linear Integro-Differential Equations of Subsonic Aeroelasticity.

    Science.gov (United States)

    1979-09-01

    coefficients w (0) are given in Table 3; it V follows that, for T > 0 and (E - K v2) non-singular, the inverse transform of M- ) has the form, using (B-I) V...degree of freedom system by expanding )M- I in the form of equation (35), obtaining its inverse transform using the v -1results of Appendix A and hence...obtaining the inverse transform of M- l . The two-dimensional case, when the characteristic equation has a zero root, is not as simple. * Assuming all

  1. Qualitative analysis of an integro-differential equation model of periodic chemotherapy

    KAUST Repository

    Jain, Harsh Vardhan

    2012-12-01

    An existing model of tumor growth that accounts for cell cycle arrest and cell death induced by chemotherapy is extended to simulate the response to treatment of a tumor growing in vivo. The tumor is assumed to undergo logistic growth in the absence of therapy, and treatment is administered periodically rather than continuously. Necessary and sufficient conditions for the global stability of the cancer-free equilibrium are derived and conditions under which the system evolves to periodic solutions are determined. © 2012 Elsevier Ltd. All rights reserved.

  2. Application of the Green's function method for 2- and 3-dimensional steady transonic flows

    Science.gov (United States)

    Tseng, K.

    1984-01-01

    A Time-Domain Green's function method for the nonlinear time-dependent three-dimensional aerodynamic potential equation is presented. The Green's theorem is being used to transform the partial differential equation into an integro-differential-delay equation. Finite-element and finite-difference methods are employed for the spatial and time discretizations to approximate the integral equation by a system of differential-delay equations. Solution may be obtained by solving for this nonlinear simultaneous system of equations in time. This paper discusses the application of the method to the Transonic Small Disturbance Equation and numerical results for lifting and nonlifting airfoils and wings in steady flows are presented.

  3. PREFACE: Nonlinearity and Geometry: connections with integrability Nonlinearity and Geometry: connections with integrability

    Science.gov (United States)

    Cieslinski, Jan L.; Ferapontov, Eugene V.; Kitaev, Alexander V.; Nimmo, Jonathan J. C.

    2009-10-01

    accessible to younger researchers. It is not out of place to recall that earlier the Institute of Theoretical of Physics of Warsaw University organized two, now legendary, Jadwisin Soliton Workshops (1977 and 1979); see the short note in Physica D: Nonlinear Phenomena (1980 vol. 1, issue 1, pp 159-163) written by Antoni Sym who was deeply engaged in the organization of these conferences. In scale and scope both Jadwisin workshops preceded a series of very successful NEEDS conferences. Among the celebrated participants of the Jadwisin meeetings one can find names of great importance for the history of soliton theory: Martin Kruskal, Norman Zabuski, Mark Ablowitz, David Kaup, Allan Newell, Vladimir Zakharov, Sergei Manakov, Francesco Calogero, Antonio Degasperis and Ryogo Hirota. This special issue begins with an introductory historical article in which Antoni Sym presents the most important ideas in the scientific biography of Gaston Darboux. We encourage the readers discover the greatest (scientific!) love of Darboux. This is followed by five review papers. M Błaszak and B M Szablikowski discuss the general R-matrix formalism for the construction of integrable systems with infinitely many degrees of freedom. The general theory is applied to several infinite-dimensional Lie algebras leading to new examples of dispersionless and dispersive (soliton) integrable field systems in 1+1 and 2+1 dimensions. J L Cieśliński presents the Darboux-Bäcklund transformation for 1+1-dimensional integrable systems of PDEs. He compares existing approaches to the construction of multisoliton Darboux matrices, discusses the nonisospectral case and presents some new results on the linear and bilinear invariants of the Darboux-Bäcklund transformation. M Dunajski presents twistor theory as a geometric tool for solving nonlinear differential equations. Many soliton equations admit twistor interpretation in terms of holomophic vector bundles. A different approach is provided for dispersionless

  4. A domian Decomposition Method for Transient Neutron Transport with Pomrning-Eddington Approximation

    International Nuclear Information System (INIS)

    Hendi, A.A.; Abulwafa, E.E.

    2008-01-01

    The time-dependent neutron transport problem is approximated using the Pomraning-Eddington approximation. This approximation is two-flux approximation that expands the angular intensity in terms of the energy density and the net flux. This approximation converts the integro-differential Boltzmann equation into two first order differential equations. The A domian decomposition method that used to solve the linear or nonlinear differential equations is used to solve the resultant two differential equations to find the neutron energy density and net flux, which can be used to calculate the neutron angular intensity through the Pomraning-Eddington approximation

  5. A technique for determining the optimum mix of logistics service providers of a make-to-order supply chain by formulating and solving a constrained nonlinear cost optimization problem

    Directory of Open Access Journals (Sweden)

    Mrityunjoy Roy

    2013-04-01

    Full Text Available In this paper, a technique has been developed to determine the optimum mix of logistic service providers of a make-to-order (MTO supply chain. A serial MTO supply chain with different stages/ processes has been considered. For each stage different logistic service providers with different mean processing lead times, but same lead time variances are available. A realistic assumption that for each stage, the logistic service provider who charges more for his service consumes less processing lead time and vice-versa has been made in our study. Thus for each stage, for each service provider, a combination of cost and mean processing lead time is available. Using these combinations, for each stage, a polynomial curve, expressing cost of that stage as a function of mean processing lead time is fit. Cumulating all such expressions of cost for the different stages along with incorporation of suitable constraints arising out of timely delivery, results in the formulation of a constrained nonlinear cost optimization problem. On solving the problem using mathematica, optimum processing lead time for each stage is obtained. Using these optimum processing lead times and by employing a simple technique the optimum logistic service provider mix of the supply chain along with the corresponding total cost of processing is determined. Finally to examine the effect of changes in different parameters on the optimum total processing cost of the supply chain, sensitivity analysis has been carried out graphically.

  6. Nonlinear Physics of Plasmas

    CERN Document Server

    Kono, Mitsuo

    2010-01-01

    A nonlinearity is one of the most important notions in modern physics. A plasma is rich in nonlinearities and provides a variety of behaviors inherent to instabilities, coherent wave structures and turbulence. The book covers the basic concepts and mathematical methods, necessary to comprehend nonlinear problems widely encountered in contemporary plasmas, but also in other fields of physics and current research on self-organized structures and magnetized plasma turbulence. The analyses make use of strongly nonlinear models solved by analytical techniques backed by extensive simulations and available experiments. The text is written for senior undergraduates, graduate students, lecturers and researchers in laboratory, space and fusion plasmas.

  7. Exponential function method for solving nonlinear ordinary ...

    Indian Academy of Sciences (India)

    [14] introduced a new system of rational. 79 ..... Also, for k-power of function f (η), by induction, we have ..... reliability and efficiency of the method. .... electric field and the polarization effects are negligible and B(x) is assumed by Chaim [8] as.

  8. Multiscale empirical interpolation for solving nonlinear PDEs

    KAUST Repository

    Calo, Victor M.; Efendiev, Yalchin R.; Galvis, Juan; Ghommem, Mehdi

    2014-01-01

    residuals and Jacobians on the fine grid. We use empirical interpolation concepts to evaluate these residuals and Jacobians of the multiscale system with a computational cost which is proportional to the size of the coarse-scale problem rather than the fully

  9. Nonlinear Approaches in Engineering Applications

    CERN Document Server

    Jazar, Reza

    2012-01-01

    Nonlinear Approaches in Engineering Applications focuses on nonlinear phenomena that are common in the engineering field. The nonlinear approaches described in this book provide a sound theoretical base and practical tools to design and analyze engineering systems with high efficiency and accuracy and with less energy and downtime. Presented here are nonlinear approaches in areas such as dynamic systems, optimal control and approaches in nonlinear dynamics and acoustics. Coverage encompasses a wide range of applications and fields including mathematical modeling and nonlinear behavior as applied to microresonators, nanotechnologies, nonlinear behavior in soil erosion,nonlinear population dynamics, and optimization in reducing vibration and noise as well as vibration in triple-walled carbon nanotubes. This book also: Provides a complete introduction to nonlinear behavior of systems and the advantages of nonlinearity as a tool for solving engineering problems Includes applications and examples drawn from the el...

  10. A reliable treatment for nonlinear Schroedinger equations

    International Nuclear Information System (INIS)

    Khani, F.; Hamedi-Nezhad, S.; Molabahrami, A.

    2007-01-01

    Exp-function method is used to find a unified solution of nonlinear wave equation. Nonlinear Schroedinger equations with cubic and power law nonlinearity are selected to illustrate the effectiveness and simplicity of the method. It is shown that the Exp-function method, with the help of symbolic computation, provides a powerful mathematical tool for solving nonlinear equation

  11. SPARSE ELECTROMAGNETIC IMAGING USING NONLINEAR LANDWEBER ITERATIONS

    KAUST Repository

    Desmal, Abdulla; Bagci, Hakan

    2015-01-01

    minimization problem is solved using nonlinear Landweber iterations, where at each iteration a thresholding function is applied to enforce the sparseness-promoting L0/L1-norm constraint. The thresholded nonlinear Landweber iterations are applied to several two

  12. Solving the equation of neutron transport

    International Nuclear Information System (INIS)

    Nasfi, Rim

    2009-01-01

    This work is devoted to the study of some numerical methods of resolution of the problem of transport of the neutrons. We started by introducing the equation integro-differential transport of the neutrons. Then we applied the finite element method traditional for stationary and nonstationary linear problems in 2D. A great part is reserved for the presentation of the mixed numerical diagram and mixed hybrid with two types of uniform grids: triangular and rectangular. Thereafter we treated some numerical examples by implementations in Matlab in order to test the convergence of each method. To finish, we had results of simulation by the Monte Carlo method on a problem of two-dimensional transport with an aim of comparing them with the results resulting from the finite element method mixed hybrids. Some remarks and prospects conclude this work.

  13. PREFACE Integrability and nonlinear phenomena Integrability and nonlinear phenomena

    Science.gov (United States)

    Gómez-Ullate, David; Lombardo, Sara; Mañas, Manuel; Mazzocco, Marta; Nijhoff, Frank; Sommacal, Matteo

    2010-10-01

    one can generalize or adapt this construction to different settings like the integro-differential, discrete or super-symmetric ones. The emphasis is usually to find auxiliary linear systems defining an infinite set of linear commuting flows whose solutions, if some asymptotic conditions are imposed, are named wave or Baker-Akhiezer functions. These linear flows determine the so called Lax equations, another infinite set of commuting equations whose compatibility leads to the so called Zakharov-Shabat system. An alternative description of the hierarchies is achieved with the use of the bilinear equations directly linked with the tau-function description of the hierarchy. There are two paradigmatic integrable hierarchies, namely the KP and 2-dimensional Toda lattice (2DTL). These hierarchies are treated within this volume in three contributions. In particular, Takasaki [5] reconsiders the extended Toda hierarchy of Carlet, Dubrovin and Zhang in the light of Ogawa's 2 + 1D extension of the 1D Toda hierarchy. It turns out that the former may be thought of as some sort of dimensional reduction of the latter. This explains the structure of the bilinear formalism proposed by Milanov. Carlet and Manas [6] study the 2-component KP and 2D Toda hierarchies and solve explicitly several implicit constraints present in the usual Lax formulation of the hierarchy, thus identifying a set of free dependent variables for such hierarchies. Finally, the KP hierarchy is considered in the paper by Lin et al [7], which explores the extended flows of a q-deformed modified KP hierarchy leading to the introduction of self-consistent sources. By a combination of the dressing method and the method of variation of constants, the authors are able through a dressing approach to find a scheme for the construction of solutions of the corresponding integrable equations with self-consistent sources. The study of dispersionless integrable hierarchies is an active field of research, and this special issue

  14. On quantization, the generalised Schroedinger equation and classical mechanics

    International Nuclear Information System (INIS)

    Jones, K.R.W.

    1991-01-01

    A ψ-dependent linear functional operator, was defined, which solves the problem of quantization in non-relativistic quantum mechanics. Weyl ordering is implemented automatically and permits derivation of many of the quantum to classical correspondences. The parameter λ presents a natural C ∞ deformation of the dynamical structure of quantum mechanics via a non-linear integro-differential 'Generalised Schroedinger Equation', admitting an infinite family of soliton solutions. All these solutions are presented and it is shown that this equation gives an exact dynamic and energetic reproduction of classical mechanics with the correct measurement theoretic limit. 23 refs

  15. Solving applied mathematical problems with Matlab

    CERN Document Server

    Xue, Dingyu

    2008-01-01

    Computer Mathematics Language-An Overview. Fundamentals of MATLAB Programming. Calculus Problems. MATLAB Computations of Linear Algebra Problems. Integral Transforms and Complex Variable Functions. Solutions to Nonlinear Equations and Optimization Problems. MATLAB Solutions to Differential Equation Problems. Solving Interpolations and Approximations Problems. Solving Probability and Mathematical Statistics Problems. Nontraditional Solution Methods for Mathematical Problems.

  16. Error analysis in Fourier methods for option pricing for exponential Lévy processes

    KAUST Repository

    Crocce, Fabian; Hä ppö lä , Juho; Keissling, Jonas; Tempone, Raul

    2015-01-01

    We derive an error bound for utilising the discrete Fourier transform method for solving Partial Integro-Differential Equations (PIDE) that describe european option prices for exponential Lévy driven asset prices. We give sufficient conditions

  17. Nonlinear approaches in engineering applications 2

    CERN Document Server

    Jazar, Reza N

    2013-01-01

    Provides updated principles and applications of the nonlinear approaches in solving engineering and physics problems Demonstrates how nonlinear approaches may open avenues to better, safer, cheaper systems with less energy consumption Has a strong emphasis on the application, physical meaning, and methodologies of nonlinear approaches in different engineering and science problems

  18. Diffusion Influenced Adsorption Kinetics.

    Science.gov (United States)

    Miura, Toshiaki; Seki, Kazuhiko

    2015-08-27

    When the kinetics of adsorption is influenced by the diffusive flow of solutes, the solute concentration at the surface is influenced by the surface coverage of solutes, which is given by the Langmuir-Hinshelwood adsorption equation. The diffusion equation with the boundary condition given by the Langmuir-Hinshelwood adsorption equation leads to the nonlinear integro-differential equation for the surface coverage. In this paper, we solved the nonlinear integro-differential equation using the Grünwald-Letnikov formula developed to solve fractional kinetics. Guided by the numerical results, analytical expressions for the upper and lower bounds of the exact numerical results were obtained. The upper and lower bounds were close to the exact numerical results in the diffusion- and reaction-controlled limits, respectively. We examined the validity of the two simple analytical expressions obtained in the diffusion-controlled limit. The results were generalized to include the effect of dispersive diffusion. We also investigated the effect of molecular rearrangement of anisotropic molecules on surface coverage.

  19. Nonlinear ordinary differential equations analytical approximation and numerical methods

    CERN Document Server

    Hermann, Martin

    2016-01-01

    The book discusses the solutions to nonlinear ordinary differential equations (ODEs) using analytical and numerical approximation methods. Recently, analytical approximation methods have been largely used in solving linear and nonlinear lower-order ODEs. It also discusses using these methods to solve some strong nonlinear ODEs. There are two chapters devoted to solving nonlinear ODEs using numerical methods, as in practice high-dimensional systems of nonlinear ODEs that cannot be solved by analytical approximate methods are common. Moreover, it studies analytical and numerical techniques for the treatment of parameter-depending ODEs. The book explains various methods for solving nonlinear-oscillator and structural-system problems, including the energy balance method, harmonic balance method, amplitude frequency formulation, variational iteration method, homotopy perturbation method, iteration perturbation method, homotopy analysis method, simple and multiple shooting method, and the nonlinear stabilized march...

  20. Nonlinear optics

    International Nuclear Information System (INIS)

    Boyd, R.W.

    1992-01-01

    Nonlinear optics is the study of the interaction of intense laser light with matter. This book is a textbook on nonlinear optics at the level of a beginning graduate student. The intent of the book is to provide an introduction to the field of nonlinear optics that stresses fundamental concepts and that enables the student to go on to perform independent research in this field. This book covers the areas of nonlinear optics, quantum optics, quantum electronics, laser physics, electrooptics, and modern optics

  1. Integro-differential equation analysis and radioisotope imaging systems. Research proposal. [Testing of radioisotope imaging system in phantoms

    Energy Technology Data Exchange (ETDEWEB)

    Hart, H.

    1976-03-09

    Design modifications of a five-probe focusing collimator coincidence radioisotope scanning system are described. Clinical applications of the system were tested in phantoms using radioisotopes with short biological half-lives, including /sup 75/Se, /sup 192/Ir, /sup 43/K, /sup 130/I, and /sup 82/Br. Data processing methods are also described. (CH)

  2. Contribution of non integer integro-differential operators (NIDO) to the geometrical understanding of Riemann's conjecture-(II)

    International Nuclear Information System (INIS)

    Le Mehaute, Alain; El Kaabouchi, Abdelaziz; Nivanen, Laurent

    2008-01-01

    Advances in fractional analysis suggest a new way for the physics understanding of Riemann's conjecture. It asserts that, if s is a complex number, the non trivial zeros of zeta function 1/(ζ(s)) =Σ n=1 ∞ (μ(n))/(n s ) in the gap [0, 1], is characterized by s=1/2 (1+2iθ). This conjecture can be understood as a consequence of 1/2-order fractional differential characteristics of automorph dynamics upon opened punctuated torus with an angle at infinity equal to π/4. This physical interpretation suggests new opportunities for revisiting the cryptographic methodologies

  3. Asymptotic analysis and optimal control of an integro-differential system modelling healthy and cancer cells exposed to chemotherapy

    KAUST Repository

    Pouchol, Camille; Clairambault, Jean; Lorz, Alexander; Tré lat, Emmanuel

    2017-01-01

    to the treatment. We analyse the asymptotic behaviour of the model under constant infusion of drugs. By designing an appropriate Lyapunov function, we prove that both cell densities converge to Dirac masses. We then define an optimal control problem, by considering

  4. Nonlinear dynamics of resistive electrostatic drift waves

    DEFF Research Database (Denmark)

    Korsholm, Søren Bang; Michelsen, Poul; Pécseli, H.L.

    1999-01-01

    The evolution of weakly nonlinear electrostatic drift waves in an externally imposed strong homogeneous magnetic field is investigated numerically in three spatial dimensions. The analysis is based on a set of coupled, nonlinear equations, which are solved for an initial condition which is pertur......The evolution of weakly nonlinear electrostatic drift waves in an externally imposed strong homogeneous magnetic field is investigated numerically in three spatial dimensions. The analysis is based on a set of coupled, nonlinear equations, which are solved for an initial condition which...... polarity, i.e. a pair of electrostatic convective cells....

  5. Methods of solving nonstandard problems

    CERN Document Server

    Grigorieva, Ellina

    2015-01-01

    This book, written by an accomplished female mathematician, is the second to explore nonstandard mathematical problems – those that are not directly solved by standard mathematical methods but instead rely on insight and the synthesis of a variety of mathematical ideas.   It promotes mental activity as well as greater mathematical skills, and is an ideal resource for successful preparation for the mathematics Olympiad. Numerous strategies and techniques are presented that can be used to solve intriguing and challenging problems of the type often found in competitions.  The author uses a friendly, non-intimidating approach to emphasize connections between different fields of mathematics and often proposes several different ways to attack the same problem.  Topics covered include functions and their properties, polynomials, trigonometric and transcendental equations and inequalities, optimization, differential equations, nonlinear systems, and word problems.   Over 360 problems are included with hints, ...

  6. Nonlinear optics

    CERN Document Server

    Bloembergen, Nicolaas

    1996-01-01

    Nicolaas Bloembergen, recipient of the Nobel Prize for Physics (1981), wrote Nonlinear Optics in 1964, when the field of nonlinear optics was only three years old. The available literature has since grown by at least three orders of magnitude.The vitality of Nonlinear Optics is evident from the still-growing number of scientists and engineers engaged in the study of new nonlinear phenomena and in the development of new nonlinear devices in the field of opto-electronics. This monograph should be helpful in providing a historical introduction and a general background of basic ideas both for expe

  7. Fully implicit kinetic modelling of collisional plasmas

    International Nuclear Information System (INIS)

    Mousseau, V.A.

    1996-05-01

    This dissertation describes a numerical technique, Matrix-Free Newton Krylov, for solving a simplified Vlasov-Fokker-Planck equation. This method is both deterministic and fully implicit, and may not have been a viable option before current developments in numerical methods. Results are presented that indicate the efficiency of the Matrix-Free Newton Krylov method for these fully-coupled, nonlinear integro-differential equations. The use and requirement for advanced differencing is also shown. To this end, implementations of Chang-Cooper differencing and flux limited Quadratic Upstream Interpolation for Convective Kinematics (QUICK) are presented. Results are given for a fully kinetic ion-electron problem with a self consistent electric field calculated from the ion and electron distribution functions. This numerical method, including advanced differencing, provides accurate solutions, which quickly converge on workstation class machines. It is demonstrated that efficient steady-state solutions can be achieved to the non-linear integro-differential equation, obtaining quadratic convergence, without incurring the large memory requirements of an integral operator. Model problems are presented which simulate plasma impinging on a plate with both high and low neutral particle recycling typical of a divertor in a Tokamak device. These model problems demonstrate the performance of the new solution method

  8. Nonlinear Dynamics of Electrostatically Actuated MEMS Arches

    KAUST Repository

    Al Hennawi, Qais M.

    2015-01-01

    In this thesis, we present theoretical and experimental investigation into the nonlinear statics and dynamics of clamped-clamped in-plane MEMS arches when excited by an electrostatic force. Theoretically, we first solve the equation of motion using

  9. Solution of linear and nonlinear matrix systems. Application to a nonlinear diffusion equation

    International Nuclear Information System (INIS)

    Bonnet, M.; Meurant, G.

    1978-01-01

    The object of this study is to compare different methods of solving linear and nonlinear algebraic systems and to apply them to the nonlinear system obtained by discretizing a nonlinear diffusion equation. For linear systems the conventional methods of alternating direction type or Gauss Seidel's methods are compared to more recent ones of the type of generalized conjugate gradient; the superiority of the latter is shown by numerical examples. For nonlinear systems, a method of nonlinear conjugate gradient is studied together with Newton's method and some of its variants. It should be noted, however, that Newton's method is found to be more efficient when coupled with a good method for solving the linear system. As a conclusion, these methods are used to solve a nonlinear diffusion problem and the numerical results obtained are compared [fr

  10. Nonlinear Science

    CERN Document Server

    Yoshida, Zensho

    2010-01-01

    This book gives a general, basic understanding of the mathematical structure "nonlinearity" that lies in the depths of complex systems. Analyzing the heterogeneity that the prefix "non" represents with respect to notions such as the linear space, integrability and scale hierarchy, "nonlinear science" is explained as a challenge of deconstruction of the modern sciences. This book is not a technical guide to teach mathematical tools of nonlinear analysis, nor a zoology of so-called nonlinear phenomena. By critically analyzing the structure of linear theories, and cl

  11. Nonlinear oscillations

    CERN Document Server

    Nayfeh, Ali Hasan

    1995-01-01

    Nonlinear Oscillations is a self-contained and thorough treatment of the vigorous research that has occurred in nonlinear mechanics since 1970. The book begins with fundamental concepts and techniques of analysis and progresses through recent developments and provides an overview that abstracts and introduces main nonlinear phenomena. It treats systems having a single degree of freedom, introducing basic concepts and analytical methods, and extends concepts and methods to systems having degrees of freedom. Most of this material cannot be found in any other text. Nonlinear Oscillations uses sim

  12. International Conference on Applications in Nonlinear Dynamics

    CERN Document Server

    Longhini, Patrick; Palacios, Antonio

    2017-01-01

    This book presents collaborative research works carried out by experimentalists and theorists around the world in the field of nonlinear dynamical systems. It provides a forum for applications of nonlinear systems while solving practical problems in science and engineering. Topics include: Applied Nonlinear Optics, Sensor, Radar & Communication Signal Processing, Nano Devices, Nonlinear Biomedical Applications, Circuits & Systems, Coupled Nonlinear Oscillator, Precision Timing Devices, Networks, and other contemporary topics in the general field of Nonlinear Science. This book provides a comprehensive report of the various research projects presented at the International Conference on Applications in Nonlinear Dynamics (ICAND 2016) held in Denver, Colorado, 2016. It can be a valuable tool for scientists and engineering interested in connecting ideas and methods in nonlinear dynamics with actual design, fabrication and implementation of engineering applications or devices.

  13. NR-code: Nonlinear reconstruction code

    Science.gov (United States)

    Yu, Yu; Pen, Ue-Li; Zhu, Hong-Ming

    2018-04-01

    NR-code applies nonlinear reconstruction to the dark matter density field in redshift space and solves for the nonlinear mapping from the initial Lagrangian positions to the final redshift space positions; this reverses the large-scale bulk flows and improves the precision measurement of the baryon acoustic oscillations (BAO) scale.

  14. Nonlinear systems

    CERN Document Server

    Palmero, Faustino; Lemos, M; Sánchez-Rey, Bernardo; Casado-Pascual, Jesús

    2018-01-01

    This book presents an overview of the most recent advances in nonlinear science. It provides a unified view of nonlinear properties in many different systems and highlights many  new developments. While volume 1 concentrates on mathematical theory and computational techniques and challenges, which are essential for the study of nonlinear science, this second volume deals with nonlinear excitations in several fields. These excitations can be localized and transport energy and matter in the form of breathers, solitons, kinks or quodons with very different characteristics, which are discussed in the book. They can also transport electric charge, in which case they are known as polarobreathers or solectrons. Nonlinear excitations can influence function and structure in biology, as for example, protein folding. In crystals and other condensed matter, they can modify transport properties, reaction kinetics and interact with defects. There are also engineering applications in electric lattices, Josephson junction a...

  15. Cosmological effects of nonlinear electrodynamics

    International Nuclear Information System (INIS)

    Novello, M; Goulart, E; Salim, J M; Bergliaffa, S E Perez

    2007-01-01

    It will be shown that a given realization of nonlinear electrodynamics, used as a source of Einstein's equations, generates a cosmological model with interesting features, namely a phase of current cosmic acceleration, and the absence of an initial singularity, thus pointing to a way of solving two important problems in cosmology

  16. Nonlinear optics

    CERN Document Server

    Boyd, Robert W

    2013-01-01

    Nonlinear Optics is an advanced textbook for courses dealing with nonlinear optics, quantum electronics, laser physics, contemporary and quantum optics, and electrooptics. Its pedagogical emphasis is on fundamentals rather than particular, transitory applications. As a result, this textbook will have lasting appeal to a wide audience of electrical engineering, physics, and optics students, as well as those in related fields such as materials science and chemistry.Key Features* The origin of optical nonlinearities, including dependence on the polarization of light* A detailed treatment of the q

  17. Nonlinear data assimilation

    CERN Document Server

    Van Leeuwen, Peter Jan; Reich, Sebastian

    2015-01-01

    This book contains two review articles on nonlinear data assimilation that deal with closely related topics but were written and can be read independently. Both contributions focus on so-called particle filters. The first contribution by Jan van Leeuwen focuses on the potential of proposal densities. It discusses the issues with present-day particle filters and explorers new ideas for proposal densities to solve them, converging to particle filters that work well in systems of any dimension, closing the contribution with a high-dimensional example. The second contribution by Cheng and Reich discusses a unified framework for ensemble-transform particle filters. This allows one to bridge successful ensemble Kalman filters with fully nonlinear particle filters, and allows a proper introduction of localization in particle filters, which has been lacking up to now.

  18. New method for solving multidimensional scattering problem

    International Nuclear Information System (INIS)

    Melezhik, V.S.

    1991-01-01

    A new method is developed for solving the quantum mechanical problem of scattering of a particle with internal structure. The multichannel scattering problem is formulated as a system of nonlinear functional equations for the wave function and reaction matrix. The method is successfully tested for the scattering from a nonspherical potential well and a long-range nonspherical scatterer. The method is also applicable to solving the multidimensional Schroedinger equation with a discrete spectrum. As an example the known problem of a hydrogen atom in a homogeneous magnetic field is analyzed

  19. Solving inversion problems with neural networks

    Science.gov (United States)

    Kamgar-Parsi, Behzad; Gualtieri, J. A.

    1990-01-01

    A class of inverse problems in remote sensing can be characterized by Q = F(x), where F is a nonlinear and noninvertible (or hard to invert) operator, and the objective is to infer the unknowns, x, from the observed quantities, Q. Since the number of observations is usually greater than the number of unknowns, these problems are formulated as optimization problems, which can be solved by a variety of techniques. The feasibility of neural networks for solving such problems is presently investigated. As an example, the problem of finding the atmospheric ozone profile from measured ultraviolet radiances is studied.

  20. Nonlinear systems

    National Research Council Canada - National Science Library

    Drazin, P. G

    1992-01-01

    This book is an introduction to the theories of bifurcation and chaos. It treats the solution of nonlinear equations, especially difference and ordinary differential equations, as a parameter varies...

  1. Nonlinear analysis

    CERN Document Server

    Gasinski, Leszek

    2005-01-01

    Hausdorff Measures and Capacity. Lebesgue-Bochner and Sobolev Spaces. Nonlinear Operators and Young Measures. Smooth and Nonsmooth Analysis and Variational Principles. Critical Point Theory. Eigenvalue Problems and Maximum Principles. Fixed Point Theory.

  2. Functional possibilities of nonlinear crystals for frequency conversion: uniaxial crystals

    Energy Technology Data Exchange (ETDEWEB)

    Andreev, Yu M [Institute of Monitoring of Climatic and Ecological Systems, Siberian Branch of the Russian Academy of Sciences, Tomsk (Russian Federation); Arapov, Yu D; Kasyanov, I V [E.I. Zababakhin All-Russian Scientific-Research Institute of Technical Physics, Russian Federal Nuclear Centre, Snezhinsk, Chelyabinsk region (Russian Federation); Grechin, S G; Nikolaev, P P [N.E. Bauman Moscow State Technical University, Moscow (Russian Federation)

    2016-01-31

    The method and results of the analysis of phase-matching and nonlinear properties for all point groups of symmetry of uniaxial crystals that determine their functional possibilities for solving various problems of nonlinear frequency conversion of laser radiation are presented. (nonlinear optical phenomena)

  3. Nonlinear Hamiltonian systems

    DEFF Research Database (Denmark)

    Jørgensen, Michael Finn

    1995-01-01

    It is generally very difficult to solve nonlinear systems, and such systems often possess chaotic solutions. In the rare event that a system is completely solvable, it is said to integrable. Such systems never have chaotic solutions. Using the Inverse Scattering Transform Method (ISTM) two...... particular configurations of the Discrete Self-Trapping (DST) system are shown to be completely solvable. One of these systems includes the Toda lattice in a certain limit. An explicit integration is carried through for this Near-Toda lattice. The Near-Toda lattice is then generalized to include singular...

  4. Dynamics and vibrations progress in nonlinear analysis

    CERN Document Server

    Kachapi, Seyed Habibollah Hashemi

    2014-01-01

    Dynamical and vibratory systems are basically an application of mathematics and applied sciences to the solution of real world problems. Before being able to solve real world problems, it is necessary to carefully study dynamical and vibratory systems and solve all available problems in case of linear and nonlinear equations using analytical and numerical methods. It is of great importance to study nonlinearity in dynamics and vibration; because almost all applied processes act nonlinearly, and on the other hand, nonlinear analysis of complex systems is one of the most important and complicated tasks, especially in engineering and applied sciences problems. There are probably a handful of books on nonlinear dynamics and vibrations analysis. Some of these books are written at a fundamental level that may not meet ambitious engineering program requirements. Others are specialized in certain fields of oscillatory systems, including modeling and simulations. In this book, we attempt to strike a balance between th...

  5. Nonlinear dynamics of quadratically cubic systems

    International Nuclear Information System (INIS)

    Rudenko, O V

    2013-01-01

    We propose a modified form of the well-known nonlinear dynamic equations with quadratic relations used to model a cubic nonlinearity. We show that such quadratically cubic equations sometimes allow exact solutions and sometimes make the original problem easier to analyze qualitatively. Occasionally, exact solutions provide a useful tool for studying new phenomena. Examples considered include nonlinear ordinary differential equations and Hopf, Burgers, Korteweg–de Vries, and nonlinear Schrödinger partial differential equations. Some problems are solved exactly in the space–time and spectral representations. Unsolved problems potentially solvable by the proposed approach are listed. (methodological notes)

  6. Soliton bag models

    International Nuclear Information System (INIS)

    Wilets, L.

    1988-01-01

    Soliton models are well-suited for dynamical calculations, such as hadron-hadron interactions and collisions, since for each variable in the Lagrangian the time derivative of that variable also appears. For such models, constrained (deformed) mean field solutions provide a basis for generator coordinate dynamical calculations. This requires the solution of a large number of coupled, nonlinear, differential equations involving the quark and scalar fields. The Henyey-Wilets method reduces the problem to the solution of a set of coupled, linear, inhomogeneous, differential equations to be iterated. In the chromodielectric model, color confinement is effected by the self and mutual interactios of the quarks through the chromelectric field. This requires the self-consistent calculation of the gluon propagator in a spatially varying dielectric function. This now involves the solution of a set of coupled, nonlinear integro-differential equations, which can be linearized and solved by iterations. The problem is computation intensive. 20 refs

  7. The use of symbolic computation in radiative, energy, and neutron transport calculations. Technical report, 15 August 1992--14 August 1994

    International Nuclear Information System (INIS)

    Frankel, J.I.

    1995-01-01

    This investigation uses symbolic computation in developing analytical methods and general computational strategies for solving both linear and nonlinear, regular and singular, integral and integro-differential equations which appear in radiative and combined mode energy transport. This technical report summarizes the research conducted during the first nine months of the present investigation. The use of Chebyshev polynomials augmented with symbolic computation has clearly been demonstrated in problems involving radiative (or neutron) transport, and mixed-mode energy transport. Theoretical issues related to convergence, errors, and accuracy have also been pursued. Three manuscripts have resulted from the funded research. These manuscripts have been submitted to archival journals. At the present time, an investigation involving a conductive and radiative medium is underway. The mathematical formulation leads to a system of nonlinear, weakly-singular integral equations involving the unknown temperature and various Legendre moments of the radiative intensity in a participating medium. Some preliminary results are presented illustrating the direction of the proposed research

  8. The use of symbolic computation in radiative, energy, and neutron transport calculations

    Science.gov (United States)

    Frankel, J. I.

    This investigation uses symbolic computation in developing analytical methods and general computational strategies for solving both linear and nonlinear, regular and singular, integral and integro-differential equations which appear in radiative and combined mode energy transport. This technical report summarizes the research conducted during the first nine months of the present investigation. The use of Chebyshev polynomials augmented with symbolic computation has clearly been demonstrated in problems involving radiative (or neutron) transport, and mixed-mode energy transport. Theoretical issues related to convergence, errors, and accuracy have also been pursued. Three manuscripts have resulted from the funded research. These manuscripts have been submitted to archival journals. At the present time, an investigation involving a conductive and radiative medium is underway. The mathematical formulation leads to a system of nonlinear, weakly-singular integral equations involving the unknown temperature and various Legendre moments of the radiative intensity in a participating medium. Some preliminary results are presented illustrating the direction of the proposed research.

  9. Scaling laws of free dendritic growth in a forced Oseen flow

    International Nuclear Information System (INIS)

    Kurnatowski, M von; Kassner, K

    2014-01-01

    We use the method presented in M von Kurnatowski et al (2013 Phys. Rev. E 87 042405) to solve the nonlinear problem of free dendritic growth in an Oseen flow. The growth process is assumed to be limited by thermal transport via diffusion and convection. A singular perturbation expansion is treated to lowest nontrivial order in the framework of asymptotic decomposition. The resulting complex integro-differential equation is solved using an elaborate numerical method. The approximate scaling laws V∝U 2/3 and ρ∝U −1/3 for the growth velocity and the tip radius of curvature of the dendrite, respectively, are found as a function of the forced flow velocity. The results are compared to those by Pelcé and Bouissou, constituting the only other attempt so far to treat the problem analytically. (paper)

  10. A nonlinear plate control without linearization

    Directory of Open Access Journals (Sweden)

    Yildirim Kenan

    2017-03-01

    Full Text Available In this paper, an optimal vibration control problem for a nonlinear plate is considered. In order to obtain the optimal control function, wellposedness and controllability of the nonlinear system is investigated. The performance index functional of the system, to be minimized by minimum level of control, is chosen as the sum of the quadratic 10 functional of the displacement. The velocity of the plate and quadratic functional of the control function is added to the performance index functional as a penalty term. By using a maximum principle, the nonlinear control problem is transformed to solving a system of partial differential equations including state and adjoint variables linked by initial-boundary-terminal conditions. Hence, it is shown that optimal control of the nonlinear systems can be obtained without linearization of the nonlinear term and optimal control function can be obtained analytically for nonlinear systems without linearization.

  11. Introduction to nonlinear finite element analysis

    CERN Document Server

    Kim, Nam-Ho

    2015-01-01

    This book introduces the key concepts of nonlinear finite element analysis procedures. The book explains the fundamental theories of the field and provides instructions on how to apply the concepts to solving practical engineering problems. Instead of covering many nonlinear problems, the book focuses on three representative problems: nonlinear elasticity, elastoplasticity, and contact problems. The book is written independent of any particular software, but tutorials and examples using four commercial programs are included as appendices: ANSYS, NASTRAN, ABAQUS, and MATLAB. In particular, the MATLAB program includes all source codes so that students can develop their own material models, or different algorithms. This book also: ·         Presents clear explanations of nonlinear finite element analysis for elasticity, elastoplasticity, and contact problems ·         Includes many informative examples of nonlinear analyses so that students can clearly understand the nonlinear theory ·    ...

  12. Nonlinear magnetohydrodynamics of edge localized mode precursors

    Energy Technology Data Exchange (ETDEWEB)

    Guo, Z. B., E-mail: guozhipku@gmail.com [State Key Laboratory of Nuclear Physics and Technology, School of Physics, Peking University, Beijing (China); WCI Center for Fusion Theory, NFRI, Gwahangno 113, Yusung-gu, Daejeon 305-333 (Korea, Republic of); Wang, Lu [SEEE, Huazhong University of Science and Technology, Wuhan, Hubei 430074 (China); Wang, X. G. [State Key Laboratory of Nuclear Physics and Technology, School of Physics, Peking University, Beijing (China)

    2015-02-15

    A possible origin of edge-localized-mode (ELM) precursors based on nonlinear ideal peeling-ballooning mode is reported. Via nonlinear variational principle, a nonlinear evolution equation of the radial displacement is derived and solved, analytically. Besides an explosive growth in the initial nonlinear phase, it is found that the local displacement evolves into an oscillating state in the developed nonlinear phase. The nonlinear frequency of the ELM precursors scales as ω{sub pre}∼x{sup 1/3}ξ{sup ^}{sub ψ,in}{sup 2/3}n, with x position in radial direction, ξ{sup ^}{sub ψ,in} strength of initial perturbation, and n toroidal mode number.

  13. Automatic interpretation of magnetic data using Euler deconvolution with nonlinear background

    Digital Repository Service at National Institute of Oceanography (India)

    Dewangan, P.; Ramprasad, T.; Ramana, M.V.; Desa, M.; Shailaja, B.

    are close to each other. A possible solution to these problems is prposed by simultaneously estimating the source location, depth and structural index assuming nonlinear background. The Euler equation is solved in a nonlinear fashion using the optimization...

  14. Problem Solving and Learning

    Science.gov (United States)

    Singh, Chandralekha

    2009-07-01

    One finding of cognitive research is that people do not automatically acquire usable knowledge by spending lots of time on task. Because students' knowledge hierarchy is more fragmented, "knowledge chunks" are smaller than those of experts. The limited capacity of short term memory makes the cognitive load high during problem solving tasks, leaving few cognitive resources available for meta-cognition. The abstract nature of the laws of physics and the chain of reasoning required to draw meaningful inferences makes these issues critical. In order to help students, it is crucial to consider the difficulty of a problem from the perspective of students. We are developing and evaluating interactive problem-solving tutorials to help students in the introductory physics courses learn effective problem-solving strategies while solidifying physics concepts. The self-paced tutorials can provide guidance and support for a variety of problem solving techniques, and opportunity for knowledge and skill acquisition.

  15. Teaching Creative Problem Solving.

    Science.gov (United States)

    Christensen, Kip W.; Martin, Loren

    1992-01-01

    Interpersonal and cognitive skills, adaptability, and critical thinking can be developed through problem solving and cooperative learning in technology education. These skills have been identified as significant needs of the workplace as well as for functioning in society. (SK)

  16. Cascaded nonlinearities for ultrafast nonlinear optical science and applications

    DEFF Research Database (Denmark)

    Bache, Morten

    the cascading nonlinearity is investigated in detail, especially with focus on femtosecond energetic laser pulses being subjected to this nonlinear response. Analytical, numerical and experimental results are used to understand the cascading interaction and applications are demonstrated. The defocusing soliton...... observations with analogies in fiber optics are observed numerically and experimentally, including soliton self-compression, soliton-induced resonant radiation, supercontinuum generation, optical wavebreaking and shock-front formation. All this happens despite no waveguide being present, thanks...... is of particular interest here, since it is quite unique and provides the solution to a number of standing challenges in the ultrafast nonlinear optics community. It solves the problem of catastrophic focusing and formation of a filaments in bulk glasses, which even under controlled circumstances is limited...

  17. Multiparameter extrapolation and deflation methods for solving equation systems

    Directory of Open Access Journals (Sweden)

    A. J. Hughes Hallett

    1984-01-01

    Full Text Available Most models in economics and the applied sciences are solved by first order iterative techniques, usually those based on the Gauss-Seidel algorithm. This paper examines the convergence of multiparameter extrapolations (accelerations of first order iterations, as an improved approximation to the Newton method for solving arbitrary nonlinear equation systems. It generalises my earlier results on single parameter extrapolations. Richardson's generalised method and the deflation method for detecting successive solutions in nonlinear equation systems are also presented as multiparameter extrapolations of first order iterations. New convergence results are obtained for those methods.

  18. Solving PDEs in Python the FEniCS tutorial I

    CERN Document Server

    Langtangen, Hans Petter

    2016-01-01

    This book offers a concise and gentle introduction to finite element programming in Python based on the popular FEniCS software library. Using a series of examples, including the Poisson equation, the equations of linear elasticity, the incompressible Navier–Stokes equations, and systems of nonlinear advection–diffusion–reaction equations, it guides readers through the essential steps to quickly solving a PDE in FEniCS, such as how to define a finite variational problem, how to set boundary conditions, how to solve linear and nonlinear systems, and how to visualize solutions and structure finite element Python programs. This book is open access under a CC BY license.

  19. Interactive Nonlinear Multiobjective Optimization Methods

    OpenAIRE

    Miettinen, Kaisa; Hakanen, Jussi; Podkopaev, Dmitry

    2016-01-01

    An overview of interactive methods for solving nonlinear multiobjective optimization problems is given. In interactive methods, the decision maker progressively provides preference information so that the most satisfactory Pareto optimal solution can be found for her or his. The basic features of several methods are introduced and some theoretical results are provided. In addition, references to modifications and applications as well as to other methods are indicated. As the...

  20. Approximate and renormgroup symmetries

    Energy Technology Data Exchange (ETDEWEB)

    Ibragimov, Nail H. [Blekinge Institute of Technology, Karlskrona (Sweden). Dept. of Mathematics Science; Kovalev, Vladimir F. [Russian Academy of Sciences, Moscow (Russian Federation). Inst. of Mathematical Modeling

    2009-07-01

    ''Approximate and Renormgroup Symmetries'' deals with approximate transformation groups, symmetries of integro-differential equations and renormgroup symmetries. It includes a concise and self-contained introduction to basic concepts and methods of Lie group analysis, and provides an easy-to-follow introduction to the theory of approximate transformation groups and symmetries of integro-differential equations. The book is designed for specialists in nonlinear physics - mathematicians and non-mathematicians - interested in methods of applied group analysis for investigating nonlinear problems in physical science and engineering. (orig.)

  1. Approximate and renormgroup symmetries

    International Nuclear Information System (INIS)

    Ibragimov, Nail H.; Kovalev, Vladimir F.

    2009-01-01

    ''Approximate and Renormgroup Symmetries'' deals with approximate transformation groups, symmetries of integro-differential equations and renormgroup symmetries. It includes a concise and self-contained introduction to basic concepts and methods of Lie group analysis, and provides an easy-to-follow introduction to the theory of approximate transformation groups and symmetries of integro-differential equations. The book is designed for specialists in nonlinear physics - mathematicians and non-mathematicians - interested in methods of applied group analysis for investigating nonlinear problems in physical science and engineering. (orig.)

  2. expansion method for solving nonlinear space–time fractional

    Indian Academy of Sciences (India)

    2016-07-06

    Jul 6, 2016 ... Department of Mathematics, Faculty of Arts and Sciences, Uludag University, 16059, Bursa, Turkey. ∗ ... of fractional calculus dates back to three hundred years ago. ... tions by fractional complex transformation [12,13].

  3. Neoclassical transport including collisional nonlinearity.

    Science.gov (United States)

    Candy, J; Belli, E A

    2011-06-10

    In the standard δf theory of neoclassical transport, the zeroth-order (Maxwellian) solution is obtained analytically via the solution of a nonlinear equation. The first-order correction δf is subsequently computed as the solution of a linear, inhomogeneous equation that includes the linearized Fokker-Planck collision operator. This equation admits analytic solutions only in extreme asymptotic limits (banana, plateau, Pfirsch-Schlüter), and so must be solved numerically for realistic plasma parameters. Recently, numerical codes have appeared which attempt to compute the total distribution f more accurately than in the standard ordering by retaining some nonlinear terms related to finite-orbit width, while simultaneously reusing some form of the linearized collision operator. In this work we show that higher-order corrections to the distribution function may be unphysical if collisional nonlinearities are ignored.

  4. SPARSE ELECTROMAGNETIC IMAGING USING NONLINEAR LANDWEBER ITERATIONS

    KAUST Repository

    Desmal, Abdulla

    2015-07-29

    A scheme for efficiently solving the nonlinear electromagnetic inverse scattering problem on sparse investigation domains is described. The proposed scheme reconstructs the (complex) dielectric permittivity of an investigation domain from fields measured away from the domain itself. Least-squares data misfit between the computed scattered fields, which are expressed as a nonlinear function of the permittivity, and the measured fields is constrained by the L0/L1-norm of the solution. The resulting minimization problem is solved using nonlinear Landweber iterations, where at each iteration a thresholding function is applied to enforce the sparseness-promoting L0/L1-norm constraint. The thresholded nonlinear Landweber iterations are applied to several two-dimensional problems, where the ``measured\\'\\' fields are synthetically generated or obtained from actual experiments. These numerical experiments demonstrate the accuracy, efficiency, and applicability of the proposed scheme in reconstructing sparse profiles with high permittivity values.

  5. Variational iteration method for solving coupled-KdV equations

    International Nuclear Information System (INIS)

    Assas, Laila M.B.

    2008-01-01

    In this paper, the He's variational iteration method is applied to solve the non-linear coupled-KdV equations. This method is based on the use of Lagrange multipliers for identification of optimal value of a parameter in a functional. This technique provides a sequence of functions which converge to the exact solution of the coupled-KdV equations. This procedure is a powerful tool for solving coupled-KdV equations

  6. Combined algorithms in nonlinear problems of magnetostatics

    International Nuclear Information System (INIS)

    Gregus, M.; Khoromskij, B.N.; Mazurkevich, G.E.; Zhidkov, E.P.

    1988-01-01

    To solve boundary problems of magnetostatics in unbounded two- and three-dimensional regions, we construct combined algorithms based on a combination of the method of boundary integral equations with the grid methods. We study the question of substantiation of the combined method of nonlinear magnetostatic problem without the preliminary discretization of equations and give some results on the convergence of iterative processes that arise in non-linear cases. We also discuss economical iterative processes and algorithms that solve boundary integral equations on certain surfaces. Finally, examples of numerical solutions of magnetostatic problems that arose when modelling the fields of electrophysical installations are given too. 14 refs.; 2 figs.; 1 tab

  7. Network science, nonlinear science and infrastructure systems

    CERN Document Server

    2007-01-01

    Network Science, Nonlinear Science and Infrastructure Systems has been written by leading scholars in these areas. Its express purpose is to develop common theoretical underpinnings to better solve modern infrastructural problems. It is felt by many who work in these fields that many modern communication problems, ranging from transportation networks to telecommunications, Internet, supply chains, etc., are fundamentally infrastructure problems. Moreover, these infrastructure problems would benefit greatly from a confluence of theoretical and methodological work done with the areas of Network Science, Dynamical Systems and Nonlinear Science. This book is dedicated to the formulation of infrastructural tools that will better solve these types of infrastructural problems. .

  8. Distributed Problem-Solving

    DEFF Research Database (Denmark)

    Chemi, Tatiana

    2016-01-01

    This chapter aims to deconstruct some persistent myths about creativity: the myth of individualism and of the genius. By looking at literature that approaches creativity as a participatory and distributed phenomenon and by bringing empirical evidence from artists’ studios, the author presents a p......, what can educators at higher education learn from the ways creative groups solve problems? How can artists contribute to inspiring higher education?......This chapter aims to deconstruct some persistent myths about creativity: the myth of individualism and of the genius. By looking at literature that approaches creativity as a participatory and distributed phenomenon and by bringing empirical evidence from artists’ studios, the author presents...... a perspective that is relevant to higher education. The focus here is on how artists solve problems in distributed paths, and on the elements of creative collaboration. Creative problem-solving will be looked at as an ongoing dialogue that artists engage with themselves, with others, with recipients...

  9. Nonlinear Elliptic Differential Equations with Multivalued Nonlinearities

    Indian Academy of Sciences (India)

    In this paper we study nonlinear elliptic boundary value problems with monotone and nonmonotone multivalued nonlinearities. First we consider the case of monotone nonlinearities. In the first result we assume that the multivalued nonlinearity is defined on all R R . Assuming the existence of an upper and of a lower ...

  10. Solving Environmental Problems

    DEFF Research Database (Denmark)

    Ørding Olsen, Anders; Sofka, Wolfgang; Grimpe, Christoph

    2017-01-01

    for Research and Technological Development (FP7), our results indicate that the problem-solving potential of a search strategy increases with the diversity of existing knowledge of the partners in a consortium and with the experience of the partners involved. Moreover, we identify a substantial negative effect...... dispersed. Hence, firms need to collaborate. We shed new light on collaborative search strategies led by firms in general and for solving environmental problems in particular. Both topics are largely absent in the extant open innovation literature. Using data from the European Seventh Framework Program...

  11. Modulated Langmuir waves and nonlinear Landau damping

    International Nuclear Information System (INIS)

    Yajima, Nobuo; Oikawa, Masayuki; Satsuma, Junkichi; Namba, Chusei.

    1975-01-01

    The nonlinear Schroedinger euqation with an integral term, iusub(t)+P/2.usub(xx)+Q/u/ 2 u+RP∫sub(-infinity)sup(infinity)[/u(x',t)/ 2 /(x-x')]dx'u=0, which describes modulated Langmuir waves with the nonlinear Landau damping effect, is solved by numerical calculations. Especially, the effects of nonlinear Landau damping on solitary wave solutions are studied. For both cases, PQ>0 and PQ<0, the results show that the solitary waves deform in an asymmetric way changing its velocity. (auth.)

  12. On Stabilization of Nonautonomous Nonlinear Systems

    International Nuclear Information System (INIS)

    Bogdanov, A. Yu.

    2008-01-01

    The procedures to obtain the sufficient conditions of asymptotic stability for nonlinear nonstationary continuous-time systems are discussed. We consider different types of the following general controlled system: x = X(t,x,u) = F(t,x)+B(t,x)u, x(t 0 ) = x 0 . (*) The basis of investigation is limiting equations, limiting Lyapunov functions, etc. The improved concept of observability of the pair of functional matrices is presented. By these results the problem of synthesis of asymptotically stable control nonlinear nonautonomous systems (with linear parts) involving the quadratic time-dependent Lyapunov functions is solved as well as stabilizing a given unstable system with nonlinear control law.

  13. Nonlinear single-spin spectrum analyzer.

    Science.gov (United States)

    Kotler, Shlomi; Akerman, Nitzan; Glickman, Yinnon; Ozeri, Roee

    2013-03-15

    Qubits have been used as linear spectrum analyzers of their environments. Here we solve the problem of nonlinear spectral analysis, required for discrete noise induced by a strongly coupled environment. Our nonperturbative analytical model shows a nonlinear signal dependence on noise power, resulting in a spectral resolution beyond the Fourier limit as well as frequency mixing. We develop a noise characterization scheme adapted to this nonlinearity. We then apply it using a single trapped ion as a sensitive probe of strong, non-Gaussian, discrete magnetic field noise. Finally, we experimentally compared the performance of equidistant vs Uhrig modulation schemes for spectral analysis.

  14. Introspection in Problem Solving

    Science.gov (United States)

    Jäkel, Frank; Schreiber, Cornell

    2013-01-01

    Problem solving research has encountered an impasse. Since the seminal work of Newell und Simon (1972) researchers do not seem to have made much theoretical progress (Batchelder and Alexander, 2012; Ohlsson, 2012). In this paper we argue that one factor that is holding back the field is the widespread rejection of introspection among cognitive…

  15. Problem Solving in Practice

    Science.gov (United States)

    Greene, Kim; Heyck-Williams, Jeff; Timpson Gray, Elicia

    2017-01-01

    Problem solving spans all grade levels and content areas, as evidenced by this compilation of projects from schools across the United States. In one project, high school girls built a solar-powered tent to serve their city's homeless population. In another project, 4th graders explored historic Jamestown to learn about the voices lost to history.…

  16. Solving Linear Differential Equations

    NARCIS (Netherlands)

    Nguyen, K.A.; Put, M. van der

    2010-01-01

    The theme of this paper is to 'solve' an absolutely irreducible differential module explicitly in terms of modules of lower dimension and finite extensions of the differential field K. Representations of semi-simple Lie algebras and differential Galo is theory are the main tools. The results extend

  17. Solving a binary puzzle

    NARCIS (Netherlands)

    Utomo, P.H.; Makarim, R.H.

    2017-01-01

    A Binary puzzle is a Sudoku-like puzzle with values in each cell taken from the set {0,1} {0,1}. Let n≥4 be an even integer, a solved binary puzzle is an n×n binary array that satisfies the following conditions: (1) no three consecutive ones and no three consecutive zeros in each row and each

  18. Electric Current Solves Mazes

    Science.gov (United States)

    Ayrinhac, Simon

    2014-01-01

    We present in this work a demonstration of the maze-solving problem with electricity. Electric current flowing in a maze as a printed circuit produces Joule heating and the right way is instantaneously revealed with infrared thermal imaging. The basic properties of electric current can be discussed in this context, with this challenging question:…

  19. Transport equation solving methods

    International Nuclear Information System (INIS)

    Granjean, P.M.

    1984-06-01

    This work is mainly devoted to Csub(N) and Fsub(N) methods. CN method: starting from a lemma stated by Placzek, an equivalence is established between two problems: the first one is defined in a finite medium bounded by a surface S, the second one is defined in the whole space. In the first problem the angular flux on the surface S is shown to be the solution of an integral equation. This equation is solved by Galerkin's method. The Csub(N) method is applied here to one-velocity problems: in plane geometry, slab albedo and transmission with Rayleigh scattering, calculation of the extrapolation length; in cylindrical geometry, albedo and extrapolation length calculation with linear scattering. Fsub(N) method: the basic integral transport equation of the Csub(N) method is integrated on Case's elementary distributions; another integral transport equation is obtained: this equation is solved by a collocation method. The plane problems solved by the Csub(N) method are also solved by the Fsub(N) method. The Fsub(N) method is extended to any polynomial scattering law. Some simple spherical problems are also studied. Chandrasekhar's method, collision probability method, Case's method are presented for comparison with Csub(N) and Fsub(N) methods. This comparison shows the respective advantages of the two methods: a) fast convergence and possible extension to various geometries for Csub(N) method; b) easy calculations and easy extension to polynomial scattering for Fsub(N) method [fr

  20. On Solving Linear Recurrences

    Science.gov (United States)

    Dobbs, David E.

    2013-01-01

    A direct method is given for solving first-order linear recurrences with constant coefficients. The limiting value of that solution is studied as "n to infinity." This classroom note could serve as enrichment material for the typical introductory course on discrete mathematics that follows a calculus course.

  1. Multistage Spectral Relaxation Method for Solving the Hyperchaotic Complex Systems

    Directory of Open Access Journals (Sweden)

    Hassan Saberi Nik

    2014-01-01

    Full Text Available We present a pseudospectral method application for solving the hyperchaotic complex systems. The proposed method, called the multistage spectral relaxation method (MSRM is based on a technique of extending Gauss-Seidel type relaxation ideas to systems of nonlinear differential equations and using the Chebyshev pseudospectral methods to solve the resulting system on a sequence of multiple intervals. In this new application, the MSRM is used to solve famous hyperchaotic complex systems such as hyperchaotic complex Lorenz system and the complex permanent magnet synchronous motor. We compare this approach to the Runge-Kutta based ode45 solver to show that the MSRM gives accurate results.

  2. Toward Solving the Problem of Problem Solving: An Analysis Framework

    Science.gov (United States)

    Roesler, Rebecca A.

    2016-01-01

    Teaching is replete with problem solving. Problem solving as a skill, however, is seldom addressed directly within music teacher education curricula, and research in music education has not examined problem solving systematically. A framework detailing problem-solving component skills would provide a needed foundation. I observed problem solving…

  3. Spectral theory and nonlinear functional analysis

    CERN Document Server

    Lopez-Gomez, Julian

    2001-01-01

    This Research Note addresses several pivotal problems in spectral theory and nonlinear functional analysis in connection with the analysis of the structure of the set of zeroes of a general class of nonlinear operators. It features the construction of an optimal algebraic/analytic invariant for calculating the Leray-Schauder degree, new methods for solving nonlinear equations in Banach spaces, and general properties of components of solutions sets presented with minimal use of topological tools. The author also gives several applications of the abstract theory to reaction diffusion equations and systems.The results presented cover a thirty-year period and include recent, unpublished findings of the author and his coworkers. Appealing to a broad audience, Spectral Theory and Nonlinear Functional Analysis contains many important contributions to linear algebra, linear and nonlinear functional analysis, and topology and opens the door for further advances.

  4. Noether and Lie symmetries for charged perfect fluids

    International Nuclear Information System (INIS)

    Kweyama, M C; Govinder, K S; Maharaj, S D

    2011-01-01

    We study the underlying nonlinear partial differential equation that governs the behaviour of spherically symmetric charged fluids in general relativity. We investigate the conditions for the equation to admit a first integral or be reduced to quadratures using symmetry methods for differential equations. A general Noether first integral is found. We also undertake a comprehensive group analysis of the underlying equation using Lie point symmetries. The existence of a Lie symmetry is subject to solving an integro-differential equation in general; we investigate the conditions under which it can be reduced to quadratures. Earlier results for uncharged fluids and particular first integrals for charged matter are regained as special cases of our treatment.

  5. Solution of linear and nonlinear matrix systems. Application to a nonlinear diffusion equation

    International Nuclear Information System (INIS)

    Bonnet, M.; Meurant, G.

    1978-01-01

    Different methods of solution of linear and nonlinear algebraic systems are applied to the nonlinear system obtained by discretizing a nonlinear diffusion equation. For linear systems, methods in general use of alternating directions type or Gauss Seidel's methods are compared to more recent ones of the type of generalized conjugate gradient; the superiority of the latter is shown by numerical examples. For nonlinear systems, a method on nonlinear conjugate gradient is studied as also Newton's method and some of its variants. It should be noted, however that Newton's method is found to be more efficient when coupled with a good method for solution of the linear system. To conclude, such methods are used to solve a nonlinear diffusion problem and the numerical results obtained are to be compared [fr

  6. Nonlinear behaviour of cantilevered carbon nanotube resonators based on a new nonlinear electrostatic load model

    Science.gov (United States)

    Farokhi, Hamed; Païdoussis, Michael P.; Misra, Arun K.

    2018-04-01

    The present study examines the nonlinear behaviour of a cantilevered carbon nanotube (CNT) resonator and its mass detection sensitivity, employing a new nonlinear electrostatic load model. More specifically, a 3D finite element model is developed in order to obtain the electrostatic load distribution on cantilevered CNT resonators. A new nonlinear electrostatic load model is then proposed accounting for the end effects due to finite length. Additionally, a new nonlinear size-dependent continuum model is developed for the cantilevered CNT resonator, employing the modified couple stress theory (to account for size-effects) together with the Kelvin-Voigt model (to account for nonlinear damping); the size-dependent model takes into account all sources of nonlinearity, i.e. geometrical and inertial nonlinearities as well as nonlinearities associated with damping, small-scale, and electrostatic load. The nonlinear equation of motion of the cantilevered CNT resonator is obtained based on the new models developed for the CNT resonator and the electrostatic load. The Galerkin method is then applied to the nonlinear equation of motion, resulting in a set of nonlinear ordinary differential equations, consisting of geometrical, inertial, electrical, damping, and size-dependent nonlinear terms. This high-dimensional nonlinear discretized model is solved numerically utilizing the pseudo-arclength continuation technique. The nonlinear static and dynamic responses of the system are examined for various cases, investigating the effect of DC and AC voltages, length-scale parameter, nonlinear damping, and electrostatic load. Moreover, the mass detection sensitivity of the system is examined for possible application of the CNT resonator as a nanosensor.

  7. Relation of deformed nonlinear algebras with linear ones

    International Nuclear Information System (INIS)

    Nowicki, A; Tkachuk, V M

    2014-01-01

    The relation between nonlinear algebras and linear ones is established. For a one-dimensional nonlinear deformed Heisenberg algebra with two operators we find the function of deformation for which this nonlinear algebra can be transformed to a linear one with three operators. We also establish the relation between the Lie algebra of total angular momentum and corresponding nonlinear one. This relation gives a possibility to simplify and to solve the eigenvalue problem for the Hamiltonian in a nonlinear case using the reduction of this problem to the case of linear algebra. It is demonstrated in an example of a harmonic oscillator. (paper)

  8. Flutter analysis of an airfoil with multiple nonlinearities and uncertainties

    Directory of Open Access Journals (Sweden)

    Haitao Liao

    2013-09-01

    Full Text Available An original method for calculating the limit cycle oscillations of nonlinear aero-elastic system is presented. The problem of determining the maximum vibration amplitude of limit cycle is transformed into a nonlinear optimization problem. The harmonic balance method and the Floquet theory are selected to construct the general nonlinear equality and inequality constraints. The resulting constrained maximization problem is then solved by using the MultiStart algorithm. Finally, the proposed approach is validated and used to analyse the limit cycle oscillations of an airfoil with multiple nonlinearities and uncertainties. Numerical examples show that the coexistence of multiple nonlinearities may lead to low amplitude limit cycle oscillation.

  9. Solving Fuzzy Fractional Differential Equations Using Zadeh's Extension Principle

    Science.gov (United States)

    Ahmad, M. Z.; Hasan, M. K.; Abbasbandy, S.

    2013-01-01

    We study a fuzzy fractional differential equation (FFDE) and present its solution using Zadeh's extension principle. The proposed study extends the case of fuzzy differential equations of integer order. We also propose a numerical method to approximate the solution of FFDEs. To solve nonlinear problems, the proposed numerical method is then incorporated into an unconstrained optimisation technique. Several numerical examples are provided. PMID:24082853

  10. A numerical method for solving singular De`s

    Energy Technology Data Exchange (ETDEWEB)

    Mahaver, W.T.

    1996-12-31

    A numerical method is developed for solving singular differential equations using steepest descent based on weighted Sobolev gradients. The method is demonstrated on a variety of first and second order problems, including linear constrained, unconstrained, and partially constrained first order problems, a nonlinear first order problem with irregular singularity, and two second order variational problems.

  11. Variational iteration method for one dimensional nonlinear thermoelasticity

    International Nuclear Information System (INIS)

    Sweilam, N.H.; Khader, M.M.

    2007-01-01

    This paper applies the variational iteration method to solve the Cauchy problem arising in one dimensional nonlinear thermoelasticity. The advantage of this method is to overcome the difficulty of calculation of Adomian's polynomials in the Adomian's decomposition method. The numerical results of this method are compared with the exact solution of an artificial model to show the efficiency of the method. The approximate solutions show that the variational iteration method is a powerful mathematical tool for solving nonlinear problems

  12. MINPACK-1, Subroutine Library for Nonlinear Equation System

    International Nuclear Information System (INIS)

    Garbow, Burton S.

    1984-01-01

    1 - Description of problem or function: MINPACK1 is a package of FORTRAN subprograms for the numerical solution of systems of non- linear equations and nonlinear least-squares problems. The individual programs are: Identification/Description: - CHKDER: Check gradients for consistency with functions, - DOGLEG: Determine combination of Gauss-Newton and gradient directions, - DPMPAR: Provide double precision machine parameters, - ENORM: Calculate Euclidean norm of vector, - FDJAC1: Calculate difference approximation to Jacobian (nonlinear equations), - FDJAC2: Calculate difference approximation to Jacobian (least squares), - HYBRD: Solve system of nonlinear equations (approximate Jacobian), - HYBRD1: Easy-to-use driver for HYBRD, - HYBRJ: Solve system of nonlinear equations (analytic Jacobian), - HYBRJ1: Easy-to-use driver for HYBRJ, - LMDER: Solve nonlinear least squares problem (analytic Jacobian), - LMDER1: Easy-to-use driver for LMDER, - LMDIF: Solve nonlinear least squares problem (approximate Jacobian), - LMDIF1: Easy-to-use driver for LMDIF, - LMPAR: Determine Levenberg-Marquardt parameter - LMSTR: Solve nonlinear least squares problem (analytic Jacobian, storage conserving), - LMSTR1: Easy-to-use driver for LMSTR, - QFORM: Accumulate orthogonal matrix from QR factorization QRFAC Compute QR factorization of rectangular matrix, - QRSOLV: Complete solution of least squares problem, - RWUPDT: Update QR factorization after row addition, - R1MPYQ: Apply orthogonal transformations from QR factorization, - R1UPDT: Update QR factorization after rank-1 addition, - SPMPAR: Provide single precision machine parameters. 4. Method of solution - MINPACK1 uses the modified Powell hybrid method and the Levenberg-Marquardt algorithm

  13. Nonlinear Elasticity

    Science.gov (United States)

    Fu, Y. B.; Ogden, R. W.

    2001-05-01

    This collection of papers by leading researchers in the field of finite, nonlinear elasticity concerns itself with the behavior of objects that deform when external forces or temperature gradients are applied. This process is extremely important in many industrial settings, such as aerospace and rubber industries. This book covers the various aspects of the subject comprehensively with careful explanations of the basic theories and individual chapters each covering a different research direction. The authors discuss the use of symbolic manipulation software as well as computer algorithm issues. The emphasis is placed firmly on covering modern, recent developments, rather than the very theoretical approach often found. The book will be an excellent reference for both beginners and specialists in engineering, applied mathematics and physics.

  14. Nonlinear resonances

    CERN Document Server

    Rajasekar, Shanmuganathan

    2016-01-01

    This introductory text presents the basic aspects and most important features of various types of resonances and anti-resonances in dynamical systems. In particular, for each resonance, it covers the theoretical concepts, illustrates them with case studies, and reviews the available information on mechanisms, characterization, numerical simulations, experimental realizations, possible quantum analogues, applications and significant advances made over the years. Resonances are one of the most fundamental phenomena exhibited by nonlinear systems and refer to specific realizations of maximum response of a system due to the ability of that system to store and transfer energy received from an external forcing source. Resonances are of particular importance in physical, engineering and biological systems - they can prove to be advantageous in many applications, while leading to instability and even disasters in others. The book is self-contained, providing the details of mathematical derivations and techniques invo...

  15. Creativity and Problem Solving

    DEFF Research Database (Denmark)

    Vidal, Rene Victor Valqui

    2004-01-01

    This paper presents some modern and interdisciplinary concepts about creativity and creative processes of special relevance for Operational Research workers. Central publications in the area Creativity-Operational Research are shortly reviewed. Some creative tools and the Creative Problem Solving...... approach are also discussed. Finally, some applications of these concepts and tools are outlined. Some central references are presented for further study of themes related to creativity or creative tools....

  16. Creativity and problem Solving

    Directory of Open Access Journals (Sweden)

    René Victor Valqui Vidal

    2004-12-01

    Full Text Available This paper presents some modern and interdisciplinary concepts about creativity and creative processes of special relevance for Operational Research workers. Central publications in the area Creativity-Operational Research are shortly reviewed. Some creative tools and the Creative Problem Solving approach are also discussed. Finally, some applications of these concepts and tools are outlined. Some central references are presented for further study of themes related to creativity or creative tools.

  17. Analytical Solutions to Non-linear Mechanical Oscillation Problems

    DEFF Research Database (Denmark)

    Kaliji, H. D.; Ghadimi, M.; Barari, Amin

    2011-01-01

    In this paper, the Max-Min Method is utilized for solving the nonlinear oscillation problems. The proposed approach is applied to three systems with complex nonlinear terms in their motion equations. By means of this method, the dynamic behavior of oscillation systems can be easily approximated u...

  18. Noninteracting control of nonlinear systems based on relaxed control

    NARCIS (Netherlands)

    Jayawardhana, B.

    2010-01-01

    In this paper, we propose methodology to solve noninteracting control problem for general nonlinear systems based on the relaxed control technique proposed by Artstein. For a class of nonlinear systems which cannot be stabilized by smooth feedback, a state-feedback relaxed control can be designed to

  19. A generalized auxiliary equation method and its application to nonlinear Klein-Gordon and generalized nonlinear Camassa-Holm equations

    International Nuclear Information System (INIS)

    Yomba, Emmanuel

    2008-01-01

    With the aid of symbolic computation, a generalized auxiliary equation method is proposed to construct more general exact solutions to two types of NLPDEs. First, we present new family of solutions to a nonlinear Klein-Gordon equation, by using this auxiliary equation method including a new first-order nonlinear ODE with six-degree nonlinear term proposed by Sirendaoreji. Then, we apply an indirect F-function method very close to the F-expansion method to solve the generalized Camassa-Holm equation with fully nonlinear dispersion and fully nonlinear convection C(l,n,p). Taking advantage of the new first-order nonlinear ODE with six degree nonlinear term, this indirect F-function method is used to map the solutions of C(l,n,p) equations to those of that nonlinear ODE. As a result, we can successfully obtain in a unified way, many exact solutions

  20. Observers for Systems with Nonlinearities Satisfying an Incremental Quadratic Inequality

    Science.gov (United States)

    Acikmese, Ahmet Behcet; Corless, Martin

    2004-01-01

    We consider the problem of state estimation for nonlinear time-varying systems whose nonlinearities satisfy an incremental quadratic inequality. These observer results unifies earlier results in the literature; and extend it to some additional classes of nonlinearities. Observers are presented which guarantee that the state estimation error exponentially converges to zero. Observer design involves solving linear matrix inequalities for the observer gain matrices. Results are illustrated by application to a simple model of an underwater.

  1. Feedback options in nonlinear numerical finance

    DEFF Research Database (Denmark)

    Hugger, Jens; Mashayekhi, Sima

    2012-01-01

    on an infinite slab is presented and boundary values on a bounded domain are derived. This bounded, nonlinear, 2 dimensional initial-boundary value problem is solved numerically using a number of standard finite difference schemes and the methods incorporated in the symbolic software Maple™....

  2. Nonlinear Fredholm Integral Equation of the Second Kind with Quadrature Methods

    Directory of Open Access Journals (Sweden)

    M. Jafari Emamzadeh

    2010-06-01

    Full Text Available In this paper, a numerical method for solving the nonlinear Fredholm integral equation is presented. We intend to approximate the solution of this equation by quadrature methods and by doing so, we solve the nonlinear Fredholm integral equation more accurately. Several examples are given at the end of this paper

  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. A numerical study of the integral equations for the laser fields in free-electron lasers

    International Nuclear Information System (INIS)

    Yoo, J. G.; Park, S. H.; Jeong, Y. U.; Lee, B. C.; Rhee, Y. J.; Cho, S. O.

    2004-01-01

    The dynamics of the radiation fields in free-electron lasers is investigated on the basis of the integro-differential equations in the one-dimensional formulation. For simple cases we solved the integro-differential equations analytically and numerically to test our numerical procedures developed on the basis of the Filon method. The numerical results showed good agreement with the analytical solutions. To confirm the legitimacy of the numerical package, we carried out numerical studies on the inhomogeneous broadening effects, where no analytic solutions are available, due to the energy spread and the emittance of the electron beam.

  5. Appreciative Problem Solving

    DEFF Research Database (Denmark)

    Hansen, David

    2012-01-01

    Many industrial production work systems have increased in complexity, and their new business model scompete on innovation, rather than low cost.At a medical device production facility committed to Lean Production, a research project was carried out to use Appreciative Inquiry to better engage...... employee strengths in continuou simprovements of the work system. The research question was: “How can Lean problem solving and Appreciative Inquiry be combined for optimized work system innovation?” The research project was carried out as a co-creation process with close cooperation between researcher...

  6. Simon on problem solving

    DEFF Research Database (Denmark)

    Foss, Kirsten; Foss, Nicolai Juul

    2006-01-01

    as a general approach to problem solving. We apply these Simonian ideas to organisational issues, specifically new organisational forms. Specifically, Simonian ideas allow us to develop a morphology of new organisational forms and to point to some design problems that characterise these forms.......Two of Herbert Simon's best-known papers are 'The Architecture of Complexity' and 'The Structure of Ill-Structured Problems.' We discuss the neglected links between these two papers, highlighting the role of decomposition in the context of problems on which constraints have been imposed...

  7. Planning and Problem Solving

    Science.gov (United States)

    1982-10-01

    Artificial Intelig ~ence (Vol. III, edited by Paul R. Cohen and’ Edward A.. Feigenbaum)’, The chapter was written B’ Paul Cohen, with contributions... Artificial Intelligence (Vol. III, edited by Paul R. Cohen and EdWard A. Feigenbaum). The chapter was written by Paul R. Cohen, with contributions by Stephen...Wheevoats"EntermdI’ Planning and Problem ’Solving by Paul R. Cohen Chaptb-rXV-of Volumec III’of the Handbook of Artificial Intelligence edited by Paul R

  8. [Nonlinear magnetohydrodynamics

    International Nuclear Information System (INIS)

    1994-01-01

    Resistive MHD equilibrium, even for small resistivity, differs greatly from ideal equilibrium, as do the dynamical consequences of its instabilities. The requirement, imposed by Faraday's law, that time independent magnetic fields imply curl-free electric fields, greatly restricts the electric fields allowed inside a finite-resistivity plasma. If there is no flow and the implications of the Ohm's law are taken into account (and they need not be, for ideal equilibria), the electric field must equal the resistivity times the current density. The vanishing of the divergence of the current density then provides a partial differential equation which, together with boundary conditions, uniquely determines the scalar potential, the electric field, and the current density, for any given resistivity profile. The situation parallels closely that of driven shear flows in hydrodynamics, in that while dissipative steady states are somewhat more complex than ideal ones, there are vastly fewer of them to consider. Seen in this light, the vast majority of ideal MHD equilibria are just irrelevant, incapable of being set up in the first place. The steady state whose stability thresholds and nonlinear behavior needs to be investigated ceases to be an arbitrary ad hoc exercise dependent upon the whim of the investigator, but is determined by boundary conditions and choice of resistivity profile

  9. Nonlinear Dynamics of Nanomechanical Resonators

    Science.gov (United States)

    Ramakrishnan, Subramanian; Gulak, Yuiry; Sundaram, Bala; Benaroya, Haym

    2007-03-01

    Nanoelectromechanical systems (NEMS) offer great promise for many applications including motion and mass sensing. Recent experimental results suggest the importance of nonlinear effects in NEMS, an issue which has not been addressed fully in theory. We report on a nonlinear extension of a recent analytical model by Armour et al [1] for the dynamics of a single-electron transistor (SET) coupled to a nanomechanical resonator. We consider the nonlinear resonator motion in both (a) the Duffing and (b) nonlinear pendulum regimes. The corresponding master equations are derived and solved numerically and we consider moment approximations as well. In the Duffing case with hardening stiffness, we observe that the resonator is damped by the SET at a significantly higher rate. In the cases of softening stiffness and the pendulum, there exist regimes where the SET adds energy to the resonator. To our knowledge, this is the first instance of a single model displaying both negative and positive resonator damping in different dynamical regimes. The implications of the results for SET sensitivity as well as for, as yet unexplained, experimental results will be discussed. 1. Armour et al. Phys.Rev.B (69) 125313 (2004).

  10. Point source identification in nonlinear advection–diffusion–reaction systems

    International Nuclear Information System (INIS)

    Mamonov, A V; Tsai, Y-H R

    2013-01-01

    We consider a problem of identification of point sources in time-dependent advection–diffusion systems with a nonlinear reaction term. The linear counterpart of the problem in question can be reduced to solving a system of nonlinear algebraic equations via the use of adjoint equations. We extend this approach by constructing an algorithm that solves the problem iteratively to account for the nonlinearity of the reaction term. We study the question of improving the quality of source identification by adding more measurements adaptively using the solution obtained previously with a smaller number of measurements. (paper)

  11. Convex models and probabilistic approach of nonlinear fatigue failure

    International Nuclear Information System (INIS)

    Qiu Zhiping; Lin Qiang; Wang Xiaojun

    2008-01-01

    This paper is concerned with the nonlinear fatigue failure problem with uncertainties in the structural systems. In the present study, in order to solve the nonlinear problem by convex models, the theory of ellipsoidal algebra with the help of the thought of interval analysis is applied. In terms of the inclusion monotonic property of ellipsoidal functions, the nonlinear fatigue failure problem with uncertainties can be solved. A numerical example of 25-bar truss structures is given to illustrate the efficiency of the presented method in comparison with the probabilistic approach

  12. Nonlinear dynamics of intense EM pulses in plasma

    International Nuclear Information System (INIS)

    Mahajan, Ranju; Gill, Tarsem Singh; Kaur, Ravinder

    2010-01-01

    The evolution of laser beam in underdense/overdense plasma medium which is key to understanding of several nonlinear processes and underlying physics is governed by nonlinear parabolic equation. The nonlinearity considered here is of relativistic as well as of ponderomotive type. We have set Lagrangian for the problem and reduced Lagrangian problem is solved using appropriate trial function. Equation for the beam width and phase are derived. Further, these equations are used to solve eigenvalue problem for the stability of laser beam evolution and Hurwitz condition is satisfied.

  13. Solving Differential Equations in R: Package deSolve

    Science.gov (United States)

    In this paper we present the R package deSolve to solve initial value problems (IVP) written as ordinary differential equations (ODE), differential algebraic equations (DAE) of index 0 or 1 and partial differential equations (PDE), the latter solved using the method of lines appr...

  14. Solving Differential Equations in R: Package deSolve

    NARCIS (Netherlands)

    Soetaert, K.E.R.; Petzoldt, T.; Setzer, R.W.

    2010-01-01

    In this paper we present the R package deSolve to solve initial value problems (IVP) written as ordinary differential equations (ODE), differential algebraic equations (DAE) of index 0 or 1 and partial differential equations (PDE), the latter solved using the method of lines approach. The

  15. Identification of Nonlinear Dynamic Systems Possessing Some Non-linearities

    Directory of Open Access Journals (Sweden)

    Y. N. Pavlov

    2015-01-01

    system of the second-order with nonlinearity of the type "quadratic friction" in combination with nonlinearity of the type "dry friction", was developed a software to simulate a process for providing pseudo experimental data containing random accuracy and to determine the parameters of the system. A conducted computational experiment enabled an estimate of the accuracy with which the proposed algorithm determines the parameters of the system. The illustrative numerical simulation has demonstrated that with using the proposed nonlinear dynamic system identification algorithm in frequency hodograph the accuracy of determining the coefficient values of the frequency transfer function of the second order system with a dry and quadratic friction is comparable with the range of measurement accuracy of experimental samples of this system hodograph. Well-known publications do not mention this identification method of the nonlinear dynamic systems. The nonlinear dynamical systems identification method the article describes can find application when determining parameters of various kinds of actuators. The using method of harmonic linearization and identification of dynamical systems by hodographs is promising for solving the problem of the identification of nonlinear systems with different types of nonlinearities.

  16. Application of HPEM to investigate the response and stability of nonlinear problems in vibration

    DEFF Research Database (Denmark)

    Mohammadi, M.H.; Mohammadi, A.; Kimiaeifar, A.

    2010-01-01

    In this work, a powerful analytical method, called He's Parameter Expanding Methods (HPEM) is used to obtain the exact solution of nonlinear problems in nonlinear vibration. In this work, the governing equation is obtained by using Lagrange method, then the nonlinear governing equation is solved...

  17. FEATURES APPLICATION CIRCUIT MOMENT FINITE ELEMENT (MSSE) NONLINEAR CALCULATIONS OF PLATES AND SHELLS

    OpenAIRE

    Bazhenov V.A.; Sacharov A.S.; Guliar A. I.; Pyskunov S.O.; Maksymiuk Y.V.

    2014-01-01

    Based MSSE created shell CE general type, which allows you to analyze the stress-strain state of axisymmetrical shells and plates in problems of physical and geometric nonlinearity. The principal nonlinear elasticity theory, algorithms for solving systems of nonlinear equations for determining the temperature and plastic deformation.

  18. FEATURES APPLICATION CIRCUIT MOMENT FINITE ELEMENT (MSSE NONLINEAR CALCULATIONS OF PLATES AND SHELLS

    Directory of Open Access Journals (Sweden)

    Bazhenov V.A.

    2014-06-01

    Full Text Available Based MSSE created shell CE general type, which allows you to analyze the stress-strain state of axisymmetrical shells and plates in problems of physical and geometric nonlinearity. The principal nonlinear elasticity theory, algorithms for solving systems of nonlinear equations for determining the temperature and plastic deformation.

  19. Non-linear partial differential equations an algebraic view of generalized solutions

    CERN Document Server

    Rosinger, Elemer E

    1990-01-01

    A massive transition of interest from solving linear partial differential equations to solving nonlinear ones has taken place during the last two or three decades. The availability of better computers has often made numerical experimentations progress faster than the theoretical understanding of nonlinear partial differential equations. The three most important nonlinear phenomena observed so far both experimentally and numerically, and studied theoretically in connection with such equations have been the solitons, shock waves and turbulence or chaotical processes. In many ways, these phenomen

  20. A nonlinear complementarity approach for the national energy modeling system

    International Nuclear Information System (INIS)

    Gabriel, S.A.; Kydes, A.S.

    1995-01-01

    The National Energy Modeling System (NEMS) is a large-scale mathematical model that computes equilibrium fuel prices and quantities in the U.S. energy sector. At present, to generate these equilibrium values, NEMS sequentially solves a collection of linear programs and nonlinear equations. The NEMS solution procedure then incorporates the solutions of these linear programs and nonlinear equations in a nonlinear Gauss-Seidel approach. The authors describe how the current version of NEMS can be formulated as a particular nonlinear complementarity problem (NCP), thereby possibly avoiding current convergence problems. In addition, they show that the NCP format is equally valid for a more general form of NEMS. They also describe several promising approaches for solving the NCP form of NEMS based on recent Newton type methods for general NCPs. These approaches share the feature of needing to solve their direction-finding subproblems only approximately. Hence, they can effectively exploit the sparsity inherent in the NEMS NCP

  1. Continuous nonlinear optimization for engineering applications in GAMS technology

    CERN Document Server

    Andrei, Neculai

    2017-01-01

    This book presents the theoretical details and computational performances of algorithms used for solving continuous nonlinear optimization applications imbedded in GAMS. Aimed toward scientists and graduate students who utilize optimization methods to model and solve problems in mathematical programming, operations research, business, engineering, and industry, this book enables readers with a background in nonlinear optimization and linear algebra to use GAMS technology to understand and utilize its important capabilities to optimize algorithms for modeling and solving complex, large-scale, continuous nonlinear optimization problems or applications. Beginning with an overview of constrained nonlinear optimization methods, this book moves on to illustrate key aspects of mathematical modeling through modeling technologies based on algebraically oriented modeling languages. Next, the main feature of GAMS, an algebraically oriented language that allows for high-level algebraic representation of mathematical opti...

  2. Nonlinear beam mechanics

    NARCIS (Netherlands)

    Westra, H.J.R.

    2012-01-01

    In this Thesis, nonlinear dynamics and nonlinear interactions are studied from a micromechanical point of view. Single and doubly clamped beams are used as model systems where nonlinearity plays an important role. The nonlinearity also gives rise to rich dynamic behavior with phenomena like

  3. The problem of evolution of toroidal plasma equilibrium

    International Nuclear Information System (INIS)

    Kostomarov, D.; Zaitsev, F.; Shishkin, A.

    1999-03-01

    This paper is devoted to an advanced mathematical model for a self-consistent description of the evolution of free boundary toroidal plasmas, with a description of numerical algorithms for the solution of the appropriate non-linear system of integro-differential equations, and discussion of some results from the model. (author)

  4. Solved problems in electromagnetics

    CERN Document Server

    Salazar Bloise, Félix; Bayón Rojo, Ana; Gascón Latasa, Francisco

    2017-01-01

    This book presents the fundamental concepts of electromagnetism through problems with a brief theoretical introduction at the beginning of each chapter. The present book has a strong  didactic character. It explains all the mathematical steps and the theoretical concepts connected with the development of the problem. It guides the reader to understand the employed procedures to learn to solve the exercises independently. The exercises are structured in a similar way: The chapters begin with easy problems increasing progressively in the level of difficulty. This book is written for students of physics and engineering in the framework of the new European Plans of Study for Bachelor and Master and also for tutors and lecturers. .

  5. Solved problems in electrochemistry

    International Nuclear Information System (INIS)

    Piron, D.L.

    2004-01-01

    This book presents calculated solutions to problems in fundamental and applied electrochemistry. It uses industrial data to illustrate scientific concepts and scientific knowledge to solve practical problems. It is subdivided into three parts. The first uses modern basic concepts, the second studies the scientific basis for electrode and electrolyte thermodynamics (including E-pH diagrams and the minimum energy involved in transformations) and the kinetics of rate processes (including the energy lost in heat and in parasite reactions). The third part treats larger problems in electrolysis and power generation, as well as in corrosion and its prevention. Each chapter includes three sections: the presentation of useful principles; some twenty problems with their solutions; and, a set of unsolved problems

  6. A study of discrete nonlinear systems

    International Nuclear Information System (INIS)

    Dhillon, H.S.

    2001-04-01

    An investigation of various spatially discrete time-independent nonlinear models was undertaken. These models are generically applicable to many different physical systems including electron-phonon interactions in solids, magnetic multilayers, layered superconductors and classical lattice systems. To characterise the possible magnetic structures created on magnetic multilayers a model has been formulated and studied. The Euler-Lagrange equation for this model is a discrete version of the Sine-Gordon equation. Solutions of this equation are generated by applying the methods of Chaotic Dynamics - treating the space variable associated with the layer number as a discrete time variable. The states found indicate periodic, quasiperiodic and chaotic structures. Analytic solutions to the discrete nonlinear Schroedinger Equation (DNSE) with cubic nonlinearity are presented in the strong coupling limit. Using these as a starting point, a procedure is developed to determine the wave function and the energy eigenvalue for moderate coupling. The energy eigenvalues of the different structures of the wave function are found to be in excellent agreement with the exact strong coupling result. The solutions to the DNSE indicate commensurate and incommensurate spatial structures associated with different localisation patterns of the wave function. The states which arise may be fractal, periodic, quasiperiodic or chaotic. This work is then extended to solve a first order discrete nonlinear equation. The exact solutions for both the first and second order discrete nonlinear equations with cubic nonlinearity suggests that this method of studying discrete nonlinear equations may be applied to solve discrete equations with any order difference and cubic nonlinearity. (author)

  7. An analytical theory of a scattering of radio waves on meteoric ionization - II. Solution of the integro-differential equation in case of backscatter

    Czech Academy of Sciences Publication Activity Database

    Pecina, Petr

    2016-01-01

    Roč. 463, č. 2 (2016), s. 1185-1198 ISSN 0035-8711 Institutional support: RVO:67985815 Keywords : scattering * radar astronomy * meteorites * meteors * meteoroids Subject RIV: BN - Astronomy , Celestial Mechanics, Astrophysics Impact factor: 4.961, year: 2016

  8. Decomposition of a hierarchy of nonlinear evolution equations

    International Nuclear Information System (INIS)

    Geng Xianguo

    2003-01-01

    The generalized Hamiltonian structures for a hierarchy of nonlinear evolution equations are established with the aid of the trace identity. Using the nonlinearization approach, the hierarchy of nonlinear evolution equations is decomposed into a class of new finite-dimensional Hamiltonian systems. The generating function of integrals and their generator are presented, based on which the finite-dimensional Hamiltonian systems are proved to be completely integrable in the Liouville sense. As an application, solutions for the hierarchy of nonlinear evolution equations are reduced to solving the compatible Hamiltonian systems of ordinary differential equations

  9. Sparse electromagnetic imaging using nonlinear iterative shrinkage thresholding

    KAUST Repository

    Desmal, Abdulla; Bagci, Hakan

    2015-01-01

    A sparse nonlinear electromagnetic imaging scheme is proposed for reconstructing dielectric contrast of investigation domains from measured fields. The proposed approach constructs the optimization problem by introducing the sparsity constraint to the data misfit between the scattered fields expressed as a nonlinear function of the contrast and the measured fields and solves it using the nonlinear iterative shrinkage thresholding algorithm. The thresholding is applied to the result of every nonlinear Landweber iteration to enforce the sparsity constraint. Numerical results demonstrate the accuracy and efficiency of the proposed method in reconstructing sparse dielectric profiles.

  10. Sparse electromagnetic imaging using nonlinear iterative shrinkage thresholding

    KAUST Repository

    Desmal, Abdulla

    2015-04-13

    A sparse nonlinear electromagnetic imaging scheme is proposed for reconstructing dielectric contrast of investigation domains from measured fields. The proposed approach constructs the optimization problem by introducing the sparsity constraint to the data misfit between the scattered fields expressed as a nonlinear function of the contrast and the measured fields and solves it using the nonlinear iterative shrinkage thresholding algorithm. The thresholding is applied to the result of every nonlinear Landweber iteration to enforce the sparsity constraint. Numerical results demonstrate the accuracy and efficiency of the proposed method in reconstructing sparse dielectric profiles.

  11. Overlapping Schwarz for Nonlinear Problems. An Element Agglomeration Nonlinear Additive Schwarz Preconditioned Newton Method for Unstructured Finite Element Problems

    Energy Technology Data Exchange (ETDEWEB)

    Cai, X C; Marcinkowski, L; Vassilevski, P S

    2005-02-10

    This paper extends previous results on nonlinear Schwarz preconditioning ([4]) to unstructured finite element elliptic problems exploiting now nonlocal (but small) subspaces. The non-local finite element subspaces are associated with subdomains obtained from a non-overlapping element partitioning of the original set of elements and are coarse outside the prescribed element subdomain. The coarsening is based on a modification of the agglomeration based AMGe method proposed in [8]. Then, the algebraic construction from [9] of the corresponding non-linear finite element subproblems is applied to generate the subspace based nonlinear preconditioner. The overall nonlinearly preconditioned problem is solved by an inexact Newton method. Numerical illustration is also provided.

  12. Scalable Nonlinear Compact Schemes

    Energy Technology Data Exchange (ETDEWEB)

    Ghosh, Debojyoti [Argonne National Lab. (ANL), Argonne, IL (United States); Constantinescu, Emil M. [Univ. of Chicago, IL (United States); Brown, Jed [Univ. of Colorado, Boulder, CO (United States)

    2014-04-01

    In this work, we focus on compact schemes resulting in tridiagonal systems of equations, specifically the fifth-order CRWENO scheme. We propose a scalable implementation of the nonlinear compact schemes by implementing a parallel tridiagonal solver based on the partitioning/substructuring approach. We use an iterative solver for the reduced system of equations; however, we solve this system to machine zero accuracy to ensure that no parallelization errors are introduced. It is possible to achieve machine-zero convergence with few iterations because of the diagonal dominance of the system. The number of iterations is specified a priori instead of a norm-based exit criterion, and collective communications are avoided. The overall algorithm thus involves only point-to-point communication between neighboring processors. Our implementation of the tridiagonal solver differs from and avoids the drawbacks of past efforts in the following ways: it introduces no parallelization-related approximations (multiprocessor solutions are exactly identical to uniprocessor ones), it involves minimal communication, the mathematical complexity is similar to that of the Thomas algorithm on a single processor, and it does not require any communication and computation scheduling.

  13. Exploring hadronic physics by solving QCD with a teraflops computer

    International Nuclear Information System (INIS)

    Negele, J.

    1993-01-01

    Quantum chromodynamics, the theory believed to govern the nucleons, mesons, and other strongly interacting particles making up most of the known mass of the universe is such a challenging, nonlinear many-body problem that it has never been solved using conventional analytical techniques. This talk will describe how this theory can be solved numerically on a space-time lattice, show what has already been understood about the structure of hadrons and the quark gluon phase transition. and describe an exciting initiative to build a dedicated Teraflops computer capable of performing 10 12 operations per second to make fundamental advances in QCD

  14. Pedestrian Flow in the Mean Field Limit

    KAUST Repository

    Haji Ali, Abdul Lateef

    2012-01-01

    -dependent density of two-dimensional pedestrians satisfies a four-dimensional integro-differential Fokker-Planck equation. To approximate the solution of the Fokker-Planck equation we use a time-splitting approach and solve the diffusion part using a Crank

  15. Application of New Variational Homotopy Perturbation Method For ...

    African Journals Online (AJOL)

    This paper discusses the application of the New Variational Homotopy Perturbation Method (NVHPM) for solving integro-differential equations. The advantage of the new Scheme is that it does not require discretization, linearization or any restrictive assumption of any form be fore it is applied. Several test problems are ...

  16. Application of the Sumudu Transform to Discrete Dynamic Systems

    Science.gov (United States)

    Asiru, Muniru Aderemi

    2003-01-01

    The Sumudu transform is an integral transform introduced to solve differential equations and control engineering problems. The transform possesses many interesting properties that make visualization easier and application has been demonstrated in the solution of partial differential equations, integral equations, integro-differential equations and…

  17. Numerical Analysis of Strongly Nonlinear Oscillation Systems using He's Max-Min Method

    DEFF Research Database (Denmark)

    Babazadeh, H; Domairry, G; Barari, Amin

    2011-01-01

    Nonlinear functions are crucial points and terms in engineering problems. Actual and physical problems can be solved by solving and processing such functions. Thus, most scientists and engineers focus on solving these equations. This paper presents a novel method called the max-min method...

  18. Nonlinear problems in fluid dynamics and inverse scattering: Nonlinear waves and inverse scattering

    Science.gov (United States)

    Ablowitz, Mark J.

    1994-12-01

    Research investigations involving the fundamental understanding and applications of nonlinear wave motion and related studies of inverse scattering and numerical computation have been carried out and a number of significant results have been obtained. A class of nonlinear wave equations which can be solved by the inverse scattering transform (IST) have been studied, including the Kadaomtsev-Petviashvili (KP) equation, the Davey-Stewartson equation, and the 2+1 Toda system. The solutions obtained by IST correspond to the Cauchy initial value problem with decaying initial data. We have also solved two important systems via the IST method: a 'Volterra' system in 2+1 dimensions and a new one dimensional nonlinear equation which we refer to as the Toda differential-delay equation. Research in computational chaos in moderate to long time numerical simulations continues.

  19. Wave propagation in elastic medium with heterogeneous quadratic nonlinearity

    International Nuclear Information System (INIS)

    Tang Guangxin; Jacobs, Laurence J.; Qu Jianmin

    2011-01-01

    This paper studies the one-dimensional wave propagation in an elastic medium with spatially non-uniform quadratic nonlinearity. Two problems are solved analytically. One is for a time-harmonic wave propagating in a half-space where the displacement is prescribed on the surface of the half-space. It is found that spatial non-uniformity of the material nonlinearity causes backscattering of the second order harmonic, which when combined with the forward propagating waves generates a standing wave in steady-state wave motion. The second problem solved is the reflection from and transmission through a layer of finite thickness embedded in an otherwise linearly elastic medium of infinite extent, where it is assumed that the layer has a spatially non-uniform quadratic nonlinearity. The results show that the transmission coefficient for the second order harmonic is proportional to the spatial average of the nonlinearity across the thickness of the layer, independent of the spatial distribution of the nonlinearity. On the other hand, the coefficient of reflection is proportional to a weighted average of the nonlinearity across the layer thickness. The weight function in this weighted average is related to the propagating phase, thus making the coefficient of reflection dependent on the spatial distribution of the nonlinearity. Finally, the paper concludes with some discussions on how to use the reflected and transmitted second harmonic waves to evaluate the variance and autocorrelation length of nonlinear parameter β when the nonlinearity distribution in the layer is a stochastic process.

  20. The presentation of explicit analytical solutions of a class of nonlinear evolution equations

    International Nuclear Information System (INIS)

    Feng Jinshun; Guo Mingpu; Yuan Deyou

    2009-01-01

    In this paper, we introduce a function set Ω m . There is a conjecture that an arbitrary explicit travelling-wave analytical solution of a real constant coefficient nonlinear evolution equation is necessarily a linear (or nonlinear) combination of the product of some elements in Ω m . A widespread applicable approach for solving a class of nonlinear evolution equations is established. The new analytical solutions to two kinds of nonlinear evolution equations are described with the aid of the guess.

  1. Analytical solution of strongly nonlinear Duffing oscillators

    OpenAIRE

    El-Naggar, A.M.; Ismail, G.M.

    2016-01-01

    In this paper, a new perturbation technique is employed to solve strongly nonlinear Duffing oscillators, in which a new parameter α=α(ε)α=α(ε) is defined such that the value of α is always small regardless of the magnitude of the original parameter εε. Therefore, the strongly nonlinear Duffing oscillators with large parameter ε are transformed into a small parameter system with respect to αα. Approximate solution obtained by the present method is compared with the solution of energy balance m...

  2. Entropy viscosity method for nonlinear conservation laws

    KAUST Repository

    Guermond, Jean-Luc

    2011-05-01

    A new class of high-order numerical methods for approximating nonlinear conservation laws is described (entropy viscosity method). The novelty is that a nonlinear viscosity based on the local size of an entropy production is added to the numerical discretization at hand. This new approach does not use any flux or slope limiters, applies to equations or systems supplemented with one or more entropy inequalities and does not depend on the mesh type and polynomial approximation. Various benchmark problems are solved with finite elements, spectral elements and Fourier series to illustrate the capability of the proposed method. © 2010 Elsevier Inc.

  3. Handbook of Nonlinear Partial Differential Equations

    CERN Document Server

    Polyanin, Andrei D

    2011-01-01

    New to the Second Edition More than 1,000 pages with over 1,500 new first-, second-, third-, fourth-, and higher-order nonlinear equations with solutions Parabolic, hyperbolic, elliptic, and other systems of equations with solutions Some exact methods and transformations Symbolic and numerical methods for solving nonlinear PDEs with Maple(t), Mathematica(R), and MATLAB(R) Many new illustrative examples and tables A large list of references consisting of over 1,300 sources To accommodate different mathematical backgrounds, the authors avoid wherever possible the use of special terminology. They

  4. Entropy viscosity method for nonlinear conservation laws

    KAUST Repository

    Guermond, Jean-Luc; Pasquetti, Richard; Popov, Bojan

    2011-01-01

    A new class of high-order numerical methods for approximating nonlinear conservation laws is described (entropy viscosity method). The novelty is that a nonlinear viscosity based on the local size of an entropy production is added to the numerical discretization at hand. This new approach does not use any flux or slope limiters, applies to equations or systems supplemented with one or more entropy inequalities and does not depend on the mesh type and polynomial approximation. Various benchmark problems are solved with finite elements, spectral elements and Fourier series to illustrate the capability of the proposed method. © 2010 Elsevier Inc.

  5. Nonlinear Single Spin Spectrum Analayzer

    Science.gov (United States)

    Kotler, Shlomi; Akerman, Nitzan; Glickman, Yinnon; Ozeri, Roee

    2014-05-01

    Qubits are excellent probes of their environment. When operating in the linear regime, they can be used as linear spectrum analyzers of the noise processes surrounding them. These methods fail for strong non-Gaussian noise where the qubit response is no longer linear. Here we solve the problem of nonlinear spectral analysis, required for strongly coupled environments. Our non-perturbative analytic model shows a nonlinear signal dependence on noise power, resulting in a spectral resolution beyond the Fourier limit as well as frequency mixing. We developed a noise characterization scheme adapted to this non-linearity. We then applied it using a single trapped 88Sr+ ion as the a sensitive probe of strong, non-Gaussian, discrete magnetic field noise. With this method, we attained a ten fold improvement over the standard Fourier limit. Finally, we experimentally compared the performance of equidistant vs. Uhrig modulation schemes for spectral analysis. Phys. Rev. Lett. 110, 110503 (2013), Synopsis at http://physics.aps.org/synopsis-for/10.1103/PhysRevLett.110.110503 Current position: National Institute of Standards and Tehcnology, Boulder, CO.

  6. Nonlinear H-infinity control, Hamiltonian systems and Hamilton-Jacobi equations

    CERN Document Server

    Aliyu, MDS

    2011-01-01

    A comprehensive overview of nonlinear Haeu control theory for both continuous-time and discrete-time systems, Nonlinear Haeu-Control, Hamiltonian Systems and Hamilton-Jacobi Equations covers topics as diverse as singular nonlinear Haeu-control, nonlinear Haeu -filtering, mixed H2/ Haeu-nonlinear control and filtering, nonlinear Haeu-almost-disturbance-decoupling, and algorithms for solving the ubiquitous Hamilton-Jacobi-Isaacs equations. The link between the subject and analytical mechanics as well as the theory of partial differential equations is also elegantly summarized in a single chapter

  7. Exp-function method for solving Maccari's system

    International Nuclear Information System (INIS)

    Zhang Sheng

    2007-01-01

    In this Letter, the Exp-function method is used to seek exact solutions of Maccari's system. As a result, single and combined generalized solitonary solutions are obtained, from which some known solutions obtained by extended sine-Gordon equation method and improved hyperbolic function method are recovered as special cases. It is shown that the Exp-function method provides a very effective and powerful mathematical tool for solving nonlinear evolution equations in mathematical physics

  8. On Solving the Lorenz System by Differential Transformation Method

    International Nuclear Information System (INIS)

    Al-Sawalha, M. Mossa; Noorani, M. S. M.

    2008-01-01

    The differential transformation method (DTM) is employed to solve a nonlinear differential equation, namely the Lorenz system. Numerical results are compared to those obtained by the Runge–Kutta method to illustrate the preciseness and effectiveness of the proposed method. In particular, we examine the accuracy of the (DTM) as the Lorenz system changes from a non-chaotic system to a chaotic one. It is shown that the (DTM) is robust, accurate and easy to apply

  9. AZTEC: A parallel iterative package for the solving linear systems

    Energy Technology Data Exchange (ETDEWEB)

    Hutchinson, S.A.; Shadid, J.N.; Tuminaro, R.S. [Sandia National Labs., Albuquerque, NM (United States)

    1996-12-31

    We describe a parallel linear system package, AZTEC. The package incorporates a number of parallel iterative methods (e.g. GMRES, biCGSTAB, CGS, TFQMR) and preconditioners (e.g. Jacobi, Gauss-Seidel, polynomial, domain decomposition with LU or ILU within subdomains). Additionally, AZTEC allows for the reuse of previous preconditioning factorizations within Newton schemes for nonlinear methods. Currently, a number of different users are using this package to solve a variety of PDE applications.

  10. The solution of a coupled system of nonlinear physical problems using the homotopy analysis method

    International Nuclear Information System (INIS)

    El-Wakil, S A; Abdou, M A

    2010-01-01

    In this article, the homotopy analysis method (HAM) has been applied to solve coupled nonlinear evolution equations in physics. The validity of this method has been successfully demonstrated by applying it to two nonlinear evolution equations, namely coupled nonlinear diffusion reaction equations and the (2+1)-dimensional Nizhnik-Novikov Veselov system. The results obtained by this method show good agreement with the ones obtained by other methods. The proposed method is a powerful and easy to use analytic tool for nonlinear problems and does not need small parameters in the equations. The HAM solutions contain an auxiliary parameter that provides a convenient way of controlling the convergence region of series solutions. The results obtained here reveal that the proposed method is very effective and simple for solving nonlinear evolution equations. The basic ideas of this approach can be widely employed to solve other strongly nonlinear problems.

  11. Nonlinear partial differential equations of second order

    CERN Document Server

    Dong, Guangchang

    1991-01-01

    This book addresses a class of equations central to many areas of mathematics and its applications. Although there is no routine way of solving nonlinear partial differential equations, effective approaches that apply to a wide variety of problems are available. This book addresses a general approach that consists of the following: Choose an appropriate function space, define a family of mappings, prove this family has a fixed point, and study various properties of the solution. The author emphasizes the derivation of various estimates, including a priori estimates. By focusing on a particular approach that has proven useful in solving a broad range of equations, this book makes a useful contribution to the literature.

  12. Explicit Nonlinear Model Predictive Control Theory and Applications

    CERN Document Server

    Grancharova, Alexandra

    2012-01-01

    Nonlinear Model Predictive Control (NMPC) has become the accepted methodology to solve complex control problems related to process industries. The main motivation behind explicit NMPC is that an explicit state feedback law avoids the need for executing a numerical optimization algorithm in real time. The benefits of an explicit solution, in addition to the efficient on-line computations, include also verifiability of the implementation and the possibility to design embedded control systems with low software and hardware complexity. This book considers the multi-parametric Nonlinear Programming (mp-NLP) approaches to explicit approximate NMPC of constrained nonlinear systems, developed by the authors, as well as their applications to various NMPC problem formulations and several case studies. The following types of nonlinear systems are considered, resulting in different NMPC problem formulations: Ø  Nonlinear systems described by first-principles models and nonlinear systems described by black-box models; �...

  13. Homogenized description and retrieval method of nonlinear metasurfaces

    Science.gov (United States)

    Liu, Xiaojun; Larouche, Stéphane; Smith, David R.

    2018-03-01

    A patterned, plasmonic metasurface can strongly scatter incident light, functioning as an extremely low-profile lens, filter, reflector or other optical device. When the metasurface is patterned uniformly, its linear optical properties can be expressed using effective surface electric and magnetic polarizabilities obtained through a homogenization procedure. The homogenized description of a nonlinear metasurface, however, presents challenges both because of the inherent anisotropy of the medium as well as the much larger set of potential wave interactions available, making it challenging to assign effective nonlinear parameters to the otherwise inhomogeneous layer of metamaterial elements. Here we show that a homogenization procedure can be developed to describe nonlinear metasurfaces, which derive their nonlinear response from the enhanced local fields arising within the structured plasmonic elements. With the proposed homogenization procedure, we are able to assign effective nonlinear surface polarization densities to a nonlinear metasurface, and link these densities to the effective nonlinear surface susceptibilities and averaged macroscopic pumping fields across the metasurface. These effective nonlinear surface polarization densities are further linked to macroscopic nonlinear fields through the generalized sheet transition conditions (GSTCs). By inverting the GSTCs, the effective nonlinear surface susceptibilities of the metasurfaces can be solved for, leading to a generalized retrieval method for nonlinear metasurfaces. The application of the homogenization procedure and the GSTCs are demonstrated by retrieving the nonlinear susceptibilities of a SiO2 nonlinear slab. As an example, we investigate a nonlinear metasurface which presents nonlinear magnetoelectric coupling in near infrared regime. The method is expected to apply to any patterned metasurface whose thickness is much smaller than the wavelengths of operation, with inclusions of arbitrary geometry

  14. On Poisson Nonlinear Transformations

    Directory of Open Access Journals (Sweden)

    Nasir Ganikhodjaev

    2014-01-01

    Full Text Available We construct the family of Poisson nonlinear transformations defined on the countable sample space of nonnegative integers and investigate their trajectory behavior. We have proved that these nonlinear transformations are regular.

  15. Advances in nonlinear optics

    CERN Document Server

    Chen, Xianfeng; Zeng, Heping; Guo, Qi; She, Weilong

    2015-01-01

    This book presents an overview of the state of the art of nonlinear optics from weak light nonlinear optics, ultrafast nonlinear optics to electro-optical theory and applications. Topics range from the fundamental studies of the interaction between matter and radiation to the development of devices, components, and systems of tremendous commercial interest for widespread applications in optical telecommunications, medicine, and biotechnology.

  16. Difficulties in Genetics Problem Solving.

    Science.gov (United States)

    Tolman, Richard R.

    1982-01-01

    Examined problem-solving strategies of 30 high school students as they solved genetics problems. Proposes a new sequence of teaching genetics based on results: meiosis, sex chromosomes, sex determination, sex-linked traits, monohybrid and dihybrid crosses (humans), codominance (humans), and Mendel's pea experiments. (JN)

  17. Problem Solving, Scaffolding and Learning

    Science.gov (United States)

    Lin, Shih-Yin

    2012-01-01

    Helping students to construct robust understanding of physics concepts and develop good solving skills is a central goal in many physics classrooms. This thesis examine students' problem solving abilities from different perspectives and explores strategies to scaffold students' learning. In studies involving analogical problem solving…

  18. Problem Solving on a Monorail.

    Science.gov (United States)

    Barrow, Lloyd H.; And Others

    1994-01-01

    This activity was created to address a lack of problem-solving activities for elementary children. A "monorail" activity from the Evening Science Program for K-3 Students and Parents program is presented to illustrate the problem-solving format. Designed for performance at stations by groups of two students. (LZ)

  19. Solving complex fisheries management problems

    DEFF Research Database (Denmark)

    Petter Johnsen, Jahn; Eliasen, Søren Qvist

    2011-01-01

    A crucial issue for the new EU common fisheries policy is how to solve the discard problem. Through a study of the institutional set up and the arrangements for solving the discard problem in Denmark, the Faroe Islands, Iceland and Norway, the article identifies the discard problem as related...

  20. Nonlinear programming with feedforward neural networks.

    Energy Technology Data Exchange (ETDEWEB)

    Reifman, J.

    1999-06-02

    We provide a practical and effective method for solving constrained optimization problems by successively training a multilayer feedforward neural network in a coupled neural-network/objective-function representation. Nonlinear programming problems are easily mapped into this representation which has a simpler and more transparent method of solution than optimization performed with Hopfield-like networks and poses very mild requirements on the functions appearing in the problem. Simulation results are illustrated and compared with an off-the-shelf optimization tool.

  1. Nonlinear evolution equations having a physical meaning

    International Nuclear Information System (INIS)

    Nakach, R.

    1976-06-01

    The non stationary self-similar solutions of the nonlinear evolution equations which can be solved by the inverse scattering method are studied. It turns out, as shown by means of several examples, that when the L linear operator associated with these equations, is of second order and only then, the self-similar solutions can be expressed in terms of the various Painleve's transcendents [fr

  2. Picosecond optical nonlinearities in symmetrical and unsymmetrical ...

    Indian Academy of Sciences (India)

    It is evident that the saturable absorption (SA) behaviour changed to reverse sat- urable absorption (RSA) and the nonlinear coefficients were obtained using the equation α = α0I/[1 + (I/Is)]. The open-aperture scans were fitted by solving the propagation equation for homogeneous medium dI/dz = {−α0I/[1+(I/Is)]}−βI2.

  3. Nonlinear flow model for well production in an underground formation

    Directory of Open Access Journals (Sweden)

    J. C. Guo

    2013-05-01

    Full Text Available Fluid flow in underground formations is a nonlinear process. In this article we modelled the nonlinear transient flow behaviour of well production in an underground formation. Based on Darcy's law and material balance equations, we used quadratic pressure gradients to deduce diffusion equations and discuss the origins of nonlinear flow issues. By introducing an effective-well-radius approach that considers skin factor, we established a nonlinear flow model for both gas and liquid (oil or water. The liquid flow model was solved using a semi-analytical method, while the gas flow model was solved using numerical simulations because the diffusion equation of gas flow is a stealth function of pressure. For liquid flow, a series of standard log-log type curves of pressure transients were plotted and nonlinear transient flow characteristics were analyzed. Qualitative and quantitative analyses were used to compare the solutions of the linear and nonlinear models. The effect of nonlinearity upon pressure transients should not be ignored. For gas flow, pressure transients were simulated and compared with oil flow under the same formation and well conditions, resulting in the conclusion that, under the same volume rate production, oil wells demand larger pressure drops than gas wells. Comparisons between theoretical data and field data show that nonlinear models will describe fluid flow in underground formations realistically and accurately.

  4. Numerical Simulations of Light Bullets, Using The Full Vector, Time Dependent, Nonlinear Maxwell Equations

    Science.gov (United States)

    Goorjian, Peter M.; Silberberg, Yaron; Kwak, Dochan (Technical Monitor)

    1995-01-01

    This paper will present results in computational nonlinear optics. An algorithm will be described that solves the full vector nonlinear Maxwell's equations exactly without the approximations that we currently made. Present methods solve a reduced scalar wave equation, namely the nonlinear Schrodinger equation, and neglect the optical carrier. Also, results will be shown of calculations of 2-D electromagnetic nonlinear waves computed by directly integrating in time the nonlinear vector Maxwell's equations. The results will include simulations of 'light bullet' like pulses. Here diffraction and dispersion will be counteracted by nonlinear effects. The time integration efficiently implements linear and nonlinear convolutions for the electric polarization, and can take into account such quantum effects as Karr and Raman interactions. The present approach is robust and should permit modeling 2-D and 3-D optical soliton propagation, scattering, and switching directly from the full-vector Maxwell's equations.

  5. Nonlinear acceleration of SN transport calculations

    Energy Technology Data Exchange (ETDEWEB)

    Fichtl, Erin D [Los Alamos National Laboratory; Warsa, James S [Los Alamos National Laboratory; Calef, Matthew T [Los Alamos National Laboratory

    2010-12-20

    The use of nonlinear iterative methods, Jacobian-Free Newton-Krylov (JFNK) in particular, for solving eigenvalue problems in transport applications has recently become an active subject of research. While JFNK has been shown to be effective for k-eigenvalue problems, there are a number of input parameters that impact computational efficiency, making it difficult to implement efficiently in a production code using a single set of default parameters. We show that different selections for the forcing parameter in particular can lead to large variations in the amount of computational work for a given problem. In contrast, we present a nonlinear subspace method that sits outside and effectively accelerates nonlinear iterations of a given form and requires only a single input parameter, the subspace size. It is shown to consistently and significantly reduce the amount of computational work when applied to fixed-point iteration, and this combination of methods is shown to be more efficient than JFNK for our application.

  6. Nonlinear theory of electroelastic and magnetoelastic interactions

    CERN Document Server

    Dorfmann, Luis

    2014-01-01

    This book provides a unified theory of nonlinear electro-magnetomechanical interactions of soft materials capable of large elastic deformations. The authors include an overview of the basic principles of the classical theory of electromagnetism from the fundamental notions of point charges and magnetic dipoles through to distributions of charge and current in a non-deformable continuum, time-dependent electromagnetic fields and Maxwell’s equations. They summarize the basic ingredients of continuum mechanics that are required to account for the deformability of material and present nonlinear constitutive frameworks for electroelastic and magnetoelastic interactions in a highly deformable material. The equations contained in the book are used to formulate and solve a variety of representative boundary-value problems for both nonlinear electroelasticity and magnetoelasticity.

  7. Advances in iterative methods for nonlinear equations

    CERN Document Server

    Busquier, Sonia

    2016-01-01

    This book focuses on the approximation of nonlinear equations using iterative methods. Nine contributions are presented on the construction and analysis of these methods, the coverage encompassing convergence, efficiency, robustness, dynamics, and applications. Many problems are stated in the form of nonlinear equations, using mathematical modeling. In particular, a wide range of problems in Applied Mathematics and in Engineering can be solved by finding the solutions to these equations. The book reveals the importance of studying convergence aspects in iterative methods and shows that selection of the most efficient and robust iterative method for a given problem is crucial to guaranteeing a good approximation. A number of sample criteria for selecting the optimal method are presented, including those regarding the order of convergence, the computational cost, and the stability, including the dynamics. This book will appeal to researchers whose field of interest is related to nonlinear problems and equations...

  8. Quantum Nonlinear Optics

    CERN Document Server

    Hanamura, Eiichi; Yamanaka, Akio

    2007-01-01

    This graduate-level textbook gives an introductory overview of the fundamentals of quantum nonlinear optics. Based on the quantum theory of radiation, Quantum Nonlinear Optics incorporates the exciting developments in novel nonlinear responses of materials (plus laser oscillation and superradiance) developed over the past decade. It deals with the organization of radiation field, interaction between electronic system and radiation field, statistics of light, mutual manipulation of light and matter, laser oscillation, dynamics of light, nonlinear optical response, and nonlinear spectroscopy, as well as ultrashort and ultrastrong laser pulse. Also considered are Q-switching, mode locking and pulse compression. Experimental and theoretical aspects are intertwined throughout.

  9. Nonlinear dynamics and complexity

    CERN Document Server

    Luo, Albert; Fu, Xilin

    2014-01-01

    This important collection presents recent advances in nonlinear dynamics including analytical solutions, chaos in Hamiltonian systems, time-delay, uncertainty, and bio-network dynamics. Nonlinear Dynamics and Complexity equips readers to appreciate this increasingly main-stream approach to understanding complex phenomena in nonlinear systems as they are examined in a broad array of disciplines. The book facilitates a better understanding of the mechanisms and phenomena in nonlinear dynamics and develops the corresponding mathematical theory to apply nonlinear design to practical engineering.

  10. Rapid assessment of nonlinear optical propagation effects in dielectrics

    Science.gov (United States)

    Hoyo, J. Del; de La Cruz, A. Ruiz; Grace, E.; Ferrer, A.; Siegel, J.; Pasquazi, A.; Assanto, G.; Solis, J.

    2015-01-01

    Ultrafast laser processing applications need fast approaches to assess the nonlinear propagation of the laser beam in order to predict the optimal range of processing parameters in a wide variety of cases. We develop here a method based on the simple monitoring of the nonlinear beam shaping against numerical prediction. The numerical code solves the nonlinear Schrödinger equation with nonlinear absorption under simplified conditions by employing a state-of-the art computationally efficient approach. By comparing with experimental results we can rapidly estimate the nonlinear refractive index and nonlinear absorption coefficients of the material. The validity of this approach has been tested in a variety of experiments where nonlinearities play a key role, like spatial soliton shaping or fs-laser waveguide writing. The approach provides excellent results for propagated power densities for which free carrier generation effects can be neglected. Above such a threshold, the peculiarities of the nonlinear propagation of elliptical beams enable acquiring an instantaneous picture of the deposition of energy inside the material realistic enough to estimate the effective nonlinear refractive index and nonlinear absorption coefficients that can be used for predicting the spatial distribution of energy deposition inside the material and controlling the beam in the writing process.

  11. Distributed nonlinear optical response

    DEFF Research Database (Denmark)

    Nikolov, Nikola Ivanov

    2005-01-01

    of bound states of out of phase bright solitons and dark solitons. Also, the newly introduced analogy between the nonlocal cubic nonlinear and the quadratic nonlinear media, presented in paper B and Chapter 3 is discussed. In particular it supplies intuitive physical meaning of the formation of solitons...... in quadratic nonlinear media. In the second part of the report (Chapter 4), the possibility to obtain light with ultrabroad spectrum due to the interplay of many nonlinear effects based on cubic nonlinearity is investigated thoroughly. The contribution of stimulated Raman scattering, a delayed nonlinear...... a modified nonlinear Schroedinger model equation. Chapter 4 and papers D and E are dedicated to this part of the research....

  12. Nonlinear Multiplicative Schwarz Preconditioning in Natural Convection Cavity Flow

    KAUST Repository

    Liu, Lulu; Zhang, Wei; Keyes, David E.

    2017-01-01

    A natural convection cavity flow problem is solved using nonlinear multiplicative Schwarz preconditioners, as a Gauss-Seidel-like variant of additive Schwarz preconditioned inexact Newton (ASPIN). The nonlinear preconditioning extends the domain of convergence of Newton’s method to high Rayleigh numbers. Convergence performance varies widely with respect to different groupings of the fields of this multicomponent problem, and with respect to different orderings of the groupings.

  13. Probing nonlinear electrodynamics in slowly rotating spacetimes through neutrino astrophysics

    OpenAIRE

    Cuesta, Herman J. Mosquera; Lambiase, Gaetano; Pereira, Jonas P.

    2017-01-01

    Huge electromagnetic fields are known to be present during the late stages of the dynamics of supernovae. Thus, when dealing with electrodynamics in this context, the possibility may arise to probe nonlinear theories (generalizations of the Maxwellian electromagnetism). We firstly solve Einstein field equations minimally coupled to an arbitrary (current-free) nonlinear Lagrangian of electrodynamics (NLED) in the slow rotation regime $a\\ll M$ (black hole's mass), up to first order in $a/M$. We...

  14. Nonlinear Multiplicative Schwarz Preconditioning in Natural Convection Cavity Flow

    KAUST Repository

    Liu, Lulu

    2017-03-17

    A natural convection cavity flow problem is solved using nonlinear multiplicative Schwarz preconditioners, as a Gauss-Seidel-like variant of additive Schwarz preconditioned inexact Newton (ASPIN). The nonlinear preconditioning extends the domain of convergence of Newton’s method to high Rayleigh numbers. Convergence performance varies widely with respect to different groupings of the fields of this multicomponent problem, and with respect to different orderings of the groupings.

  15. Analytical exact solution of the non-linear Schroedinger equation

    International Nuclear Information System (INIS)

    Martins, Alisson Xavier; Rocha Filho, Tarcisio Marciano da

    2011-01-01

    Full text: In this work we present how to classify and obtain analytical solutions of the Schroedinger equation with a generic non-linearity in 1+1 dimensions. Our approach is based on the determination of Lie symmetry transformation mapping solutions into solutions, and non-classical symmetry transformations, mapping a given solution into itself. From these symmetries it is then possible to reduce the equation to a system of ordinary differential equations which can then be solved using standard methods. The generic non-linearity is handled by considering it as an additional unknown in the determining equations for the symmetry transformations. This results in an over-determined system of non-linear partial differential equations. Its solution can then be determined in some cases by reducing it to the so called involutive (triangular) form, and then solved. This reduction is very tedious and can only performed using a computer algebra system. Once the determining system is solved, we obtain the explicit form for the non-linearity admitting a Lie or non-classical symmetry. The analytical solutions are then derived by solving the reduced ordinary differential equations. The non-linear determining system for the non-classical symmetry transformations and Lie symmetry generators are obtaining using the computer algebra package SADE (symmetry analysis of differential equations), developed at our group. (author)

  16. Problem Solving with General Semantics.

    Science.gov (United States)

    Hewson, David

    1996-01-01

    Discusses how to use general semantics formulations to improve problem solving at home or at work--methods come from the areas of artificial intelligence/computer science, engineering, operations research, and psychology. (PA)

  17. How to solve mathematical problems

    CERN Document Server

    Wickelgren, Wayne A

    1995-01-01

    Seven problem-solving techniques include inference, classification of action sequences, subgoals, contradiction, working backward, relations between problems, and mathematical representation. Also, problems from mathematics, science, and engineering with complete solutions.

  18. Interactive Problem-Solving Interventions

    African Journals Online (AJOL)

    Frew Demeke Alemu

    concerted efforts of unofficial actors to establish unofficial communication ... Frew Demeke Alemu (LLB, LLM in International Human Rights Law from Lund ..... 24 Tamra Pearson d'Estrée (2009), “Problem-Solving Approaches”, (in The SAGE ...

  19. Moment methods for nonlinear maps

    International Nuclear Information System (INIS)

    Pusch, G.D.; Atomic Energy of Canada Ltd., Chalk River, ON

    1993-01-01

    It is shown that Differential Algebra (DA) may be used to push moments of distributions through a map, at a computational cost per moment comparable to pushing a single particle. The algorithm is independent of order, and whether or not the map is symplectic. Starting from the known result that moment-vectors transform linearly - like a tensor - even under a nonlinear map, I suggest that the form of the moment transformation rule indicates that the moment-vectors are elements of the dual to DA-vector space. I propose several methods of manipulating moments and constructing invariants using DA. I close with speculations on how DA might be used to ''close the circle'' to solve the inverse moment problem, yielding an entirely DA-and-moment-based space-charge code. (Author)

  20. New Exact Solutions for New Model Nonlinear Partial Differential Equation

    OpenAIRE

    Maher, A.; El-Hawary, H. M.; Al-Amry, M. S.

    2013-01-01

    In this paper we propose a new form of Padé-II equation, namely, a combined Padé-II and modified Padé-II equation. The mapping method is a promising method to solve nonlinear evaluation equations. Therefore, we apply it, to solve the combined Padé-II and modified Padé-II equation. Exact travelling wave solutions are obtained and expressed in terms of hyperbolic functions, trigonometric functions, rational functions, and elliptic functions.

  1. The Gas Transmission Problem Solved by an Extension of the Simplex Algorithm

    OpenAIRE

    Daniel De Wolf; Yves Smeers

    2000-01-01

    The problem of distributing gas through a network of pipelines is formulated as a cost minimization subject to nonlinear flow-pressure relations, material balances, and pressure bounds. The solution method is based on piecewise linear approximations of the nonlinear flow-pressure relations. The approximated problem is solved by an extension of the Simplex method. The solution method is tested on real-world data and compared with alternative solution methods.

  2. Nonlinear dynamics and control of a vibrating rectangular plate

    Science.gov (United States)

    Shebalin, J. V.

    1983-01-01

    The von Karman equations of nonlinear elasticity are solved for the case of a vibrating rectangular plate by meams of a Fourier spectral transform method. The amplification of a particular Fourier mode by nonlinear transfer of energy is demonstrated for this conservative system. The multi-mode system is reduced to a minimal (two mode) system, retaining the qualitative features of the multi-mode system. The effect of a modal control law on the dynamics of this minimal nonlinear elastic system is examined.

  3. GHM method for obtaining rationalsolutions of nonlinear differential equations.

    Science.gov (United States)

    Vazquez-Leal, Hector; Sarmiento-Reyes, Arturo

    2015-01-01

    In this paper, we propose the application of the general homotopy method (GHM) to obtain rational solutions of nonlinear differential equations. It delivers a high precision representation of the nonlinear differential equation using a few linear algebraic terms. In order to assess the benefits of this proposal, three nonlinear problems are solved and compared against other semi-analytic methods or numerical methods. The obtained results show that GHM is a powerful tool, capable to generate highly accurate rational solutions. AMS subject classification 34L30.

  4. Nonlinear steady-state coupling of LH waves

    International Nuclear Information System (INIS)

    Ko, K.; Krapchev, V.B.

    1981-02-01

    The coupling of lower hybrid waves at the plasma edge by a two waveguide array with self-consistent density modulation is solved numerically. For a linear density profile, the governing nonlinear Klein-Gordon equation for the electric field can be written as a system of nonlinearly modified Airy equations in Fourier k/sub z/-space. Numerical solutions to the nonlinear system satisfying radiation condition are obtained. Spectra broadening and modifications to resonance cone trajectories are observed with increase of incident power

  5. Discrete-time inverse optimal control for nonlinear systems

    CERN Document Server

    Sanchez, Edgar N

    2013-01-01

    Discrete-Time Inverse Optimal Control for Nonlinear Systems proposes a novel inverse optimal control scheme for stabilization and trajectory tracking of discrete-time nonlinear systems. This avoids the need to solve the associated Hamilton-Jacobi-Bellman equation and minimizes a cost functional, resulting in a more efficient controller. Design More Efficient Controllers for Stabilization and Trajectory Tracking of Discrete-Time Nonlinear Systems The book presents two approaches for controller synthesis: the first based on passivity theory and the second on a control Lyapunov function (CLF). Th

  6. Nonlinear Dirac Equations

    Directory of Open Access Journals (Sweden)

    Wei Khim Ng

    2009-02-01

    Full Text Available We construct nonlinear extensions of Dirac's relativistic electron equation that preserve its other desirable properties such as locality, separability, conservation of probability and Poincaré invariance. We determine the constraints that the nonlinear term must obey and classify the resultant non-polynomial nonlinearities in a double expansion in the degree of nonlinearity and number of derivatives. We give explicit examples of such nonlinear equations, studying their discrete symmetries and other properties. Motivated by some previously suggested applications we then consider nonlinear terms that simultaneously violate Lorentz covariance and again study various explicit examples. We contrast our equations and construction procedure with others in the literature and also show that our equations are not gauge equivalent to the linear Dirac equation. Finally we outline various physical applications for these equations.

  7. Nonlinear graphene plasmonics

    Science.gov (United States)

    Ooi, Kelvin J. A.; Tan, Dawn T. H.

    2017-10-01

    The rapid development of graphene has opened up exciting new fields in graphene plasmonics and nonlinear optics. Graphene's unique two-dimensional band structure provides extraordinary linear and nonlinear optical properties, which have led to extreme optical confinement in graphene plasmonics and ultrahigh nonlinear optical coefficients, respectively. The synergy between graphene's linear and nonlinear optical properties gave rise to nonlinear graphene plasmonics, which greatly augments graphene-based nonlinear device performance beyond a billion-fold. This nascent field of research will eventually find far-reaching revolutionary technological applications that require device miniaturization, low power consumption and a broad range of operating wavelengths approaching the far-infrared, such as optical computing, medical instrumentation and security applications.

  8. Analytical-numerical solution of a nonlinear integrodifferential equation in econometrics

    Science.gov (United States)

    Kakhktsyan, V. M.; Khachatryan, A. Kh.

    2013-07-01

    A mixed problem for a nonlinear integrodifferential equation arising in econometrics is considered. An analytical-numerical method is proposed for solving the problem. Some numerical results are presented.

  9. Nonlinear amplitude dynamics in flagellar beating.

    Science.gov (United States)

    Oriola, David; Gadêlha, Hermes; Casademunt, Jaume

    2017-03-01

    The physical basis of flagellar and ciliary beating is a major problem in biology which is still far from completely understood. The fundamental cytoskeleton structure of cilia and flagella is the axoneme, a cylindrical array of microtubule doublets connected by passive cross-linkers and dynein motor proteins. The complex interplay of these elements leads to the generation of self-organized bending waves. Although many mathematical models have been proposed to understand this process, few attempts have been made to assess the role of dyneins on the nonlinear nature of the axoneme. Here, we investigate the nonlinear dynamics of flagella by considering an axonemal sliding control mechanism for dynein activity. This approach unveils the nonlinear selection of the oscillation amplitudes, which are typically either missed or prescribed in mathematical models. The explicit set of nonlinear equations are derived and solved numerically. Our analysis reveals the spatio-temporal dynamics of dynein populations and flagellum shape for different regimes of motor activity, medium viscosity and flagellum elasticity. Unstable modes saturate via the coupling of dynein kinetics and flagellum shape without the need of invoking a nonlinear axonemal response. Hence, our work reveals a novel mechanism for the saturation of unstable modes in axonemal beating.

  10. Tangram solved? Prefrontal cortex activation analysis during geometric problem solving.

    Science.gov (United States)

    Ayaz, Hasan; Shewokis, Patricia A; Izzetoğlu, Meltem; Çakır, Murat P; Onaral, Banu

    2012-01-01

    Recent neuroimaging studies have implicated prefrontal and parietal cortices for mathematical problem solving. Mental arithmetic tasks have been used extensively to study neural correlates of mathematical reasoning. In the present study we used geometric problem sets (tangram tasks) that require executive planning and visuospatial reasoning without any linguistic representation interference. We used portable optical brain imaging (functional near infrared spectroscopy--fNIR) to monitor hemodynamic changes within anterior prefrontal cortex during tangram tasks. Twelve healthy subjects were asked to solve a series of computerized tangram puzzles and control tasks that required same geometric shape manipulation without problem solving. Total hemoglobin (HbT) concentration changes indicated a significant increase during tangram problem solving in the right hemisphere. Moreover, HbT changes during failed trials (when no solution found) were significantly higher compared to successful trials. These preliminary results suggest that fNIR can be used to assess cortical activation changes induced by geometric problem solving. Since fNIR is safe, wearable and can be used in ecologically valid environments such as classrooms, this neuroimaging tool may help to improve and optimize learning in educational settings.

  11. Numerical Solution of Nonlinear Volterra Integral Equations System Using Simpson’s 3/8 Rule

    Directory of Open Access Journals (Sweden)

    Adem Kılıçman

    2012-01-01

    Full Text Available The Simpson’s 3/8 rule is used to solve the nonlinear Volterra integral equations system. Using this rule the system is converted to a nonlinear block system and then by solving this nonlinear system we find approximate solution of nonlinear Volterra integral equations system. One of the advantages of the proposed method is its simplicity in application. Further, we investigate the convergence of the proposed method and it is shown that its convergence is of order O(h4. Numerical examples are given to show abilities of the proposed method for solving linear as well as nonlinear systems. Our results show that the proposed method is simple and effective.

  12. Stationary nonlinear Airy beams

    International Nuclear Information System (INIS)

    Lotti, A.; Faccio, D.; Couairon, A.; Papazoglou, D. G.; Panagiotopoulos, P.; Tzortzakis, S.; Abdollahpour, D.

    2011-01-01

    We demonstrate the existence of an additional class of stationary accelerating Airy wave forms that exist in the presence of third-order (Kerr) nonlinearity and nonlinear losses. Numerical simulations and experiments, in agreement with the analytical model, highlight how these stationary solutions sustain the nonlinear evolution of Airy beams. The generic nature of the Airy solution allows extension of these results to other settings, and a variety of applications are suggested.

  13. Generalized Nonlinear Yule Models

    OpenAIRE

    Lansky, Petr; Polito, Federico; Sacerdote, Laura

    2016-01-01

    With the aim of considering models with persistent memory we propose a fractional nonlinear modification of the classical Yule model often studied in the context of macrovolution. Here the model is analyzed and interpreted in the framework of the development of networks such as the World Wide Web. Nonlinearity is introduced by replacing the linear birth process governing the growth of the in-links of each specific webpage with a fractional nonlinear birth process with completely general birth...

  14. Non-Interior Continuation Method for Solving the Monotone Semidefinite Complementarity Problem

    International Nuclear Information System (INIS)

    Huang, Z.H.; Han, J.

    2003-01-01

    Recently, Chen and Tseng extended non-interior continuation smoothing methods for solving linear/ nonlinear complementarity problems to semidefinite complementarity problems (SDCP). In this paper we propose a non-interior continuation method for solving the monotone SDCP based on the smoothed Fischer-Burmeister function, which is shown to be globally linearly and locally quadratically convergent under suitable assumptions. Our algorithm needs at most to solve a linear system of equations at each iteration. In addition, in our analysis on global linear convergence of the algorithm, we need not use the assumption that the Frechet derivative of the function involved in the SDCP is Lipschitz continuous. For non-interior continuation/ smoothing methods for solving the nonlinear complementarity problem, such an assumption has been used widely in the literature in order to achieve global linear convergence results of the algorithms

  15. Nonlinear Finite Strain Consolidation Analysis with Secondary Consolidation Behavior

    Directory of Open Access Journals (Sweden)

    Jieqing Huang

    2014-01-01

    Full Text Available This paper aims to analyze nonlinear finite strain consolidation with secondary consolidation behavior. On the basis of some assumptions about the secondary consolidation behavior, the continuity equation of pore water in Gibson’s consolidation theory is modified. Taking the nonlinear compressibility and nonlinear permeability of soils into consideration, the governing equation for finite strain consolidation analysis is derived. Based on the experimental data of Hangzhou soft clay samples, the new governing equation is solved with the finite element method. Afterwards, the calculation results of this new method and other two methods are compared. It can be found that Gibson’s method may underestimate the excess pore water pressure during primary consolidation. The new method which takes the secondary consolidation behavior, the nonlinear compressibility, and nonlinear permeability of soils into consideration can precisely estimate the settlement rate and the final settlement of Hangzhou soft clay sample.

  16. A Nonlinear Modal Aeroelastic Solver for FUN3D

    Science.gov (United States)

    Goldman, Benjamin D.; Bartels, Robert E.; Biedron, Robert T.; Scott, Robert C.

    2016-01-01

    A nonlinear structural solver has been implemented internally within the NASA FUN3D computational fluid dynamics code, allowing for some new aeroelastic capabilities. Using a modal representation of the structure, a set of differential or differential-algebraic equations are derived for general thin structures with geometric nonlinearities. ODEPACK and LAPACK routines are linked with FUN3D, and the nonlinear equations are solved at each CFD time step. The existing predictor-corrector method is retained, whereby the structural solution is updated after mesh deformation. The nonlinear solver is validated using a test case for a flexible aeroshell at transonic, supersonic, and hypersonic flow conditions. Agreement with linear theory is seen for the static aeroelastic solutions at relatively low dynamic pressures, but structural nonlinearities limit deformation amplitudes at high dynamic pressures. No flutter was found at any of the tested trajectory points, though LCO may be possible in the transonic regime.

  17. Nonlinear analysis of dynamic signature

    Science.gov (United States)

    Rashidi, S.; Fallah, A.; Towhidkhah, F.

    2013-12-01

    Signature is a long trained motor skill resulting in well combination of segments like strokes and loops. It is a physical manifestation of complex motor processes. The problem, generally stated, is that how relative simplicity in behavior emerges from considerable complexity of perception-action system that produces behavior within an infinitely variable biomechanical and environmental context. To solve this problem, we present evidences which indicate that motor control dynamic in signing process is a chaotic process. This chaotic dynamic may explain a richer array of time series behavior in motor skill of signature. Nonlinear analysis is a powerful approach and suitable tool which seeks for characterizing dynamical systems through concepts such as fractal dimension and Lyapunov exponent. As a result, they can be analyzed in both horizontal and vertical for time series of position and velocity. We observed from the results that noninteger values for the correlation dimension indicates low dimensional deterministic dynamics. This result could be confirmed by using surrogate data tests. We have also used time series to calculate the largest Lyapunov exponent and obtain a positive value. These results constitute significant evidence that signature data are outcome of chaos in a nonlinear dynamical system of motor control.

  18. Nonlinear secret image sharing scheme.

    Science.gov (United States)

    Shin, Sang-Ho; Lee, Gil-Je; Yoo, Kee-Young

    2014-01-01

    Over the past decade, most of secret image sharing schemes have been proposed by using Shamir's technique. It is based on a linear combination polynomial arithmetic. Although Shamir's technique based secret image sharing schemes are efficient and scalable for various environments, there exists a security threat such as Tompa-Woll attack. Renvall and Ding proposed a new secret sharing technique based on nonlinear combination polynomial arithmetic in order to solve this threat. It is hard to apply to the secret image sharing. In this paper, we propose a (t, n)-threshold nonlinear secret image sharing scheme with steganography concept. In order to achieve a suitable and secure secret image sharing scheme, we adapt a modified LSB embedding technique with XOR Boolean algebra operation, define a new variable m, and change a range of prime p in sharing procedure. In order to evaluate efficiency and security of proposed scheme, we use the embedding capacity and PSNR. As a result of it, average value of PSNR and embedding capacity are 44.78 (dB) and 1.74t⌈log2 m⌉ bit-per-pixel (bpp), respectively.

  19. Nonlinear evolution equations

    CERN Document Server

    Uraltseva, N N

    1995-01-01

    This collection focuses on nonlinear problems in partial differential equations. Most of the papers are based on lectures presented at the seminar on partial differential equations and mathematical physics at St. Petersburg University. Among the topics explored are the existence and properties of solutions of various classes of nonlinear evolution equations, nonlinear imbedding theorems, bifurcations of solutions, and equations of mathematical physics (Navier-Stokes type equations and the nonlinear Schrödinger equation). The book will be useful to researchers and graduate students working in p

  20. Nonlinear optics at interfaces

    International Nuclear Information System (INIS)

    Chen, C.K.

    1980-12-01

    Two aspects of surface nonlinear optics are explored in this thesis. The first part is a theoretical and experimental study of nonlinear intraction of surface plasmons and bulk photons at metal-dielectric interfaces. The second part is a demonstration and study of surface enhanced second harmonic generation at rough metal surfaces. A general formulation for nonlinear interaction of surface plasmons at metal-dielectric interfaces is presented and applied to both second and third order nonlinear processes. Experimental results for coherent second and third harmonic generation by surface plasmons and surface coherent antiStokes Raman spectroscopy (CARS) are shown to be in good agreement with the theory

  1. Nonlinear drift tearing mode

    International Nuclear Information System (INIS)

    Zelenyj, L.M.; Kuznetsova, M.M.

    1989-01-01

    Nonlinear study of magnetic perturbation development under single-mode conditions in collision-free plasma in configurations with the magnetic field shear is investigated. Results are obtained with regard of transverse component of electrical field and its effect on ion dynamics within wide range of ion Larmor radius value and values of magnetic field shear. Increments of nonlinear drift tearing mode are obtained and it is shown that excitation drastic conditions of even linearly stable modes are possible. Mechanism of instability nonlinear stabilization is considered and the value of magnetic island at the saturation threshold is estimeted. Energy of nonlinear drift tearing mode is discussed

  2. Nonlinear Fuzzy Model Predictive Control for a PWR Nuclear Power Plant

    Directory of Open Access Journals (Sweden)

    Xiangjie Liu

    2014-01-01

    Full Text Available Reliable power and temperature control in pressurized water reactor (PWR nuclear power plant is necessary to guarantee high efficiency and plant safety. Since the nuclear plants are quite nonlinear, the paper presents nonlinear fuzzy model predictive control (MPC, by incorporating the realistic constraints, to realize the plant optimization. T-S fuzzy modeling on nuclear power plant is utilized to approximate the nonlinear plant, based on which the nonlinear MPC controller is devised via parallel distributed compensation (PDC scheme in order to solve the nonlinear constraint optimization problem. Improved performance compared to the traditional PID controller for a TMI-type PWR is obtained in the simulation.

  3. A nonsmooth nonlinear conjugate gradient method for interactive contact force problems

    DEFF Research Database (Denmark)

    Silcowitz, Morten; Abel, Sarah Maria Niebe; Erleben, Kenny

    2010-01-01

    of a nonlinear complementarity problem (NCP), which can be solved using an iterative splitting method, such as the projected Gauss–Seidel (PGS) method. We present a novel method for solving the NCP problem by applying a Fletcher–Reeves type nonlinear nonsmooth conjugate gradient (NNCG) type method. We analyze...... and present experimental convergence behavior and properties of the new method. Our results show that the NNCG method has at least the same convergence rate as PGS, and in many cases better....

  4. Solving polynomial differential equations by transforming them to linear functional-differential equations

    OpenAIRE

    Nahay, John Michael

    2008-01-01

    We present a new approach to solving polynomial ordinary differential equations by transforming them to linear functional equations and then solving the linear functional equations. We will focus most of our attention upon the first-order Abel differential equation with two nonlinear terms in order to demonstrate in as much detail as possible the computations necessary for a complete solution. We mention in our section on further developments that the basic transformation idea can be generali...

  5. Polarization Nonlinear Optics of Quadratically Nonlinear Azopolymers

    International Nuclear Information System (INIS)

    Konorov, S.O.; Akimov, D.A.; Ivanov, A.A.; Petrov, A.N.; Alfimov, M.V.; Yakimanskii, A.V.; Smirnov, N.N.; Ivanova, V.N.; Kudryavtsev, V.V.; Podshivalov, A.A.; Sokolova, I.M.; Zheltikov, A.M.

    2005-01-01

    The polarization properties of second harmonic and sum-frequency signals generated by femtosecond laser pulses in films of polymers containing covalent groups of an azobenzothiazole chromophore polarized by an external electric field are investigated. It is shown that the methods of polarization nonlinear optics make it possible to determine the structure of oriented molecular dipoles and reveal important properties of the motion of collectivized πelectrons in organic molecules with strong optical nonlinearities. The polarization measurements show that the tensor of quadratic nonlinear optical susceptibility of chromophore fragments oriented by an external field in macromolecules of the noted azopolymers has a degenerate form. This is indicative of a predominantly one-dimensional character of motion of collectivized π electrons along an extended group of atoms in such molecules

  6. Solving equations by topological methods

    Directory of Open Access Journals (Sweden)

    Lech Górniewicz

    2005-01-01

    Full Text Available In this paper we survey most important results from topological fixed point theory which can be directly applied to differential equations. Some new formulations are presented. We believe that our article will be useful for analysts applying topological fixed point theory in nonlinear analysis and in differential equations.

  7. Approximate Solution of Nonlinear Klein-Gordon Equation Using Sobolev Gradients

    Directory of Open Access Journals (Sweden)

    Nauman Raza

    2016-01-01

    Full Text Available The nonlinear Klein-Gordon equation (KGE models many nonlinear phenomena. In this paper, we propose a scheme for numerical approximation of solutions of the one-dimensional nonlinear KGE. A common approach to find a solution of a nonlinear system is to first linearize the equations by successive substitution or the Newton iteration method and then solve a linear least squares problem. Here, we show that it can be advantageous to form a sum of squared residuals of the nonlinear problem and then find a zero of the gradient. Our scheme is based on the Sobolev gradient method for solving a nonlinear least square problem directly. The numerical results are compared with Lattice Boltzmann Method (LBM. The L2, L∞, and Root-Mean-Square (RMS values indicate better accuracy of the proposed method with less computational effort.

  8. Nonlinear dynamics in Nuclotron

    International Nuclear Information System (INIS)

    Dinev, D.

    1997-01-01

    The paper represents an extensive study of the nonlinear beam dynamics in the Nuclotron. Chromatic effects, including the dependence of the betatron tunes on the amplitude, and chromatic perturbations have been investigated taking into account the measured field imperfections. Beam distortion, smear, dynamic aperture and nonlinear acceptance have been calculated for different particle energies and betatron tunes

  9. Nonlinear Optics and Applications

    Science.gov (United States)

    Abdeldayem, Hossin A. (Editor); Frazier, Donald O. (Editor)

    2007-01-01

    Nonlinear optics is the result of laser beam interaction with materials and started with the advent of lasers in the early 1960s. The field is growing daily and plays a major role in emerging photonic technology. Nonlinear optics play a major role in many of the optical applications such as optical signal processing, optical computers, ultrafast switches, ultra-short pulsed lasers, sensors, laser amplifiers, and many others. This special review volume on Nonlinear Optics and Applications is intended for those who want to be aware of the most recent technology. This book presents a survey of the recent advances of nonlinear optical applications. Emphasis will be on novel devices and materials, switching technology, optical computing, and important experimental results. Recent developments in topics which are of historical interest to researchers, and in the same time of potential use in the fields of all-optical communication and computing technologies, are also included. Additionally, a few new related topics which might provoke discussion are presented. The book includes chapters on nonlinear optics and applications; the nonlinear Schrodinger and associated equations that model spatio-temporal propagation; the supercontinuum light source; wideband ultrashort pulse fiber laser sources; lattice fabrication as well as their linear and nonlinear light guiding properties; the second-order EO effect (Pockels), the third-order (Kerr) and thermo-optical effects in optical waveguides and their applications in optical communication; and, the effect of magnetic field and its role in nonlinear optics, among other chapters.

  10. A Semi-Analytical Approach for the Response of Nonlinear Conservative Systems

    DEFF Research Database (Denmark)

    Kimiaeifar, Amin; Barari, Amin; Fooladi, M

    2011-01-01

    This work applies Parameter expanding method (PEM) as a powerful analytical technique in order to obtain the exact solution of nonlinear problems in the classical dynamics. Lagrange method is employed to derive the governing equations. The nonlinear governing equations are solved analytically by ...

  11. Adaptive Optimizing Nonlinear Control Design for an Over-actuated Aircraft Model

    NARCIS (Netherlands)

    Van Oort, E.R.; Sonneveldt, L.; Chu, Q.P.; Mulder, J.A.

    2011-01-01

    In this paper nonlinear adaptive flight control laws based on the backstepping approach are proposed which are applicable to over-actuated nonlinear systems. Instead of solving the control allocation exactly, update laws for the desired control effector signals are defined such that they converge to

  12. Filamentary structures of the cosmic web and the nonlinear Schroedinger type equation

    International Nuclear Information System (INIS)

    Tigrak, E; Weygaert, R van de; Jones, B J T

    2011-01-01

    We show that the filamentary type structures of the cosmic web can be modeled as solitonic waves by solving the reaction diffusion system which is the hydrodynamical analogous of the nonlinear Schroedinger type equation. We find the analytical solution of this system by applying the Hirota direct method which produces the dissipative soliton solutions to formulate the dynamical evolution of the nonlinear structure formation.

  13. Customer-centered problem solving.

    Science.gov (United States)

    Samelson, Q B

    1999-11-01

    If there is no single best way to attract new customers and retain current customers, there is surely an easy way to lose them: fail to solve the problems that arise in nearly every buyer-supplier relationship, or solve them in an unsatisfactory manner. Yet, all too frequently, companies do just that. Either we deny that a problem exists, we exert all our efforts to pin the blame elsewhere, or we "Band-Aid" the problem instead of fixing it, almost guaranteeing that we will face it again and again.

  14. Simon on Problem-Solving

    DEFF Research Database (Denmark)

    Foss, Kirsten; Foss, Nicolai Juul

    as a general approach to problem solving. We apply these Simonian ideas to organizational issues, specifically new organizational forms. Specifically, Simonian ideas allow us to develop a morphology of new organizational forms and to point to some design problems that characterize these forms.Keywords: Herbert...... Simon, problem-solving, new organizational forms. JEL Code: D23, D83......Two of Herbert Simon's best-known papers are "The Architecture of Complexity" and "The Structure of Ill-Structured Problems." We discuss the neglected links between these two papers, highlighting the role of decomposition in the context of problems on which constraints have been imposed...

  15. Interactive problem solving using LOGO

    CERN Document Server

    Boecker, Heinz-Dieter; Fischer, Gerhard

    2014-01-01

    This book is unique in that its stress is not on the mastery of a programming language, but on the importance and value of interactive problem solving. The authors focus on several specific interest worlds: mathematics, computer science, artificial intelligence, linguistics, and games; however, their approach can serve as a model that may be applied easily to other fields as well. Those who are interested in symbolic computing will find that Interactive Problem Solving Using LOGO provides a gentle introduction from which one may move on to other, more advanced computational frameworks or more

  16. Inference rule and problem solving

    Energy Technology Data Exchange (ETDEWEB)

    Goto, S

    1982-04-01

    Intelligent information processing signifies an opportunity of having man's intellectual activity executed on the computer, in which inference, in place of ordinary calculation, is used as the basic operational mechanism for such an information processing. Many inference rules are derived from syllogisms in formal logic. The problem of programming this inference function is referred to as a problem solving. Although logically inference and problem-solving are in close relation, the calculation ability of current computers is on a low level for inferring. For clarifying the relation between inference and computers, nonmonotonic logic has been considered. The paper deals with the above topics. 16 references.

  17. Nonlinear optical systems

    CERN Document Server

    Lugiato, Luigi; Brambilla, Massimo

    2015-01-01

    Guiding graduate students and researchers through the complex world of laser physics and nonlinear optics, this book provides an in-depth exploration of the dynamics of lasers and other relevant optical systems, under the umbrella of a unitary spatio-temporal vision. Adopting a balanced approach, the book covers traditional as well as special topics in laser physics, quantum electronics and nonlinear optics, treating them from the viewpoint of nonlinear dynamical systems. These include laser emission, frequency generation, solitons, optically bistable systems, pulsations and chaos and optical pattern formation. It also provides a coherent and up-to-date treatment of the hierarchy of nonlinear optical models and of the rich variety of phenomena they describe, helping readers to understand the limits of validity of each model and the connections among the phenomena. It is ideal for graduate students and researchers in nonlinear optics, quantum electronics, laser physics and photonics.

  18. Nonlinear dynamics of two-phase flow

    International Nuclear Information System (INIS)

    Rizwan-uddin

    1986-01-01

    Unstable flow conditions can occur in a wide variety of laboratory and industry equipment that involve two-phase flow. Instabilities in industrial equipment, which include boiling water reactor (BWR) cores, steam generators, heated channels, cryogenic fluid heaters, heat exchangers, etc., are related to their nonlinear dynamics. These instabilities can be of static (Ledinegg instability) or dynamic (density wave oscillations) type. Determination of regions in parameters space where these instabilities can occur and knowledge of system dynamics in or near these regions is essential for the safe operation of such equipment. Many two-phase flow engineering components can be modeled as heated channels. The set of partial differential equations that describes the dynamics of single- and two-phase flow, for the special case of uniform heat flux along the length of the channel, can be reduced to a set of two coupled ordinary differential equations [in inlet velocity v/sub i/(t) and two-phase residence time tau(t)] involving history integrals: a nonlinear ordinary functional differential equation and an integral equation. Hence, to solve these equations, the dependent variables must be specified for -(nu + tau) ≤ t ≤ 0, where nu is the single-phase residence time. This system of nonlinear equations has been solved analytically using asymptotic expansion series for finite but small perturbations and numerically using finite difference techniques

  19. Use of wiener nonlinear MPC to control a CSTR with multiple steady state

    OpenAIRE

    Lusson Cervantes, A.; Agamennoni, O.E.; Figueroa, J.L.

    2003-01-01

    In this paper a Nonlinear Model Predictive Control based on a Wiener Model with a Piecewise Linear gain is presented. The major advantages of this algorithm is that it retains all the interesting properties of the classical linear MPC and the computations are easy to solve due to the canonical structure of the nonlinear gain. The proposed control scheme is applied to a nonlinear CSTR that presents multiple steady states.

  20. Spline Collocation Method for Nonlinear Multi-Term Fractional Differential Equation

    OpenAIRE

    Choe, Hui-Chol; Kang, Yong-Suk

    2013-01-01

    We study an approximation method to solve nonlinear multi-term fractional differential equations with initial conditions or boundary conditions. First, we transform the nonlinear multi-term fractional differential equations with initial conditions and boundary conditions to nonlinear fractional integral equations and consider the relations between them. We present a Spline Collocation Method and prove the existence, uniqueness and convergence of approximate solution as well as error estimatio...

  1. Iterative analysis of concrete gravity dam-nonlinear foundation ...

    African Journals Online (AJOL)

    The solution of the coupled system is accomplished by solving the two systems separately and then considering the interaction effects at the soil–structure interface enforced by a developed iterative scheme. Emphasis has been laid on the study of material nonlinearity of the foundation material in the interaction analysis.

  2. Quantum osp-invariant non-linear Schroedinger equation

    International Nuclear Information System (INIS)

    Kulish, P.P.

    1985-04-01

    The generalizations of the non-linear Schroedinger equation (NS) associated with the orthosymplectic superalgebras are formulated. The simplest osp(1/2)-NS model is solved by the quantum inverse scattering method on a finite interval under periodic boundary conditions as well as on the wholeline in the case of a finite number of excitations. (author)

  3. Analytic solutions of a class of nonlinearly dynamic systems

    International Nuclear Information System (INIS)

    Wang, M-C; Zhao, X-S; Liu, X

    2008-01-01

    In this paper, the homotopy perturbation method (HPM) is applied to solve a coupled system of two nonlinear differential with first-order similar model of Lotka-Volterra and a Bratus equation with a source term. The analytic approximate solutions are derived. Furthermore, the analytic approximate solutions obtained by the HPM with the exact solutions reveals that the present method works efficiently

  4. Exact solutions for the cubic-quintic nonlinear Schroedinger equation

    International Nuclear Information System (INIS)

    Zhu Jiamin; Ma Zhengyi

    2007-01-01

    In this paper, the cubic-quintic nonlinear Schroedinger equation is solved through the extended elliptic sub-equation method. As a consequence, many types of exact travelling wave solutions are obtained which including bell and kink profile solitary wave solutions, triangular periodic wave solutions and singular solutions

  5. Rigorous Verification for the Solution of Nonlinear Interval System ...

    African Journals Online (AJOL)

    We survey a general method for solving nonlinear interval systems of equations. In particular, we paid special attention to the computational aspects of linear interval systems since the bulk of computations are done during the stage of computing outer estimation of the including linear interval systems. The height of our ...

  6. A preconditioned inexact newton method for nonlinear sparse electromagnetic imaging

    KAUST Repository

    Desmal, Abdulla; Bagci, Hakan

    2015-01-01

    to tackle the nonlinearity of these equations. At every IN iteration, a system of equations, which involves the Frechet derivative (FD) matrix of the CS operator, is solved for the IN step. A sparsity constraint is enforced on the solution via thresholded

  7. Solve the Dilemma of Over-Simplification

    Science.gov (United States)

    Schmitt, Gerhard

    Complexity science can help to understand the functioning and the interaction of the components of a city. In 1965, Christopher Alexander gave in his book A city is not a tree a description of the complex nature of urban organization. At this time, neither high-speed computers nor urban big data existed. Today, Luis Bettencourt et al. use complexity science to analyze data for countries, regions, or cities. The results can be used globally in other cities. Objectives of complexity science with regard to future cities are the observation and identification of tendencies and regularities in behavioral patterns, and to find correlations between them and spatial configurations. Complex urban systems cannot be understood in total yet. But research focuses on describing the system by finding some simple, preferably general and emerging patterns and rules that can be used for urban planning. It is important that the influencing factors are not just geo-spatial patterns but also consider variables which are important for the design quality. Complexity science is a way to solve the dilemma of oversimplification of insights from existing cities and their applications to new cities. An example: The effects of streets, public places and city structures on citizens and their behavior depend on how they are perceived. To describe this perception, it is not sufficient to consider only particular characteristics of the urban environment. Different aspects play a role and influence each other. Complexity science could take this fact into consideration and handle the non-linearity of the system...

  8. Human Problem Solving in 2012

    Science.gov (United States)

    Funke, Joachim

    2013-01-01

    This paper presents a bibliography of 263 references related to human problem solving, arranged by subject matter. The references were taken from PsycInfo and Academic Premier data-base. Journal papers, book chapters, and dissertations are included. The topics include human development, education, neuroscience, and research in applied settings. It…

  9. Solved problems in classical electromagnetism

    CERN Document Server

    Franklin, Jerrold

    2018-01-01

    This original Dover publication is the companion to a new edition of the author's Classical Electromagnetism: Second Edition. The latter volume will feature only basic answers; this book will contain some problems from the reissue as well as many other new ones. All feature complete, worked-out solutions and form a valuable source of problem-solving material for students.

  10. Error Patterns in Problem Solving.

    Science.gov (United States)

    Babbitt, Beatrice C.

    Although many common problem-solving errors within the realm of school mathematics have been previously identified, a compilation of such errors is not readily available within learning disabilities textbooks, mathematics education texts, or teacher's manuals for school mathematics texts. Using data on error frequencies drawn from both the Fourth…

  11. Quantitative Reasoning in Problem Solving

    Science.gov (United States)

    Ramful, Ajay; Ho, Siew Yin

    2015-01-01

    In this article, Ajay Ramful and Siew Yin Ho explain the meaning of quantitative reasoning, describing how it is used in the to solve mathematical problems. They also describe a diagrammatic approach to represent relationships among quantities and provide examples of problems and their solutions.

  12. Students' Problem Solving and Justification

    Science.gov (United States)

    Glass, Barbara; Maher, Carolyn A.

    2004-01-01

    This paper reports on methods of students' justifications of their solution to a problem in the area of combinatorics. From the analysis of the problem solving of 150 students in a variety of settings from high-school to graduate study, four major forms of reasoning evolved: (1) Justification by Cases, (2) Inductive Argument, (3) Elimination…

  13. Solving Differential Equations in R: Package deSolve

    Directory of Open Access Journals (Sweden)

    Karline Soetaert

    2010-02-01

    Full Text Available In this paper we present the R package deSolve to solve initial value problems (IVP written as ordinary differential equations (ODE, differential algebraic equations (DAE of index 0 or 1 and partial differential equations (PDE, the latter solved using the method of lines approach. The differential equations can be represented in R code or as compiled code. In the latter case, R is used as a tool to trigger the integration and post-process the results, which facilitates model development and application, whilst the compiled code significantly increases simulation speed. The methods implemented are efficient, robust, and well documented public-domain Fortran routines. They include four integrators from the ODEPACK package (LSODE, LSODES, LSODA, LSODAR, DVODE and DASPK2.0. In addition, a suite of Runge-Kutta integrators and special-purpose solvers to efficiently integrate 1-, 2- and 3-dimensional partial differential equations are available. The routines solve both stiff and non-stiff systems, and include many options, e.g., to deal in an efficient way with the sparsity of the Jacobian matrix, or finding the root of equations. In this article, our objectives are threefold: (1 to demonstrate the potential of using R for dynamic modeling, (2 to highlight typical uses of the different methods implemented and (3 to compare the performance of models specified in R code and in compiled code for a number of test cases. These comparisons demonstrate that, if the use of loops is avoided, R code can efficiently integrate problems comprising several thousands of state variables. Nevertheless, the same problem may be solved from 2 to more than 50 times faster by using compiled code compared to an implementation using only R code. Still, amongst the benefits of R are a more flexible and interactive implementation, better readability of the code, and access to R’s high-level procedures. deSolve is the successor of package odesolve which will be deprecated in

  14. Problem solving skills for schizophrenia.

    Science.gov (United States)

    Xia, J; Li, Chunbo

    2007-04-18

    The severe and long-lasting symptoms of schizophrenia are often the cause of severe disability. Environmental stress such as life events and the practical problems people face in their daily can worsen the symptoms of schizophrenia. Deficits in problem solving skills in people with schizophrenia affect their independent and interpersonal functioning and impair their quality of life. As a result, therapies such as problem solving therapy have been developed to improve problem solving skills for people with schizophrenia. To review the effectiveness of problem solving therapy compared with other comparable therapies or routine care for those with schizophrenia. We searched the Cochrane Schizophrenia Group's Register (September 2006), which is based on regular searches of BIOSIS, CENTRAL, CINAHL, EMBASE, MEDLINE and PsycINFO. We inspected references of all identified studies for further trials. We included all clinical randomised trials comparing problem solving therapy with other comparable therapies or routine care. We extracted data independently. For homogenous dichotomous data we calculated random effects, relative risk (RR), 95% confidence intervals (CI) and, where appropriate, numbers needed to treat (NNT) on an intention-to-treat basis. For continuous data, we calculated weighted mean differences (WMD) using a random effects statistical model. We included only three small trials (n=52) that evaluated problem solving versus routine care, coping skills training or non-specific interaction. Inadequate reporting of data rendered many outcomes unusable. We were unable to undertake meta-analysis. Overall results were limited and inconclusive with no significant differences between treatment groups for hospital admission, mental state, behaviour, social skills or leaving the study early. No data were presented for global state, quality of life or satisfaction. We found insufficient evidence to confirm or refute the benefits of problem solving therapy as an additional

  15. Clawpack: building an open source ecosystem for solving hyperbolic PDEs

    KAUST Repository

    Mandli, Kyle T.

    2016-08-08

    Clawpack is a software package designed to solve nonlinear hyperbolic partial differential equations using high-resolution finite volume methods based on Riemann solvers and limiters. The package includes a number of variants aimed at different applications and user communities. Clawpack has been actively developed as an open source project for over 20 years. The latest major release, Clawpack 5, introduces a number of new features and changes to the code base and a new development model based on GitHub and Git submodules. This article provides a summary of the most significant changes, the rationale behind some of these changes, and a description of our current development model.

  16. Neural network error correction for solving coupled ordinary differential equations

    Science.gov (United States)

    Shelton, R. O.; Darsey, J. A.; Sumpter, B. G.; Noid, D. W.

    1992-01-01

    A neural network is presented to learn errors generated by a numerical algorithm for solving coupled nonlinear differential equations. The method is based on using a neural network to correctly learn the error generated by, for example, Runge-Kutta on a model molecular dynamics (MD) problem. The neural network programs used in this study were developed by NASA. Comparisons are made for training the neural network using backpropagation and a new method which was found to converge with fewer iterations. The neural net programs, the MD model and the calculations are discussed.

  17. Clawpack: building an open source ecosystem for solving hyperbolic PDEs

    KAUST Repository

    Mandli, Kyle T.; Ahmadia, Aron J.; Berger, Marsha; Calhoun, Donna; George, David L.; Hadjimichael, Yiannis; Ketcheson, David I.; Lemoine, Grady I.; LeVeque, Randall J.

    2016-01-01

    Clawpack is a software package designed to solve nonlinear hyperbolic partial differential equations using high-resolution finite volume methods based on Riemann solvers and limiters. The package includes a number of variants aimed at different applications and user communities. Clawpack has been actively developed as an open source project for over 20 years. The latest major release, Clawpack 5, introduces a number of new features and changes to the code base and a new development model based on GitHub and Git submodules. This article provides a summary of the most significant changes, the rationale behind some of these changes, and a description of our current development model.

  18. A neuro approach to solve fuzzy Riccati differential equations

    Energy Technology Data Exchange (ETDEWEB)

    Shahrir, Mohammad Shazri, E-mail: mshazri@gmail.com [InstitutSainsMatematik, Universiti Malaya 50603 Kuala Lumpur, Wilayah Persekutuan Kuala Lumpur (Malaysia); Telekom Malaysia, R& D TM Innovation Centre, LingkaranTeknokrat Timur, 63000 Cyberjaya, Selangor (Malaysia); Kumaresan, N., E-mail: drnk2008@gmail.com; Kamali, M. Z. M.; Ratnavelu, Kurunathan [InstitutSainsMatematik, Universiti Malaya 50603 Kuala Lumpur, Wilayah Persekutuan Kuala Lumpur (Malaysia)

    2015-10-22

    There are many applications of optimal control theory especially in the area of control systems in engineering. In this paper, fuzzy quadratic Riccati differential equation is estimated using neural networks (NN). Previous works have shown reliable results using Runge-Kutta 4th order (RK4). The solution can be achieved by solving the 1st Order Non-linear Differential Equation (ODE) that is found commonly in Riccati differential equation. Research has shown improved results relatively to the RK4 method. It can be said that NN approach shows promising results with the advantage of continuous estimation and improved accuracy that can be produced over RK4.

  19. Genetics problem solving and worldview

    Science.gov (United States)

    Dale, Esther

    The research goal was to determine whether worldview relates to traditional and real-world genetics problem solving. Traditionally, scientific literacy emphasized content knowledge alone because it was sufficient to solve traditional problems. The contemporary definition of scientific literacy is, "The knowledge and understanding of scientific concepts and processes required for personal decision-making, participation in civic and cultural affairs and economic productivity" (NRC, 1996). An expanded definition of scientific literacy is needed to solve socioscientific issues (SSI), complex social issues with conceptual, procedural, or technological associations with science. Teaching content knowledge alone assumes that students will find the scientific explanation of a phenomenon to be superior to a non-science explanation. Formal science and everyday ways of thinking about science are two different cultures (Palmer, 1999). Students address this rift with cognitive apartheid, the boxing away of science knowledge from other types of knowledge (Jedege & Aikenhead, 1999). By addressing worldview, cognitive apartheid may decrease and scientific literacy may increase. Introductory biology students at the University of Minnesota during fall semester 2005 completed a written questionnaire-including a genetics content-knowledge test, four genetic dilemmas, the Worldview Assessment Instrument (WAI) and some items about demographics and religiosity. Six students responded to the interview protocol. Based on statistical analysis and interview data, this study concluded the following: (1) Worldview, in the form of metaphysics, relates to solving traditional genetic dilemmas. (2) Worldview, in the form of agency, relates to solving traditional genetics problems. (3) Thus, worldview must be addressed in curriculum, instruction, and assessment.

  20. Clawpack: Building an open source ecosystem for solving hyperbolic PDEs

    Science.gov (United States)

    Iverson, Richard M.; Mandli, K.T.; Ahmadia, Aron J.; Berger, M.J.; Calhoun, Donna; George, David L.; Hadjimichael, Y.; Ketcheson, David I.; Lemoine, Grady L.; LeVeque, Randall J.

    2016-01-01

    Clawpack is a software package designed to solve nonlinear hyperbolic partial differential equations using high-resolution finite volume methods based on Riemann solvers and limiters. The package includes a number of variants aimed at different applications and user communities. Clawpack has been actively developed as an open source project for over 20 years. The latest major release, Clawpack 5, introduces a number of new features and changes to the code base and a new development model based on GitHub and Git submodules. This article provides a summary of the most significant changes, the rationale behind some of these changes, and a description of our current development model. Clawpack: building an open source ecosystem for solving hyperbolic PDEs.

  1. Nonlinear photonic metasurfaces

    Science.gov (United States)

    Li, Guixin; Zhang, Shuang; Zentgraf, Thomas

    2017-03-01

    Compared with conventional optical elements, 2D photonic metasurfaces, consisting of arrays of antennas with subwavelength thickness (the 'meta-atoms'), enable the manipulation of light-matter interactions on more compact platforms. The use of metasurfaces with spatially varying arrangements of meta-atoms that have subwavelength lateral resolution allows control of the polarization, phase and amplitude of light. Many exotic phenomena have been successfully demonstrated in linear optics; however, to meet the growing demand for the integration of more functionalities into a single optoelectronic circuit, the tailorable nonlinear optical properties of metasurfaces will also need to be exploited. In this Review, we discuss the design of nonlinear photonic metasurfaces — in particular, the criteria for choosing the materials and symmetries of the meta-atoms — for the realization of nonlinear optical chirality, nonlinear geometric Berry phase and nonlinear wavefront engineering. Finally, we survey the application of nonlinear photonic metasurfaces in optical switching and modulation, and we conclude with an outlook on their use for terahertz nonlinear optics and quantum information processing.

  2. Nonlinear crack mechanics

    International Nuclear Information System (INIS)

    Khoroshun, L.P.

    1995-01-01

    The characteristic features of the deformation and failure of actual materials in the vicinity of a crack tip are due to their physical nonlinearity in the stress-concentration zone, which is a result of plasticity, microfailure, or a nonlinear dependence of the interatomic forces on the distance. Therefore, adequate models of the failure mechanics must be nonlinear, in principle, although linear failure mechanics is applicable if the zone of nonlinear deformation is small in comparison with the crack length. Models of crack mechanics are based on analytical solutions of the problem of the stress-strain state in the vicinity of the crack. On account of the complexity of the problem, nonlinear models are bason on approximate schematic solutions. In the Leonov-Panasyuk-Dugdale nonlinear model, one of the best known, the actual two-dimensional plastic zone (the nonlinearity zone) is replaced by a narrow one-dimensional zone, which is then modeled by extending the crack with a specified normal load equal to the yield point. The condition of finite stress is applied here, and hence the length of the plastic zone is determined. As a result of this approximation, the displacement in the plastic zone at the abscissa is nonzero

  3. Electromagnetic pulses at the boundary of a nonlinear plasma

    International Nuclear Information System (INIS)

    Satorius, E.H.

    1975-01-01

    An investigation was made of the behavior of strong electromagnetic pulses at the boundary of a nonlinear, cold, collisionless, and uniform plasma. The nonlinearity considered here is due to the nonlinear terms in the fluid equation which is used to describe the plasma. Two cases are studied. First, the case where there is a voltage pulse applied across the plane boundary of a semi-infinite, nonlinear plasma. Two different voltage pulses are considered, i.e., a delta function pulse and a suddenly turned-on sinusoidal pulse. The resulting electromagnetic fields propagating in the nonlinear plasma are found in this case. In the second case, the reflection of incident E-polarized and H-polarized, electromagnetic pulses at various angles of incidence from a nonlinear, semi-infinite plasma are considered. Again, two forms of incident pulses are considered: a delta function pulse and a suddenly turned-on sinusoidal pulse. In case two, the reflected electromagnetic fields are found. In both cases, the method used for finding the fields is to first solve the fluid equation (which describes the plasma) for the nonlinear conduction current in terms of the electric field using a perturbation method (since the nonlinear effects are assumed to be small). Next, this current is substituted into Maxwell's equations, and finally the electromagnetic fields which satisfy the boundary conditions are found. (U.S.)

  4. On kinetic Boltzmann equations and related hydrodynamic flows with dry viscosity

    Directory of Open Access Journals (Sweden)

    Nikolai N. Bogoliubov (Jr.

    2007-01-01

    Full Text Available A two-component particle model of Boltzmann-Vlasov type kinetic equations in the form of special nonlinear integro-differential hydrodynamic systems on an infinite-dimensional functional manifold is discussed. We show that such systems are naturally connected with the nonlinear kinetic Boltzmann-Vlasov equations for some one-dimensional particle flows with pointwise interaction potential between particles. A new type of hydrodynamic two-component Benney equations is constructed and their Hamiltonian structure is analyzed.

  5. Asymptotic solving method for sea-air coupled oscillator ENSO model

    International Nuclear Information System (INIS)

    Zhou Xian-Chun; Yao Jing-Sun; Mo Jia-Qi

    2012-01-01

    The ENSO is an interannual phenomenon involved in the tropical Pacific ocean-atmosphere interaction. In this article, we create an asymptotic solving method for the nonlinear system of the ENSO model. The asymptotic solution is obtained. And then we can furnish weather forecasts theoretically and other behaviors and rules for the atmosphere-ocean oscillator of the ENSO. (general)

  6. He's homotopy perturbation method for solving systems of Volterra integral equations of the second kind

    International Nuclear Information System (INIS)

    Biazar, J.; Ghazvini, H.

    2009-01-01

    In this paper, the He's homotopy perturbation method is applied to solve systems of Volterra integral equations of the second kind. Some examples are presented to illustrate the ability of the method for linear and non-linear such systems. The results reveal that the method is very effective and simple.

  7. Nonlinear wave equations

    CERN Document Server

    Li, Tatsien

    2017-01-01

    This book focuses on nonlinear wave equations, which are of considerable significance from both physical and theoretical perspectives. It also presents complete results on the lower bound estimates of lifespan (including the global existence), which are established for classical solutions to the Cauchy problem of nonlinear wave equations with small initial data in all possible space dimensions and with all possible integer powers of nonlinear terms. Further, the book proposes the global iteration method, which offers a unified and straightforward approach for treating these kinds of problems. Purely based on the properties of solut ions to the corresponding linear problems, the method simply applies the contraction mapping principle.

  8. Nonlinear analysis of composite thin-walled helicopter blades

    Science.gov (United States)

    Kalfon, J. P.; Rand, O.

    Nonlinear theoretical modeling of laminated thin-walled composite helicopter rotor blades is presented. The derivation is based on nonlinear geometry with a detailed treatment of the body loads in the axial direction which are induced by the rotation. While the in-plane warping is neglected, a three-dimensional generic out-of-plane warping distribution is included. The formulation may also handle varying thicknesses and mass distribution along the cross-sectional walls. The problem is solved by successive iterations in which a system of equations is constructed and solved for each cross-section. In this method, the differential equations in the spanwise directions are formulated and solved using a finite-differences scheme which allows simple adaptation of the spanwise discretization mesh during iterations.

  9. Adaptive nonlinear control for a research reactor

    International Nuclear Information System (INIS)

    Benitez R, J.S.

    1994-01-01

    Linearization by feedback of states is based on the idea of transform the nonlinear dynamic equation of a system in a linear form. This linear behavior can be achieve well in a complete way (input state) or in partial way (input output). This can be applied to systems of single or multiple inputs, and can be used to solve problems of stabilization and tracking of references trajectories. Comparing this method with conventional ones, linearization by feedback of states is exact in certain region of the space of state, instead of linear approximations of the equations in a certain point of the operation. In the presence of parametric uncertainties in the model of the system, the introduction of adaptive schemes provide a type toughness to the control system by nonlinear feedback, which gives as result the eventual cancellation of the nonlinear terms in the dynamic relationship between the output and the input of the auxiliary control. In the same way, it has been presented the design of a nonlinearizing control for the non lineal model of a TRIGA Mark III type reactor, with the aim of tracking a predetermined power profile. The asymptotic tracking of such profile is, at the present moment, in the stage of verification by computerized simulation the relative easiness in the design of auxiliary variable of control, as well as the decoupling action of the output variable, make very attractive the utilization of the method herein presented. (Author)

  10. Nonlinear ultrasonic imaging with X wave

    Science.gov (United States)

    Du, Hongwei; Lu, Wei; Feng, Huanqing

    2009-10-01

    X wave has a large depth of field and may have important application in ultrasonic imaging to provide high frame rate (HFR). However, the HFR system suffers from lower spatial resolution. In this paper, a study of nonlinear imaging with X wave is presented to improve the resolution. A theoretical description of realizable nonlinear X wave is reported. The nonlinear field is simulated by solving the KZK nonlinear wave equation with a time-domain difference method. The results show that the second harmonic field of X wave has narrower mainlobe and lower sidelobes than the fundamental field. In order to evaluate the imaging effect with X wave, an imaging model involving numerical calculation of the KZK equation, Rayleigh-Sommerfeld integral, band-pass filtering and envelope detection is constructed to obtain 2D fundamental and second harmonic images of scatters in tissue-like medium. The results indicate that if X wave is used, the harmonic image has higher spatial resolution throughout the entire imaging region than the fundamental image, but higher sidelobes occur as compared to conventional focus imaging. A HFR imaging method with higher spatial resolution is thus feasible provided an apodization method is used to suppress sidelobes.

  11. 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.

  12. Toward Analytic Solution of Nonlinear Differential Difference Equations via Extended Sensitivity Approach

    International Nuclear Information System (INIS)

    Darmani, G.; Setayeshi, S.; Ramezanpour, H.

    2012-01-01

    In this paper an efficient computational method based on extending the sensitivity approach (SA) is proposed to find an analytic exact solution of nonlinear differential difference equations. In this manner we avoid solving the nonlinear problem directly. By extension of sensitivity approach for differential difference equations (DDEs), the nonlinear original problem is transformed into infinite linear differential difference equations, which should be solved in a recursive manner. Then the exact solution is determined in the form of infinite terms series and by intercepting series an approximate solution is obtained. Numerical examples are employed to show the effectiveness of the proposed approach. (general)

  13. Non-Linear Dynamics and Fundamental Interactions

    CERN Document Server

    Khanna, Faqir

    2006-01-01

    The book is directed to researchers and graduate students pursuing an advanced degree. It provides details of techniques directed towards solving problems in non-linear dynamics and chos that are, in general, not amenable to a perturbative treatment. The consideration of fundamental interactions is a prime example where non-perturbative techniques are needed. Extension of these techniques to finite temperature problems is considered. At present these ideas are primarily used in a perturbative context. However, non-perturbative techniques have been considered in some specific cases. Experts in the field on non-linear dynamics and chaos and fundamental interactions elaborate the techniques and provide a critical look at the present status and explore future directions that may be fruitful. The text of the main talks will be very useful to young graduate students who are starting their studies in these areas.

  14. Analytical solution of strongly nonlinear Duffing oscillators

    Directory of Open Access Journals (Sweden)

    A.M. El-Naggar

    2016-06-01

    Full Text Available In this paper, a new perturbation technique is employed to solve strongly nonlinear Duffing oscillators, in which a new parameter α=α(ε is defined such that the value of α is always small regardless of the magnitude of the original parameter ε. Therefore, the strongly nonlinear Duffing oscillators with large parameter ε are transformed into a small parameter system with respect to α. Approximate solution obtained by the present method is compared with the solution of energy balance method, homotopy perturbation method, global error minimization method and lastly numerical solution. We observe from the results that this method is very simple, easy to apply, and gives a very good accuracy not only for small parameter εbut also for large values of ε.

  15. Nonlinear elliptic equations and nonassociative algebras

    CERN Document Server

    Nadirashvili, Nikolai; Vlăduţ, Serge

    2014-01-01

    This book presents applications of noncommutative and nonassociative algebras to constructing unusual (nonclassical and singular) solutions to fully nonlinear elliptic partial differential equations of second order. The methods described in the book are used to solve a longstanding problem of the existence of truly weak, nonsmooth viscosity solutions. Moreover, the authors provide an almost complete description of homogeneous solutions to fully nonlinear elliptic equations. It is shown that even in the very restricted setting of "Hessian equations", depending only on the eigenvalues of the Hessian, these equations admit homogeneous solutions of all orders compatible with known regularity for viscosity solutions provided the space dimension is five or larger. To the contrary, in dimension four or less the situation is completely different, and our results suggest strongly that there are no nonclassical homogeneous solutions at all in dimensions three and four. Thus this book gives a complete list of dimensions...

  16. Nonlinear analysis approximation theory, optimization and applications

    CERN Document Server

    2014-01-01

    Many of our daily-life problems can be written in the form of an optimization problem. Therefore, solution methods are needed to solve such problems. Due to the complexity of the problems, it is not always easy to find the exact solution. However, approximate solutions can be found. The theory of the best approximation is applicable in a variety of problems arising in nonlinear functional analysis and optimization. This book highlights interesting aspects of nonlinear analysis and optimization together with many applications in the areas of physical and social sciences including engineering. It is immensely helpful for young graduates and researchers who are pursuing research in this field, as it provides abundant research resources for researchers and post-doctoral fellows. This will be a valuable addition to the library of anyone who works in the field of applied mathematics, economics and engineering.

  17. High-order nonlinear susceptibilities of He

    International Nuclear Information System (INIS)

    Liu, W.C.; Clark, C.W.

    1996-01-01

    High-order nonlinear optical response of noble gases to intense laser radiation is of considerable experimental interest, but is difficult to measure or calculate accurately. The authors have begun a set of calculations of frequency-dependent nonlinear susceptibilities of He 1s, within the framework of Rayleigh=Schroedinger perturbation theory at lowest applicable order, with the goal of providing critically evaluated atomic data for modelling high harmonic generation processes. The atomic Hamiltonian is decomposed in term of Hylleraas coordinates and spherical harmonics using the formalism of Ponte and Shakeshaft, and the hierarchy of inhomogeneous equations of perturbation theory is solved iteratively. A combination of Hylleraas and Frankowski basis functions is used; the compact Hylleraas basis provides a highly accurate representation of the ground state wavefunction, whereas the diffuse Frankowski basis functions efficiently reproduce the correct asymptotic structure of the perturbed orbitals

  18. SHA-1, SAT-solving, and CNF

    CSIR Research Space (South Africa)

    Motara, YM

    2017-09-01

    Full Text Available the intersection between the SHA-1 preimage problem, the encoding of that problem for SAT-solving, and SAT-solving. The results demonstrate that SAT-solving is not yet a viable approach to take to solve the preimage problem, and also indicate that some...

  19. Assessing Algebraic Solving Ability: A Theoretical Framework

    Science.gov (United States)

    Lian, Lim Hooi; Yew, Wun Thiam

    2012-01-01

    Algebraic solving ability had been discussed by many educators and researchers. There exists no definite definition for algebraic solving ability as it can be viewed from different perspectives. In this paper, the nature of algebraic solving ability in terms of algebraic processes that demonstrate the ability in solving algebraic problem is…

  20. A family of conjugate gradient methods for large-scale nonlinear equations

    Directory of Open Access Journals (Sweden)

    Dexiang Feng

    2017-09-01

    Full Text Available Abstract In this paper, we present a family of conjugate gradient projection methods for solving large-scale nonlinear equations. At each iteration, it needs low storage and the subproblem can be easily solved. Compared with the existing solution methods for solving the problem, its global convergence is established without the restriction of the Lipschitz continuity on the underlying mapping. Preliminary numerical results are reported to show the efficiency of the proposed method.

  1. A family of conjugate gradient methods for large-scale nonlinear equations.

    Science.gov (United States)

    Feng, Dexiang; Sun, Min; Wang, Xueyong

    2017-01-01

    In this paper, we present a family of conjugate gradient projection methods for solving large-scale nonlinear equations. At each iteration, it needs low storage and the subproblem can be easily solved. Compared with the existing solution methods for solving the problem, its global convergence is established without the restriction of the Lipschitz continuity on the underlying mapping. Preliminary numerical results are reported to show the efficiency of the proposed method.

  2. Photostable nonlinear optical polycarbonates

    NARCIS (Netherlands)

    Faccini, M.; Balakrishnan, M.; Diemeer, Mart; Torosantucci, Riccardo; Driessen, A.; Reinhoudt, David; Verboom, Willem

    2008-01-01

    Highly thermal and photostable nonlinear optical polymers were obtained by covalently incorporating the tricyanovinylidenediphenylaminobenzene (TCVDPA) chromophore to a polycarbonate backbone. NLO polycarbonates with different chromophore attachment modes and flexibilities were synthesized. In spite

  3. Nonlinear singular elliptic equations

    International Nuclear Information System (INIS)

    Dong Minh Duc.

    1988-09-01

    We improve the Poincare inequality, the Sobolev imbedding theorem and the Trudinger imbedding theorem and prove a Mountain pass theorem. Applying these results we study a nonlinear singular mixed boundary problem. (author). 22 refs

  4. Nonlinear Optical Terahertz Technology

    Data.gov (United States)

    National Aeronautics and Space Administration — We develop a new approach to generation of THz radiation. Our method relies on mixing two optical frequency beams in a nonlinear crystalline Whispering Gallery Mode...

  5. Nonlinear differential equations

    CERN Document Server

    Struble, Raimond A

    2017-01-01

    Detailed treatment covers existence and uniqueness of a solution of the initial value problem, properties of solutions, properties of linear systems, stability of nonlinear systems, and two-dimensional systems. 1962 edition.

  6. Terahertz semiconductor nonlinear optics

    DEFF Research Database (Denmark)

    Turchinovich, Dmitry; Hvam, Jørn Märcher; Hoffmann, Matthias

    2013-01-01

    In this proceedings we describe our recent results on semiconductor nonlinear optics, investigated using single-cycle THz pulses. We demonstrate the nonlinear absorption and self-phase modulation of strong-field THz pulses in doped semiconductors, using n-GaAs as a model system. The THz...... nonlinearity in doped semiconductors originates from the near-instantaneous heating of free electrons in the ponderomotive potential created by electric field of the THz pulse, leading to ultrafast increase of electron effective mass by intervalley scattering. Modification of effective mass in turn leads...... to a decrease of plasma frequency in semiconductor and produces a substantial modification of THz-range material dielectric function, described by the Drude model. As a result, the nonlinearity of both absorption coefficient and refractive index of the semiconductor is observed. In particular we demonstrate...

  7. Ultrafast nonlinear optics

    CERN Document Server

    Leburn, Christopher; Reid, Derryck

    2013-01-01

    The field of ultrafast nonlinear optics is broad and multidisciplinary, and encompasses areas concerned with both the generation and measurement of ultrashort pulses of light, as well as those concerned with the applications of such pulses. Ultrashort pulses are extreme events – both in terms of their durations, and also the high peak powers which their short durations can facilitate. These extreme properties make them powerful experiment tools. On one hand, their ultrashort durations facilitate the probing and manipulation of matter on incredibly short timescales. On the other, their ultrashort durations can facilitate high peak powers which can drive highly nonlinear light-matter interaction processes. Ultrafast Nonlinear Optics covers a complete range of topics, both applied and fundamental in nature, within the area of ultrafast nonlinear optics. Chapters 1 to 4 are concerned with the generation and measurement of ultrashort pulses. Chapters 5 to 7 are concerned with fundamental applications of ultrasho...

  8. Nonlinear surface Alfven waves

    International Nuclear Information System (INIS)

    Cramer, N.F.

    1991-01-01

    The problem of nonlinear surface Alfven waves propagating on an interface between a plasma and a vacuum is discussed, with dispersion provided by the finite-frequency effect, i.e. the finite ratio of the frequency to the ion-cyclotron frequency. A set of simplified nonlinear wave equations is derived using the method of stretched co-ordinates, and another approach uses the generation of a second-harmonic wave and its interaction with the first harmonic to obtain a nonlinear dispersion relation. A nonlinear Schroedinger equation is then derived, and soliton solutions found that propagate as solitary pulses in directions close to parallel and antiparallel to the background magnetic field. (author)

  9. Nonlinear Structural Analysis

    Indian Academy of Sciences (India)

    The Structures Panel of the Aeronautics Research and Development Board of India ... A great variety of topics was covered, including themes such as nonlinear finite ... or shell structures, and three are on the composite form of construction, ...

  10. A nonlinear oscillatory problem

    International Nuclear Information System (INIS)

    Zhou Qingqing.

    1991-10-01

    We have studied the nonlinear oscillatory problem of orthotropic cylindrical shell, we have analyzed the character of the oscillatory system. The stable condition of the oscillatory system has been given. (author). 6 refs

  11. Degenerate nonlinear diffusion equations

    CERN Document Server

    Favini, Angelo

    2012-01-01

    The aim of these notes is to include in a uniform presentation style several topics related to the theory of degenerate nonlinear diffusion equations, treated in the mathematical framework of evolution equations with multivalued m-accretive operators in Hilbert spaces. The problems concern nonlinear parabolic equations involving two cases of degeneracy. More precisely, one case is due to the vanishing of the time derivative coefficient and the other is provided by the vanishing of the diffusion coefficient on subsets of positive measure of the domain. From the mathematical point of view the results presented in these notes can be considered as general results in the theory of degenerate nonlinear diffusion equations. However, this work does not seek to present an exhaustive study of degenerate diffusion equations, but rather to emphasize some rigorous and efficient techniques for approaching various problems involving degenerate nonlinear diffusion equations, such as well-posedness, periodic solutions, asympt...

  12. Introduction to nonlinear science

    CERN Document Server

    Nicolis, G

    1995-01-01

    One of the most unexpected results in science in recent years is that quite ordinary systems obeying simple laws can give rise to complex, nonlinear or chaotic, behavior. In this book, the author presents a unified treatment of the concepts and tools needed to analyze nonlinear phenomena and to outline some representative applications drawn from the physical, engineering, and biological sciences. Some of the interesting topics covered include: dynamical systems with a finite number of degrees of freedom, linear stability analysis of fixed points, nonlinear behavior of fixed points, bifurcation analysis, spatially distributed systems, broken symmetries, pattern formation, and chaotic dynamics. The author makes a special effort to provide a logical connection between ordinary dynamical systems and spatially extended systems, and to balance the emphasis on chaotic behavior and more classical nonlinear behavior. He also develops a statistical approach to complex systems and compares it to traditional deterministi...

  13. Confluent-Functional solving systems

    Directory of Open Access Journals (Sweden)

    V.N. Koval

    2001-08-01

    Full Text Available The paper proposes a statistical knowledge-acquision approach. The solving systems are considered, which are able to find unknown structural dependences between situational and transforming variables on the basis of statistically analyzed input information. Situational variables describe features, states and relations between environment objects. Transforming variables describe transforming influences, exerted by a goal-oriented system onto an environment. Unknown environment rules are simulated by a structural equations system, associating situational and transforming variables.

  14. Nonlinear Wave Propagation

    Science.gov (United States)

    2015-05-07

    associated with the lattice background; the nonlinearity is derived from the inclusion of cubic nonlinearity. Often the background potential is periodic...dispersion branch we can find discrete evolution equations for the envelope associated with the lattice NLS equation (1) by looking for solutions of...spatial operator in the above NLS equation can be elliptic, hyperbolic or parabolic . We remark that further reduction is possible by going into a moving

  15. Nonlinear dynamics and astrophysics

    International Nuclear Information System (INIS)

    Vallejo, J. C.; Sanjuan, M. A. F.

    2000-01-01

    Concepts and techniques from Nonlinear Dynamics, also known as Chaos Theory, have been applied successfully to several astrophysical fields such as orbital motion, time series analysis or galactic dynamics, providing answers to old questions but also opening a few new ones. Some of these topics are described in this review article, showing the basis of Nonlinear Dynamics, and how it is applied in Astrophysics. (Author)

  16. Nonlinear elliptic partial differential equations an introduction

    CERN Document Server

    Le Dret, Hervé

    2018-01-01

    This textbook presents the essential parts of the modern theory of nonlinear partial differential equations, including the calculus of variations. After a short review of results in real and functional analysis, the author introduces the main mathematical techniques for solving both semilinear and quasilinear elliptic PDEs, and the associated boundary value problems. Key topics include infinite dimensional fixed point methods, the Galerkin method, the maximum principle, elliptic regularity, and the calculus of variations. Aimed at graduate students and researchers, this textbook contains numerous examples and exercises and provides several comments and suggestions for further study.

  17. NONLINEAR MODEL PREDICTIVE CONTROL OF CHEMICAL PROCESSES

    Directory of Open Access Journals (Sweden)

    SILVA R. G.

    1999-01-01

    Full Text Available A new algorithm for model predictive control is presented. The algorithm utilizes a simultaneous solution and optimization strategy to solve the model's differential equations. The equations are discretized by equidistant collocation, and along with the algebraic model equations are included as constraints in a nonlinear programming (NLP problem. This algorithm is compared with the algorithm that uses orthogonal collocation on finite elements. The equidistant collocation algorithm results in simpler equations, providing a decrease in computation time for the control moves. Simulation results are presented and show a satisfactory performance of this algorithm.

  18. Pescara benchmarks: nonlinear identification

    Science.gov (United States)

    Gandino, E.; Garibaldi, L.; Marchesiello, S.

    2011-07-01

    Recent nonlinear methods are suitable for identifying large systems with lumped nonlinearities, but in practice most structural nonlinearities are distributed and an ideal nonlinear identification method should cater for them as well. In order to extend the current NSI method to be applied also on realistic large engineering structures, a modal counterpart of the method is proposed in this paper. The modal NSI technique is applied on one of the reinforced concrete beams that have been tested in Pescara, under the project titled "Monitoring and diagnostics of railway bridges by means of the analysis of the dynamic response due to train crossing", financed by Italian Ministry of Research. The beam showed a softening nonlinear behaviour, so that the nonlinearity concerning the first mode is characterized and its force contribution is quantified. Moreover, estimates for the modal parameters are obtained and the model is validated by comparing the measured and the reconstructed output. The identified estimates are also used to accurately predict the behaviour of the same beam, when subject to different initial conditions.

  19. Nonlinear Multiantenna Detection Methods

    Directory of Open Access Journals (Sweden)

    Chen Sheng

    2004-01-01

    Full Text Available A nonlinear detection technique designed for multiple-antenna assisted receivers employed in space-division multiple-access systems is investigated. We derive the optimal solution of the nonlinear spatial-processing assisted receiver for binary phase shift keying signalling, which we refer to as the Bayesian detector. It is shown that this optimal Bayesian receiver significantly outperforms the standard linear beamforming assisted receiver in terms of a reduced bit error rate, at the expense of an increased complexity, while the achievable system capacity is substantially enhanced with the advent of employing nonlinear detection. Specifically, when the spatial separation expressed in terms of the angle of arrival between the desired and interfering signals is below a certain threshold, a linear beamformer would fail to separate them, while a nonlinear detection assisted receiver is still capable of performing adequately. The adaptive implementation of the optimal Bayesian detector can be realized using a radial basis function network. Two techniques are presented for constructing block-data-based adaptive nonlinear multiple-antenna assisted receivers. One of them is based on the relevance vector machine invoked for classification, while the other on the orthogonal forward selection procedure combined with the Fisher ratio class-separability measure. A recursive sample-by-sample adaptation procedure is also proposed for training nonlinear detectors based on an amalgam of enhanced -means clustering techniques and the recursive least squares algorithm.

  20. Pescara benchmarks: nonlinear identification

    International Nuclear Information System (INIS)

    Gandino, E; Garibaldi, L; Marchesiello, S

    2011-01-01

    Recent nonlinear methods are suitable for identifying large systems with lumped nonlinearities, but in practice most structural nonlinearities are distributed and an ideal nonlinear identification method should cater for them as well. In order to extend the current NSI method to be applied also on realistic large engineering structures, a modal counterpart of the method is proposed in this paper. The modal NSI technique is applied on one of the reinforced concrete beams that have been tested in Pescara, under the project titled M onitoring and diagnostics of railway bridges by means of the analysis of the dynamic response due to train crossing , financed by Italian Ministry of Research. The beam showed a softening nonlinear behaviour, so that the nonlinearity concerning the first mode is characterized and its force contribution is quantified. Moreover, estimates for the modal parameters are obtained and the model is validated by comparing the measured and the reconstructed output. The identified estimates are also used to accurately predict the behaviour of the same beam, when subject to different initial conditions.

  1. Introduction to nonlinear acoustics

    Science.gov (United States)

    Bjørnø, Leif

    2010-01-01

    A brief review of the basic principles of fluid mechanics needed for development of linear and nonlinear ultrasonic concepts will be given. The fundamental equations of nonlinear ultrasonics will be derived and their physical properties explained. It will be shown how an originally monochromatic finite-amplitude ultrasonic wave, due to nonlinear effects, will distort during its propagation in time and space to form higher harmonics to its fundamental frequency. The concepts of shock formation will be presented. The material nonlinearity, described by the nonlinearity parameter B/A of the material, and the convective nonlinearity, described by the ultrasonic Mach Number, will be explained. Two procedures for determination of B/A will briefly be described and some B/A-values characterizing biological materials will be presented. Shock formation, described by use of the Goldberg Number,and Ultrasonic Saturation will be discussed.. An introduction to focused ultrasonic fields will be given and it will be shown how the ultrasonic intensity will vary axially and laterally in and near the focal region and how the field parameters of interest to biomedical applications may be described by use of the KZK-Model. Finally, an introduction will be given to the parametric acoustic array formed by mixing and interaction of two monochromatic, finite-amplitude ultrasonic waves in a liquid and the potentials of this mixing process in biomedical ultrasound will briefly be mentioned.

  2. Strongly nonlinear free vibration of four edges simply supported stiffened plates with geometric imperfections

    Energy Technology Data Exchange (ETDEWEB)

    Chen, Zhaoting; Wang, Rong Hui; Chen, Li; Dong, Chung Uang [School of Civil Engineering and Transportation, South China University of Technology, Guangzhou (China)

    2016-08-15

    This article investigated the strongly nonlinear free vibration of four edges simply supported stiffened plates with geometric imperfections. The von Karman nonlinear strain-displacement relationships are applied. The nonlinear vibration of stiffened plate is reduced to a one-degree-of-freedom nonlinear system by assuming mode shapes. The Multiple scales Lindstedt-Poincare method (MSLP) and Modified Lindstedt-Poincare method (MLP) are used to solve the governing equations of vibration. Numerical examples for stiffened plates with different initial geometric imperfections are presented in order to discuss the influences to the strongly nonlinear free vibration of the stiffened plate. The results showed that: the frequency ratio reduced as the initial geometric imperfections of plate increased, which showed that the increase of the initial geometric imperfections of plate can lead to the decrease of nonlinear effect; by comparing the results calculated by MSLP method, using MS method to study strongly nonlinear vibration can lead to serious mistakes.

  3. Nonlinear hydromagnetic Rayleigh-Taylor instability for strong viscous fluids in porous media

    CERN Document Server

    El-Dib, Y O

    2003-01-01

    In the present work a weakly nonlinear stability for magnetic fluid is discussed. The research of an interface between two strong viscous homogeneous incompressible fluids through porous medium is investigated theoretically and graphically. The effect of the vertical magnetic field has been demonstrated in this study. The linear form of equation of motion is solved in the light of the nonlinear boundary conditions. The boundary value problem leads to construct nonlinear characteristic equation having complex coefficients in elevation function. The nonlinearity is kept to third-order expansion. The nonlinear characteristic equation leads to derive the well-known nonlinear Schroedinger equation. This equation having complex coefficients of the disturbance amplitude varies in both space and time. Stability criteria have been performed for nonlinear Chanderasekhar dispersion relation including the porous effects. Stability conditions are discussed through the assumption of equal kinematic viscosity. The calculati...

  4. Specular reflection treatment for the 3D radiative transfer equation solved with the discrete ordinates method

    Energy Technology Data Exchange (ETDEWEB)

    Le Hardy, D. [Université de Nantes, LTN UMR CNRS 6607 (France); Favennec, Y., E-mail: yann.favennec@univ-nantes.fr [Université de Nantes, LTN UMR CNRS 6607 (France); Rousseau, B. [Université de Nantes, LTN UMR CNRS 6607 (France); Hecht, F. [Sorbonne Universités, UPMC Université Paris 06, UMR 7598, inria de Paris, Laboratoire Jacques-Louis Lions, F-75005, Paris (France)

    2017-04-01

    The contribution of this paper relies in the development of numerical algorithms for the mathematical treatment of specular reflection on borders when dealing with the numerical solution of radiative transfer problems. The radiative transfer equation being integro-differential, the discrete ordinates method allows to write down a set of semi-discrete equations in which weights are to be calculated. The calculation of these weights is well known to be based on either a quadrature or on angular discretization, making the use of such method straightforward for the state equation. Also, the diffuse contribution of reflection on borders is usually well taken into account. However, the calculation of accurate partition ratio coefficients is much more tricky for the specular condition applied on arbitrary geometrical borders. This paper presents algorithms that calculate analytically partition ratio coefficients needed in numerical treatments. The developed algorithms, combined with a decentered finite element scheme, are validated with the help of comparisons with analytical solutions before being applied on complex geometries.

  5. Nonlinear Maps and their Applications 2011 International Workshop

    CERN Document Server

    Fournier-Prunaret, Daniele; Ueta, Tetsushi; Nishio, Yoshifumi

    2014-01-01

    In the field of Dynamical Systems, nonlinear iterative processes play an important role. Nonlinear mappings can be found as immediate models for many systems from different scientific areas, such as engineering, economics, biology, or can also be obtained via numerical methods permitting to solve non-linear differential equations. In both cases, the understanding of specific dynamical behaviors and phenomena is of the greatest interest for scientists. This volume contains papers that were presented at the International Workshop on Nonlinear Maps and their Applications (NOMA 2011) held in Évora, Portugal, on September 15-16, 2011. This kind of collaborative effort is of paramount importance in promoting communication among the various groups that work in dynamical systems and networks in their research theoretical studies as well as for applications. This volume is suitable for graduate students as well as researchers in the field.

  6. Nonlinear correction to the longitudinal structure function at small x

    International Nuclear Information System (INIS)

    Boroun, G.R.

    2010-01-01

    We computed the longitudinal proton structure function F L , using the nonlinear Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (NLDGLAP) evolution equation approach at small x. For the gluon distribution, the nonlinear effects are related to the longitudinal structure function. As the very small-x behavior of the gluon distribution is obtained by solving the Gribov, Levin, Ryskin, Mueller and Qiu (GLR-MQ) evolution equation with the nonlinear shadowing term incorporated, we show that the strong rise that corresponds to the linear QCD evolution equations can be tamed by screening effects. Consequently, the obtained longitudinal structure function shows a tamed growth at small x. We computed the predictions for all details of the nonlinear longitudinal structure function in the kinematic range where it has been measured by the H1 Collaboration and made comparisons with the computation by Moch, Vermaseren and Vogt at the second order with input data from the MRST QCD fit. (orig.)

  7. The spectral cell method in nonlinear earthquake modeling

    Science.gov (United States)

    Giraldo, Daniel; Restrepo, Doriam

    2017-12-01

    This study examines the applicability of the spectral cell method (SCM) to compute the nonlinear earthquake response of complex basins. SCM combines fictitious-domain concepts with the spectral-version of the finite element method to solve the wave equations in heterogeneous geophysical domains. Nonlinear behavior is considered by implementing the Mohr-Coulomb and Drucker-Prager yielding criteria. We illustrate the performance of SCM with numerical examples of nonlinear basins exhibiting physically and computationally challenging conditions. The numerical experiments are benchmarked with results from overkill solutions, and using MIDAS GTS NX, a finite element software for geotechnical applications. Our findings show good agreement between the two sets of results. Traditional spectral elements implementations allow points per wavelength as low as PPW = 4.5 for high-order polynomials. Our findings show that in the presence of nonlinearity, high-order polynomials (p ≥ 3) require mesh resolutions above of PPW ≥ 10 to ensure displacement errors below 10%.

  8. Applications and algorithms for mixed integer nonlinear programming

    International Nuclear Information System (INIS)

    Leyffer, Sven; Munson, Todd; Linderoth, Jeff; Luedtke, James; Miller, Andrew

    2009-01-01

    The mathematical modeling of systems often requires the use of both nonlinear and discrete components. Discrete decision variables model dichotomies, discontinuities, and general logical relationships. Nonlinear functions are required to accurately represent physical properties such as pressure, stress, temperature, and equilibrium. Problems involving both discrete variables and nonlinear constraint functions are known as mixed-integer nonlinear programs (MINLPs) and are among the most challenging computational optimization problems faced by researchers and practitioners. In this paper, we describe relevant scientific applications that are naturally modeled as MINLPs, we provide an overview of available algorithms and software, and we describe ongoing methodological advances for solving MINLPs. These algorithmic advances are making increasingly larger instances of this important family of problems tractable.

  9. ROTAX: a nonlinear optimization program by axes rotation method

    International Nuclear Information System (INIS)

    Suzuki, Tadakazu

    1977-09-01

    A nonlinear optimization program employing the axes rotation method has been developed for solving nonlinear problems subject to nonlinear inequality constraints and its stability and convergence efficiency were examined. The axes rotation method is a direct search of the optimum point by rotating the orthogonal coordinate system in a direction giving the minimum objective. The searching direction is rotated freely in multi-dimensional space, so the method is effective for the problems represented with the contours having deep curved valleys. In application of the axes rotation method to the optimization problems subject to nonlinear inequality constraints, an improved version of R.R. Allran and S.E.J. Johnsen's method is used, which deals with a new objective function composed of the original objective and a penalty term to consider the inequality constraints. The program is incorporated in optimization code system SCOOP. (auth.)

  10. Nonlinear physics with Maple for scientists and engineers

    CERN Document Server

    Enns, Richard H

    1997-01-01

    Philosophy of the Text This text has been designed to be an introductory survey of the basic concepts and applied mathematical methods of nonlinear science. Students in engineer­ ing, physics, chemistry, mathematics, computing science, and biology should be able to successfully use this text. In an effort to provide the students with a cutting edge approach to one of the most dynamic, often subtle, complex, and still rapidly evolving, areas of modern research-nonlinear physics-we have made extensive use of the symbolic, numeric, and plotting capabilities of Maple V Release 4 applied to examples from these disciplines. No prior knowledge of Maple or computer programming is assumed, the reader being gently introduced to Maple as an auxiliary tool as the concepts of nonlinear science are developed. The diskette which accompanies the text gives a wide variety of illustrative nonlinear examples solved with Maple. An accompanying laboratory manual of experimental activities keyed to the text allows the student the...

  11. Fundamentals of nonlinear optical materials

    Indian Academy of Sciences (India)

    Nonlinear optics; nonlinear polarization; optical fiber communication; optical switch- ing. PACS Nos 42.65Tg; ... The importance of nonlinear optics is to understand the nonlinear behavior in the induced polarization and to ..... but much work in material development and characterization remains to be done. 16. Conclusion.

  12. Application of Homotopy-Perturbation Method to Nonlinear Ozone Decomposition of the Second Order in Aqueous Solutions Equations

    DEFF Research Database (Denmark)

    Ganji, D.D; Miansari, Mo; B, Ganjavi

    2008-01-01

    In this paper, homotopy-perturbation method (HPM) is introduced to solve nonlinear equations of ozone decomposition in aqueous solutions. HPM deforms a di¢ cult problem into a simple problem which can be easily solved. The effects of some parameters such as temperature to the solutions are consid......In this paper, homotopy-perturbation method (HPM) is introduced to solve nonlinear equations of ozone decomposition in aqueous solutions. HPM deforms a di¢ cult problem into a simple problem which can be easily solved. The effects of some parameters such as temperature to the solutions...

  13. Sparse Reconstruction Schemes for Nonlinear Electromagnetic Imaging

    KAUST Repository

    Desmal, Abdulla

    2016-03-01

    Electromagnetic imaging is the problem of determining material properties from scattered fields measured away from the domain under investigation. Solving this inverse problem is a challenging task because (i) it is ill-posed due to the presence of (smoothing) integral operators used in the representation of scattered fields in terms of material properties, and scattered fields are obtained at a finite set of points through noisy measurements; and (ii) it is nonlinear simply due the fact that scattered fields are nonlinear functions of the material properties. The work described in this thesis tackles the ill-posedness of the electromagnetic imaging problem using sparsity-based regularization techniques, which assume that the scatterer(s) occupy only a small fraction of the investigation domain. More specifically, four novel imaging methods are formulated and implemented. (i) Sparsity-regularized Born iterative method iteratively linearizes the nonlinear inverse scattering problem and each linear problem is regularized using an improved iterative shrinkage algorithm enforcing the sparsity constraint. (ii) Sparsity-regularized nonlinear inexact Newton method calls for the solution of a linear system involving the Frechet derivative matrix of the forward scattering operator at every iteration step. For faster convergence, the solution of this matrix system is regularized under the sparsity constraint and preconditioned by leveling the matrix singular values. (iii) Sparsity-regularized nonlinear Tikhonov method directly solves the nonlinear minimization problem using Landweber iterations, where a thresholding function is applied at every iteration step to enforce the sparsity constraint. (iv) This last scheme is accelerated using a projected steepest descent method when it is applied to three-dimensional investigation domains. Projection replaces the thresholding operation and enforces the sparsity constraint. Numerical experiments, which are carried out using

  14. A semi-analytical iterative technique for solving chemistry problems

    Directory of Open Access Journals (Sweden)

    Majeed Ahmed AL-Jawary

    2017-07-01

    Full Text Available The main aim and contribution of the current paper is to implement a semi-analytical iterative method suggested by Temimi and Ansari in 2011 namely (TAM to solve two chemical problems. An approximate solution obtained by the TAM provides fast convergence. The current chemical problems are the absorption of carbon dioxide into phenyl glycidyl ether and the other system is a chemical kinetics problem. These problems are represented by systems of nonlinear ordinary differential equations that contain boundary conditions and initial conditions. Error analysis of the approximate solutions is studied using the error remainder and the maximal error remainder. Exponential rate for the convergence is observed. For both problems the results of the TAM are compared with other results obtained by previous methods available in the literature. The results demonstrate that the method has many merits such as being derivative-free, and overcoming the difficulty arising in calculating Adomian polynomials to handle the non-linear terms in Adomian Decomposition Method (ADM. It does not require to calculate Lagrange multiplier in Variational Iteration Method (VIM in which the terms of the sequence become complex after several iterations, thus, analytical evaluation of terms becomes very difficult or impossible in VIM. No need to construct a homotopy in Homotopy Perturbation Method (HPM and solve the corresponding algebraic equations. The MATHEMATICA® 9 software was used to evaluate terms in the iterative process.

  15. Fast Fourier Transform Pricing Method for Exponential Lévy Processes

    KAUST Repository

    Crocce, Fabian

    2014-05-04

    We describe a set of partial-integro-differential equations (PIDE) whose solutions represent the prices of european options when the underlying asset is driven by an exponential L´evy process. Exploiting the L´evy -Khintchine formula, we give a Fourier based method for solving this class of PIDEs. We present a novel L1 error bound for solving a range of PIDEs in asset pricing and use this bound to set parameters for numerical methods.

  16. Fast Fourier Transform Pricing Method for Exponential Lévy Processes

    KAUST Repository

    Crocce, Fabian; Happola, Juho; Kiessling, Jonas; Tempone, Raul

    2014-01-01

    We describe a set of partial-integro-differential equations (PIDE) whose solutions represent the prices of european options when the underlying asset is driven by an exponential L´evy process. Exploiting the L´evy -Khintchine formula, we give a Fourier based method for solving this class of PIDEs. We present a novel L1 error bound for solving a range of PIDEs in asset pricing and use this bound to set parameters for numerical methods.

  17. 50 years of nonlinear optics

    International Nuclear Information System (INIS)

    Shen Yuanrang

    2011-01-01

    This article presents a brief introduction to the birth and early investigations of nonlinear optics, such as second harmonic generation,sum and difference frequency generation, stimulated Raman scattering,and self-action of light etc. Several important research achievements and applications of nonlinear optics are presented as well, including nonlinear optical spectroscopy, phase conjugation and adaptive optics, coherent nonlinear optics, and high-order harmonic generation. In the end, current and future research topics in nonlinear optics are summarized. (authors)

  18. A novel nonlinear damage resonance intermodulation effect for structural health monitoring

    Science.gov (United States)

    Ciampa, Francesco; Scarselli, Gennaro; Meo, Michele

    2017-04-01

    This paper is aimed at developing a theoretical model able to predict the generation of nonlinear elastic effects associated to the interaction of ultrasonic waves with the steady-state nonlinear response of local defect resonance (LDR). The LDR effect is used in nonlinear elastic wave spectroscopy to enhance the excitation of the material damage at its local resonance, thus to dramatically increase the vibrational amplitude of material nonlinear phenomena. The main result of this work is to prove both analytically and experimentally the generation of novel nonlinear elastic wave effects, here named as nonlinear damage resonance intermodulation, which correspond to a nonlinear intermodulation between the driving frequency and the LDR one. Beside this intermodulation effect, other nonlinear elastic wave phenomena such as higher harmonics of the input frequency and superharmonics of LDR frequency were found. The analytical model relies on solving the nonlinear equation of motion governing bending displacement under the assumption of both quadratic and cubic nonlinear defect approximation. Experimental tests on a damaged composite laminate confirmed and validated these predictions and showed that using continuous periodic excitation, the nonlinear structural phenomena associated to LDR could also be featured at locations different from the damage resonance. These findings will provide new opportunities for material damage detection using nonlinear ultrasounds.

  19. Evolutionary algorithm based heuristic scheme for nonlinear heat transfer equations.

    Science.gov (United States)

    Ullah, Azmat; Malik, Suheel Abdullah; Alimgeer, Khurram Saleem

    2018-01-01

    In this paper, a hybrid heuristic scheme based on two different basis functions i.e. Log Sigmoid and Bernstein Polynomial with unknown parameters is used for solving the nonlinear heat transfer equations efficiently. The proposed technique transforms the given nonlinear ordinary differential equation into an equivalent global error minimization problem. Trial solution for the given nonlinear differential equation is formulated using a fitness function with unknown parameters. The proposed hybrid scheme of Genetic Algorithm (GA) with Interior Point Algorithm (IPA) is opted to solve the minimization problem and to achieve the optimal values of unknown parameters. The effectiveness of the proposed scheme is validated by solving nonlinear heat transfer equations. The results obtained by the proposed scheme are compared and found in sharp agreement with both the exact solution and solution obtained by Haar Wavelet-Quasilinearization technique which witnesses the effectiveness and viability of the suggested scheme. Moreover, the statistical analysis is also conducted for investigating the stability and reliability of the presented scheme.

  20. A Novel Nonlinear Parameter Estimation Method of Soft Tissues

    Directory of Open Access Journals (Sweden)

    Qianqian Tong

    2017-12-01

    Full Text Available The elastic parameters of soft tissues are important for medical diagnosis and virtual surgery simulation. In this study, we propose a novel nonlinear parameter estimation method for soft tissues. Firstly, an in-house data acquisition platform was used to obtain external forces and their corresponding deformation values. To provide highly precise data for estimating nonlinear parameters, the measured forces were corrected using the constructed weighted combination forecasting model based on a support vector machine (WCFM_SVM. Secondly, a tetrahedral finite element parameter estimation model was established to describe the physical characteristics of soft tissues, using the substitution parameters of Young’s modulus and Poisson’s ratio to avoid solving complicated nonlinear problems. To improve the robustness of our model and avoid poor local minima, the initial parameters solved by a linear finite element model were introduced into the parameter estimation model. Finally, a self-adapting Levenberg–Marquardt (LM algorithm was presented, which is capable of adaptively adjusting iterative parameters to solve the established parameter estimation model. The maximum absolute error of our WCFM_SVM model was less than 0.03 Newton, resulting in more accurate forces in comparison with other correction models tested. The maximum absolute error between the calculated and measured nodal displacements was less than 1.5 mm, demonstrating that our nonlinear parameters are precise.