Advanced differential quadrature methods
Zong, Zhi
2009-01-01
Modern Tools to Perform Numerical DifferentiationThe original direct differential quadrature (DQ) method has been known to fail for problems with strong nonlinearity and material discontinuity as well as for problems involving singularity, irregularity, and multiple scales. But now researchers in applied mathematics, computational mechanics, and engineering have developed a range of innovative DQ-based methods to overcome these shortcomings. Advanced Differential Quadrature Methods explores new DQ methods and uses these methods to solve problems beyond the capabilities of the direct DQ method.After a basic introduction to the direct DQ method, the book presents a number of DQ methods, including complex DQ, triangular DQ, multi-scale DQ, variable order DQ, multi-domain DQ, and localized DQ. It also provides a mathematical compendium that summarizes Gauss elimination, the Runge-Kutta method, complex analysis, and more. The final chapter contains three codes written in the FORTRAN language, enabling readers to q...
Differential quadrature time element method for structural dynamics
Institute of Scientific and Technical Information of China (English)
Yu-Feng Xing; Jing Guo
2012-01-01
An accurate and efficient differential quadrature time element method (DQTEM) is proposed for solving ordinary differential equations (ODEs),the numerical dissipation and dispersion of DQTEM is much smaller than that of the direct integration method of single/multi steps.Two methods of imposing initial conditions are given,which avoids the tediousness when derivative initial conditions are imposed,and the numerical comparisons indicate that the first method,in which the analog equations of initial displacements and velocities are used to directly replace the differential quadrature (DQ) analog equations of ODEs at the first and the last sampling points,respectively,is much more accurate than the second method,in which the DQ analog equations of initial conditions are used to directly replace the DQ analog equations of ODEs at the first two sampling points.On the contrary to the conventional step-by-step direct integration schemes,the solutions at all sampling points can be obtained simultaneously by DQTEM,and generally,one differential quadrature time element may be enough for the whole time domain.Extensive numerical comparisons validate the efficiency and accuracy of the proposed method.
Structural dynamic responses analysis applying differential quadrature method
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PU Jun-ping; ZHENG Jian-jun
2006-01-01
Unconditionally stable higher-order accurate time step integration algorithms based on the differential quadrature method (DQM) for second-order initial value problems were applied and the quadrature rules of DQM, computing of the weighting coefficients and choices of sampling grid points were discussed. Some numerical examples dealing with the heat transfer problem, the second-order differential equation of imposed vibration of linear single-degree-of-freedom systems and double-degree-of-freedom systems, the nonlinear move differential equation and a beam forced by a changing load were computed,respectively. The results indicated that the algorithm can produce highly accurate solutions with minimal time consumption, and that the system total energy can remain conservative in the numerical computation.
Axisymmetric Consolidation of Unsaturated Soils by Differential Quadrature Method
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Wan-Huan Zhou
2013-01-01
Full Text Available Axisymmetric consolidation in a sand drain foundation is a common problem in foundation engineering. In unsaturated soils, the excess pore-water and pore-air pressures simultaneously change during the consolidation procedure; and the solutions are not easy to obtain. The present paper uses the differential quadrature method (DQM for axisymmetric consolidation of unsaturated soils in a sand drain foundation. The radial seepage of sand drain foundation is considered based on the framework of Fredlund’s one-dimensional consolidation theory in unsaturated soils. With the use of Darcy’s law and Fick’s law, the polar governing equations of excess pore-air and pore-water pressures of axisymmetric consolidation are derived. By using DQM, the two governing equations are transformed into two sets of ordinary differential equations. Then the solutions of excess pore-water and pore-air pressures can be obtained by Rong-Kutta method. The DQM solution can be used to deal with the case of nonuniform initial pore-air and pore-water distributions. Finally, case studies are presented to investigate the behavior of axisymmetric consolidation of unsaturated soils. The convergence analysis and average degree of consolidation, the settlements in radial and vertical direction, and the effects of different initial excess pore pressure distributions are presented, and discussed in this paper.
Free Vibration Analysis of Laminated Composite Beams Using Differential Quadrature Method
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冯丽娟; 钟宏志; 郝照平; 吴德隆
2002-01-01
A higher-order theory for laminated composite beams is used to study the free vibration of laminated composite beams, and the differential quadrature method is employed to obtain the numerical solution of the governing differential equations. Free vibration analysis of beams with rectangular cross-section for various combinations of end conditions is studied. The results show that the differential quadrature method is reliable and accurate compared with other available results.
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R.Mokhtari; A.Samadi Toodar; N.G.Chegini
2011-01-01
@@ We the extend application of the generalized differential quadrature method (GDQM) to solve some coupled nonlinear Schr(o)dinger equations.The cosine-based GDQM is employed and the obtained system of ordinary differential equations is solved via the fourth order Runge-Kutta method.The numerical solutions coincide with the exact solutions in desired machine precision and invariant quantities are conserved sensibly.Some comparisons with the methods applied in the literature are carried out.%We the extend application of the generalized differential quadrature method (GDQM) to solve some coupled nonlinear Schrodinger equations. The cosine-based GDQM is employed and the obtained system of ordinary differential equations is solved via the fourth order Runge-Kutta method. The numerical solutions coincide with the exact solutions in desired machine precision and invariant quantities are conserved sensibly. Some comparisons with the methods applied in the literature are carried out.
Comparison of Spectral and Differential Quadrature Methods for Solving the Burger-Huxley Equation
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Jalal Izadian
2013-06-01
Full Text Available In this paper, the Burger-Huxley equation is solved by two methods: Spectral method and Differential Quadrature Method (DQM. The Chebyshev-Gauss-Lobatto point distribution is utilized in spectral method. The integrity and computational accuracy of the spectral method in solving some test problems are demonstrated through various case studies. The results show that spectral method is more accurate than DQM.
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Thoudam Roshan
2016-10-01
Full Text Available Numerical solutions of the coupled Klein-Gordon-Schrödinger equations is obtained by using differential quadrature methods based on polynomials and quintic B-spline functions for space discretization and Runge-Kutta fourth order for time discretization. Stability of the schemes are studied using matrix stability analysis. The accuracy and efficiency of the methods are shown by conducting some numerical experiments on test problems. The motion of single soliton and interaction of two solitons are simulated by the proposed methods.
Free Vibration Analysis of Sectorial Plates Using the Triangular Differential Quadrature Method
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李欣; 钟宏志; 何玉红
2004-01-01
The triangular differential quadrature method was used to analyze the free vibrations of moderately thick sectorial plates. A triangular serendipity transformation was introduced to map the sectorial domain onto a unit isosceles right triangle. The first six non-dimensional frequencies of the sectorial plates were obtained for various combinations of clamped and simply supported boundary conditions. For sectorial plates with simply supported radial edges, the present results agree well with the available exact solutions and finite element solutions, demonstrating the effectiveness of the method.
Cigeroglu, Ender; Samandari, Hamed
2014-11-01
Nonlinear free vibration analysis of curved double-walled carbon nanotubes (DWNTs) embedded in an elastic medium is studied in this study. Nonlinearities considered are due to large deflection of carbon nanotubes (geometric nonlinearity) and nonlinear interlayer van der Waals forces between inner and outer tubes. The differential quadrature method (DQM) is utilized to discretize the partial differential equations of motion in spatial domain, which resulted in a nonlinear set of algebraic equations of motion. The effect of nonlinearities, different end conditions, initial curvature, and stiffness of the surrounding elastic medium, and vibrational modes on the nonlinear free vibration of DWCNTs is studied. Results show that it is possible to detect different vibration modes occurring at a single vibration frequency when CNTs vibrate in the out-of-phase vibration mode. Moreover, it is observed that boundary conditions have significant effect on the nonlinear natural frequencies of the DWCNT including multiple solutions.
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WangLin; NiQiao; HuangYuying
2003-01-01
This paper proposes a new method for investigating the Hopf bifurcation of a curved pipe conveying fluid with nonlinear spring support. The nonlinear equation of motion is derived by forces equilibrium on microelement of the system under consideration. The spatial coordinate of the system is discretized by the differential quadrature method and then the dynamic equation is solved by the Newton-Raphson method. The numerical solutions show that the inner fluid velocity of the Hopf bifurcation point of the curved pipe varies with different values of the parameter,nonlinear spring stiffness. Based on this, the cycle and divergent motions are both found to exist at specific fluid flow velocities with a given value of the nonlinear spring stiffness. The results are useful for further study of the nonlinear dynamic mechanism of the curved fluid conveying pipe.
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李晶晶; 程昌钧
2004-01-01
Based on the Reddy' s theory of plates with the effect of higher-order shear deformations, the governing equations for bending of orthotropic plates with finite deformations were established. The differential quadrature ( DQ ) method of nonlinear analysis to the problem was presented. New DQ approach, presented by Wang and Bert (DQWB), is extended to handle the multiple boundary conditions of plates. The techniques were also further extended to simplify nonlinear computations. The numerical convergence and comparison of solutions were studied. The results show that the DQ method presented is very reliable and valid. Moreover, the influences of geometric and material parameters as well as the transverse shear deformations on nonlinear bending were investigated.Numerical results show the influence of the shear deformation on the static bending of orthotropic moderately thick plate is significant.
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H. S. Shukla
2014-11-01
Full Text Available In this paper, a numerical solution of two dimensional nonlinear coupled viscous Burger equation is discussed with appropriate initial and boundary conditions using the modified cubic B-spline differential quadrature method. In this method, the weighting coefficients are computed using the modified cubic B-spline as a basis function in the differential quadrature method. Thus, the coupled Burger equation is reduced into a system of ordinary differential equations. An optimal five stage and fourth-order strong stability preserving Runge–Kutta scheme is applied for solving the resulting system of ordinary differential equations. The accuracy of the scheme is illustrated by taking two numerical examples. Computed results are compared with the exact solutions and other results available in literature. Obtained numerical result shows that the described method is efficient and reliable scheme for solving two dimensional coupled viscous Burger equation.
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H. S. Shukla
2015-01-01
Full Text Available In this paper, a modified cubic B-spline differential quadrature method (MCB-DQM is employed for the numerical simulation of two-space dimensional nonlinear sine-Gordon equation with appropriate initial and boundary conditions. The modified cubic B-spline works as a basis function in the differential quadrature method to compute the weighting coefficients. Accordingly, two dimensional sine-Gordon equation is transformed into a system of second order ordinary differential equations (ODEs. The resultant system of ODEs is solved by employing an optimal five stage and fourth-order strong stability preserving Runge–Kutta scheme (SSP-RK54. Numerical simulation is discussed for both damped and undamped cases. Computational results are found to be in good agreement with the exact solution and other numerical results available in the literature.
Density Tracking by Quadrature for Stochastic Differential Equations
Bhat, Harish S.; Madushani, R. W. M. A.
2016-01-01
We develop and analyze a method, density tracking by quadrature (DTQ), to compute the probability density function of the solution of a stochastic differential equation. The derivation of the method begins with the discretization in time of the stochastic differential equation, resulting in a discrete-time Markov chain with continuous state space. At each time step, the DTQ method applies quadrature to solve the Chapman-Kolmogorov equation for this Markov chain. In this paper, we focus on a p...
Jiwari, Ram
2015-08-01
In this article, the author proposed two differential quadrature methods to find the approximate solution of one and two dimensional hyperbolic partial differential equations with Dirichlet and Neumann's boundary conditions. The methods are based on Lagrange interpolation and modified cubic B-splines respectively. The proposed methods reduced the hyperbolic problem into a system of second order ordinary differential equations in time variable. Then, the obtained system is changed into a system of first order ordinary differential equations and finally, SSP-RK3 scheme is used to solve the obtained system. The well known hyperbolic equations such as telegraph, Klein-Gordon, sine-Gordon, Dissipative non-linear wave, and Vander Pol type non-linear wave equations are solved to check the accuracy and efficiency of the proposed methods. The numerical results are shown in L∞ , RMS andL2 errors form.
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Ye Li
Full Text Available The use of quadrature RF magnetic fields has been demonstrated to be an efficient method to reduce transmit power and to increase the signal-to-noise (SNR in magnetic resonance (MR imaging. The goal of this project was to develop a new method using the common-mode and differential-mode (CMDM technique for compact, planar, distributed-element quadrature transmit/receive resonators for MR signal excitation and detection and to investigate its performance for MR imaging, particularly, at ultrahigh magnetic fields. A prototype resonator based on CMDM method implemented by using microstrip transmission line was designed and fabricated for 7T imaging. Both the common mode (CM and the differential mode (DM of the resonator were tuned and matched at 298MHz independently. Numerical electromagnetic simulation was performed to verify the orthogonal B1 field direction of the two modes of the CMDM resonator. Both workbench tests and MR imaging experiments were carried out to evaluate the performance. The intrinsic decoupling between the two modes of the CMDM resonator was demonstrated by the bench test, showing a better than -36 dB transmission coefficient between the two modes at resonance frequency. The MR images acquired by using each mode and the images combined in quadrature showed that the CM and DM of the proposed resonator provided similar B1 coverage and achieved SNR improvement in the entire region of interest. The simulation and experimental results demonstrate that the proposed CMDM method with distributed-element transmission line technique is a feasible and efficient technique for planar quadrature RF coil design at ultrahigh fields, providing intrinsic decoupling between two quadrature channels and high frequency capability. Due to its simple and compact geometry and easy implementation of decoupling methods, the CMDM quadrature resonator can possibly be a good candidate for design blocks in multichannel RF coil arrays.
Li, Ye; Yu, Baiying; Pang, Yong; Vigneron, Daniel B; Zhang, Xiaoliang
2013-01-01
The use of quadrature RF magnetic fields has been demonstrated to be an efficient method to reduce transmit power and to increase the signal-to-noise (SNR) in magnetic resonance (MR) imaging. The goal of this project was to develop a new method using the common-mode and differential-mode (CMDM) technique for compact, planar, distributed-element quadrature transmit/receive resonators for MR signal excitation and detection and to investigate its performance for MR imaging, particularly, at ultrahigh magnetic fields. A prototype resonator based on CMDM method implemented by using microstrip transmission line was designed and fabricated for 7T imaging. Both the common mode (CM) and the differential mode (DM) of the resonator were tuned and matched at 298MHz independently. Numerical electromagnetic simulation was performed to verify the orthogonal B1 field direction of the two modes of the CMDM resonator. Both workbench tests and MR imaging experiments were carried out to evaluate the performance. The intrinsic decoupling between the two modes of the CMDM resonator was demonstrated by the bench test, showing a better than -36 dB transmission coefficient between the two modes at resonance frequency. The MR images acquired by using each mode and the images combined in quadrature showed that the CM and DM of the proposed resonator provided similar B1 coverage and achieved SNR improvement in the entire region of interest. The simulation and experimental results demonstrate that the proposed CMDM method with distributed-element transmission line technique is a feasible and efficient technique for planar quadrature RF coil design at ultrahigh fields, providing intrinsic decoupling between two quadrature channels and high frequency capability. Due to its simple and compact geometry and easy implementation of decoupling methods, the CMDM quadrature resonator can possibly be a good candidate for design blocks in multichannel RF coil arrays.
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AL-SAIF A.S.J.; ZHU Zheng-you
2005-01-01
The problem of two-dimensional steady flow of an incompressible second-order viscoelastic fluid coupled with heat transfer between parallel plates was considered.A viscous dissipation function was included in the energy equation.When the elastic property of the fluid is weaker, the zeroth-order and first-order approximate governing equations were obtained by means of the perturbation method.To understand the behavior of flow near the tube wall, the half-domain was divided into two sub-domains, in which one is a thin layer near the wall called the inner domain and the remainder is called the outer domain.The governing equations in the inner domain and in the outer domain were discretized respectively by using the Differential Quadrature Method (DQM).The matching conditions at the interface between the inner and outer domains were presented.An iterative method for solving these discretized equations was given in this paper.The numerical results obtained agree with existing results.
Malekzadeh, P.; Setoodeh, A. R.; Barmshouri, E.
2008-08-01
An accurate and efficient solution procedure based on the two-dimensional elasticity theory for free vibration of arbitrary laminated thick circular deep arches with some combinations of classical boundary conditions is introduced. In order to accurately represent the variation of strain across the thickness, the layerwise theory is used to approximate the displacement components in the radial direction. Employing Hamilton's principle, the discretized form of the equations of motion and the related boundary conditions in the radial direction are obtained. The resulting governing equations are then discretized using the differential quadrature method (DQM). After performing the convergence studies, new results for laminated arches with different set of boundary conditions are developed. Additionally, different values of the arch parameters such as opening angle, thickness-to-length and orthotropy ratios are considered. In all cases, comparisons with the results obtained using the finite element software 'ABAQUS' and also with those of the first- and higher-order shear deformation theories available in the literature are performed. Close agreements, especially with those of ABAQUS, are achieved.
Triangular Differential Quadrature for Bending Analysis of Reissner Plates with Curved Boundaries
Institute of Scientific and Technical Information of China (English)
华永霞; 钟宏志
2003-01-01
The recently proposed concept of the triangular differential quadrature method (TDQM) is applied to the bending analysis of Reissner plates with various curvilinear geometries subjected to various combinations of boundary conditions. A unit isosceles right triangle is used as the standard triangle for all the derivatives expressed using the triangular differential quadrature rule. Geometric transformations are introduced using basis functions to determine the weighting coefficients for the triangular differential quadrature to map an arbitrary curvilinear triangle into the standard triangle. The triangular differential quadrature method provides good accuracy and rapid convergence relative to other available exact and numerical results.
Golbabai, Ahmad; Nikpour, Ahmad
2016-10-01
In this paper, two-dimensional Schrödinger equations are solved by differential quadrature method. Key point in this method is the determination of the weight coefficients for approximation of spatial derivatives. Multiquadric (MQ) radial basis function is applied as test functions to compute these weight coefficients. Unlike traditional DQ methods, which were originally defined on meshes of node points, the RBFDQ method requires no mesh-connectivity information and allows straightforward implementation in an unstructured nodes. Moreover, the calculation of coefficients using MQ function includes a shape parameter c. A new variable shape parameter is introduced and its effect on the accuracy and stability of the method is studied. We perform an analysis for the dispersion error and different internal parameters of the algorithm are studied in order to examine the behavior of this error. Numerical examples show that MQDQ method can efficiently approximate problems in complexly shaped domains.
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A.S.J.AL-SAIF; 朱正佑
2003-01-01
The traditional differential quadrature method was improved by using the upwind difference scheme for the convectiveterms to solve the coupled two-dimensional incompressible Navier-stokes equations and heat equation. The new method was comparedwith the conventional differential quadrature method in the aspects of convergence and accuracy. The results show that the newmethod is more accurate, and has better convergence than the conventional differential quadrature method for numerically computingthe steady-state solution.
Investigation of turbulent plane mixing layer using generalized differential quadrature
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Basirat Tabrizi, H.; Rezaei Niya, S.M.; Fariborz, S.J. [Amirkabir Univ. of Tech., Mechanical Engineering Dept., Tehran (Iran, Islamic Republic of)]. E-mail: hbasirat@aut.ac.ir; H.Basirat@dal.ca
2004-07-01
There is considerable interest in two-dimensional turbulent mixing layer, to name a few e.g. nature, combustion chamber, premixers of gas turbine combustor and many other technological applications. There features are the presence of large vortical structure, free turbulent characteristics, asymptotic behavior, faster growth rate. Some of the parameters that are known to affect the mixing layer behavior are investigated through the numerical models and experimental analysis during these past decades. A suitable solution for turbulent plane mixing layer requires the use of variable mesh size and an appropriate discretization scheme. The Generalized Differential Quadrature (GDQ) method is utilized to solve the problem. It can be a tool for evaluating the equations obtained for plane mixing layer. The present approach works well by refining mesh size, simplifying the calculation algorithms and less time for calculation anticipated. The numerical simulation is compared with the reported numerical and experimental results of others. (author)
GALERKIN MESHLESS METHODS BASED ON PARTITION OF UNITY QUADRATURE
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ZENG Qing-hong; LU De-tang
2005-01-01
Numerical quadrature is an important ingredient of Galerkin meshless methods. A new numerical quadrature technique, partition of unity quadrature (PUQ),for Galerkin meshless methods was presented. The technique is based on finite covering and partition of unity. There is no need to decompose the physical domain into small cell. It possesses remarkable integration accuracy. Using Element-free Galerkin methods as example, Galerkin meshless methods based on PUQ were studied in detail. Meshing is always not required in the procedure of constitution of approximate function or numerical quadrature, so Galerkin meshless methods based on PUQ are "truly"meshless methods.
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Francesco Tornabene
2017-01-01
Full Text Available The main aim of the present paper is to solve numerically the free vibration problem of sandwich shell structures with variable thickness and made of Functionally Graded Materials (FGMs. Several Higher-order Shear Deformation Theories (HSDTs, defined by a unified formulation, are employed in the study. The FGM structures are characterized by variable mechanical properties due to the through-the-thickness variation of the volume fraction distribution of the two constituents and the arbitrary thickness profile. A four-parameter power law expression is introduced to describe the FGMs, whereas general relations are used to define the thickness variation, which can affect both the principal coordinates of the shell reference domain. A local scheme of the Generalized Differential Quadrature (GDQ method is employed as numerical tool. The natural frequencies are obtained varying the exponent of the volume fraction distributions using higher-order theories based on a unified formulation. The structural models considered are two-dimensional and require less degrees of freedom when compared to the corresponding three-dimensional finite element (FE models, which require a huge number of elements to describe the same geometries accurately. A comparison of the present results with the FE solutions is carried out for the isotropic cases only, whereas the numerical results available in the literature are used to prove the validity as well as accuracy of the current approach in dealing with FGM structures characterized by a variable thickness profile.
Analysis of thin plates by the weak form quadrature element method
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ZHONG HongZhi; YUE ZhiGuang
2012-01-01
The recently proposed weak form quadrature element method (QEM) is applied to flexural and vibrational analysis of thin plates.The integrals involved in the variational description of a thin plate are evaluated by an efficient numerical scheme and the partial derivatives at the integration sampling points are then approximated using differential quadrature analogs.Neither the grid pattern nor the number of nodes is fixed,being adjustable according to convergence need.The C1 continuity conditions characterizing the thin plate theory are discussed and the robustness of the weak form quadrature element for thin plates against shape distortion is examined.Examples are presented and comparisons with analytical solutions and the results of the finite element method are made to demonstrate the convergence and computational efficiency of the weak form quadrature element method.It is shown that the present formulation is applicable to thin plates with varying thickness as well as uniform plates.
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宗智; 李章锐; 董婧
2011-01-01
The localized differential quadrature (LDQ) method is a numerical technique with high accuracy for solving most kinds of nonlinear problems in engineering and can overcome the difficulties of other methods (such as difference method) to numerically evaluate the derivatives of the functions. Its high efficiency and accuracy attract many engineers to apply the method to solve most of the numerical problems in engineering.However, difficulties can still be found in some particular problems. In the following study, the LDQ was applied to solve the Sod shock tube problem. This problem is a very particular kind of problem, which challenges many common numerical methods. Three different examples were given for testing the robustness and accuracy of the LDQ. In the first example, in which common initial conditions and solving methods were given, the numerical oscillations could be found dramatically; in the second example, the initial conditions were adjusted appropriately and the numerical oscillations were less dramatic than that in the first example; in the third example, the momentum equation of the Sod shock tube problem was corrected by adding artificial viscosity, causing the numerical oscillations to nearly disappear in the process of calculation. The numerical results presented demonstrate the detailed difficulties encountered in the calculations, which need to be improved in future work. However, in summary, the localized differential quadrature is shown to be a trustworthy method for solving most of the nonlinear problems in engineering.
Buckling analysis of an orthotropic thin shell of revolution using differential quadrature
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Redekop, D. [Department of Mechanical Engineering, University of Ottawa, 161 Louis Pasteur, Ottawa, ON, K1N 6N5 (Canada)]. E-mail: dredekop@tesla.cc.uottawa.ca
2005-08-01
A method is developed to predict the buckling characteristics of an orthotropic shell of revolution of arbitrary meridian subjected to a normal pressure. The solution is given within the context of the linearized Sanders-Budiansky shell buckling theory and makes use of the differential quadrature method. Numerical results for buckling pressures and mode shapes are given for complete toroidal shells. Both completely free shells and shells with circumferential line restraints are covered. The loadings considered consist either of uniform pressure or circumferential bands of constant pressure. It is demonstrated that the differential quadrature method is numerically stable and converges. For isotropic toroidal shells, good agreement is observed with previously published analytical and finite element results. New results for buckling pressures and mode numbers are given for orthotropic shells and for band loaded shells.
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McGraw, R [Environmental Sciences Department, Atmospheric Sciences Division, Brookhaven National Laboratory, Upton, NY 11973-5000 (United States); Leng, L; Zhu, W [Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY 11794-3600 (United States); Riemer, N [Atmospheric Sciences Department, University of Illinois at Urbana-Champaign, Urbana, IL 61801-3070 (United States); West, M [Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801-3070 (United States)], E-mail: rlm@bnl.gov
2008-07-15
The method of moments (MOM) is a statistically based alternative to sectional and modal methods for aerosol simulation. The MOM is highly efficient as the aerosol distribution is represented by its lower-order moments and only these, not the full distribution itself, are tracked during simulation. Quadrature is introduced to close the moment equations under very general growth laws and to compute aerosol physical and optical properties directly from moments. In this paper the quadrature method of moments (QMOM) is used in a bivariate test tracking of aerosol mixing state. Two aerosol populations, one enriched in soot and the other in sulfate, are allowed to interact through coagulation to form a generally-mixed third particle population. Quadratures of varying complexity (including two candidate schemes for use in climate models) are described and compared with benchmark results obtained by using particle-resolved simulation. Low-order quadratures are found to be highly accurate, and Gauss and Gauss-Radau quadratures appear to give nested lower and upper bounds, respectively, to aerosol mixing rate. These results suggest that the QMOM makes it feasible to represent the generallymixed states of aerosols and track their evolution in climate models.
Flutter analysis of hypersonic airfoil skin by differential quadrature method%基于微分求积法的高超声速机翼蒙皮颤振研究
Institute of Scientific and Technical Information of China (English)
钮耀斌; 王中伟; 毛佳; 张礼学
2012-01-01
机翼蒙皮在高超声速气流中会发生颤振等气动弹性问题,破坏结构.引入微分求积方法,可以有效地分析机翼蒙皮的颤振问题.将机翼蒙皮等效成薄板,基于一阶活塞理论,根据克希霍夫假设及弹性理论建立蒙皮的气动弹性偏微分方程,采用微分求积法将偏微分方程离散为常微分方程,并根据频率重合理论对颤振问题进行求解.得到的颤振速度与有限元方法计算结果进行比较,误差为0 58％,验证了微分求积法在求解颤振偏微分方程时的有效性.分析了蒙皮面积、厚度、纵横比等不同参数对蒙皮颤振速度的影响.结果表明,颤振速度随蒙皮面积的增大而减小,随纵横比、厚度的增大而增大.%Flutter analysis plays a vital role in the design of hypersonic airfoil skin. This research introduces he differential quadrature method into the aeroelastic problem of hypersonic skin. The aeroelastic model was presented based on the elasticity theory, and the hypersonic piston theory was used for the modeling of supersonic aerodynamic loads. The validity of the differential quadrature method was confirmed by comparing the FEM solutions for the natural frequencies and the flutter velocity of the airfoil skin, and the relative error is 0. 58%. A detailed parametric study was carried out to study the influences of the thickness, area and aspect ratio on the hypersonic flutter behavior of airfoil skins. The result shows that, the flutter velocity increases with the aspect ratio and thickness increased, and decreases with the area increased.
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陈继宇; 张涛锋; 孙建安; 石玉仁; 马明义
2011-01-01
采用余弦微分求积法(CDQM)对(1+1)维非线性KdV-Burgers方程进行了数值求解.结果表明,所得数值解与方程的精确解相比具有明显的高精度且稳定性高,相对于其他常用方法,且公式简单,使用方便;计算量小,时间复杂性好.%The cosine expansion based differential quadrature method(CDQM) has been used to obtain numerical solutions to the (1+1)-dimensional nonlinear KdV-Burgers equation. The numerical solutions are compared with the exact solutions, The results show that the numerical solutions are in good agreement with the exact solutions. Compared with some regulate methods, the computation efforts are relatively smaller and the time of computation is shorter, it is also seen that the formulas of the method are very simple and easy to use.
Sparse aerosol models beyond the quadrature method of moments
McGraw, Robert
2013-05-01
This study examines a class of sparse aerosol models derived from linear programming (LP). The widely used quadrature method of moments (QMOM) is shown to fall into this class. Here it is shown how other sparse aerosol models can be constructed, which are not based on moments of the particle size distribution. The new methods enable one to bound atmospheric aerosol physical and optical properties using arbitrary combinations of model parameters and measurements. Rigorous upper and lower bounds, e.g. on the number of aerosol particles that can activate to form cloud droplets, can be obtained this way from measurement constraints that may include total particle number concentration and size distribution moments. The new LP-based methods allow a much wider range of aerosol properties, such as light backscatter or extinction coefficient, which are not easily connected to particle size moments, to also be assimilated into a list of constraints. Finally, it is shown that many of these more general aerosol properties can be tracked directly in an aerosol dynamics simulation, using SAMs, in much the same way that moments are tracked directly in the QMOM.
Agachev, J. R.; Galimyanov, A. F.
2016-11-01
In this paper the method of mechanical quadrature solutions fractional integral equation. Computational scheme quadrature method is based on the quadrature formula of rectangles with equidistant nodes, which is the formula of the highest trigonometric degree of accuracy, using a regularizing parameter. This decision is taken for the approximate trigonometric interpolation polynomial constructed from the values that make up the solution of the quadrature method. The substantiation of the method in Holder spaces.
Directory of Open Access Journals (Sweden)
Xinwei Wang
2016-11-01
Full Text Available Sandwich structures are widely used in practice and thus various engineering theories adopting simplifying assumptions are available. However, most engineering theories of beams, plates and shells cannot recover all stresses accurately through their constitutive equations. Therefore, the soft-core is directly modeled by two-dimensional (2D elasticity theory without any pre-assumption on the displacement field. The top and bottom faces act like the elastic supports on the top and bottom edges of the core. The differential equations of the 2D core are then solved by the harmonic differential quadrature method (HDQM. To circumvent the difficulties in dealing with the locally distributed load by point discrete methods such as the HDQM, a general and rigorous way is proposed to treat the locally distributed load. Detailed formulations are provided. The static behavior of sandwich panels under different locally distributed loads is investigated. For verification, results are compared with data obtained by ABAQUS with very fine meshes. A high degree of accuracy on both displacement and stress has been observed.
Optimization and Experimentation of Dual-Mass MEMS Gyroscope Quadrature Error Correction Methods
Directory of Open Access Journals (Sweden)
Huiliang Cao
2016-01-01
Full Text Available This paper focuses on an optimal quadrature error correction method for the dual-mass MEMS gyroscope, in order to reduce the long term bias drift. It is known that the coupling stiffness and demodulation error are important elements causing bias drift. The coupling stiffness in dual-mass structures is analyzed. The experiment proves that the left and right masses’ quadrature errors are different, and the quadrature correction system should be arranged independently. The process leading to quadrature error is proposed, and the Charge Injecting Correction (CIC, Quadrature Force Correction (QFC and Coupling Stiffness Correction (CSC methods are introduced. The correction objects of these three methods are the quadrature error signal, force and the coupling stiffness, respectively. The three methods are investigated through control theory analysis, model simulation and circuit experiments, and the results support the theoretical analysis. The bias stability results based on CIC, QFC and CSC are 48 °/h, 9.9 °/h and 3.7 °/h, respectively, and this value is 38 °/h before quadrature error correction. The CSC method is proved to be the better method for quadrature correction, and it improves the Angle Random Walking (ARW value, increasing it from 0.66 °/√h to 0.21 °/√h. The CSC system general test results show that it works well across the full temperature range, and the bias stabilities of the six groups’ output data are 3.8 °/h, 3.6 °/h, 3.4 °/h, 3.1 °/h, 3.0 °/h and 4.2 °/h, respectively, which proves the system has excellent repeatability.
Optimization and Experimentation of Dual-Mass MEMS Gyroscope Quadrature Error Correction Methods.
Cao, Huiliang; Li, Hongsheng; Kou, Zhiwei; Shi, Yunbo; Tang, Jun; Ma, Zongmin; Shen, Chong; Liu, Jun
2016-01-07
This paper focuses on an optimal quadrature error correction method for the dual-mass MEMS gyroscope, in order to reduce the long term bias drift. It is known that the coupling stiffness and demodulation error are important elements causing bias drift. The coupling stiffness in dual-mass structures is analyzed. The experiment proves that the left and right masses' quadrature errors are different, and the quadrature correction system should be arranged independently. The process leading to quadrature error is proposed, and the Charge Injecting Correction (CIC), Quadrature Force Correction (QFC) and Coupling Stiffness Correction (CSC) methods are introduced. The correction objects of these three methods are the quadrature error signal, force and the coupling stiffness, respectively. The three methods are investigated through control theory analysis, model simulation and circuit experiments, and the results support the theoretical analysis. The bias stability results based on CIC, QFC and CSC are 48 °/h, 9.9 °/h and 3.7 °/h, respectively, and this value is 38 °/h before quadrature error correction. The CSC method is proved to be the better method for quadrature correction, and it improves the Angle Random Walking (ARW) value, increasing it from 0.66 °/√h to 0.21 °/√h. The CSC system general test results show that it works well across the full temperature range, and the bias stabilities of the six groups' output data are 3.8 °/h, 3.6 °/h, 3.4 °/h, 3.1 °/h, 3.0 °/h and 4.2 °/h, respectively, which proves the system has excellent repeatability.
Friedberg, R; Zhao Wei Qin
2000-01-01
We present a new method to derive low-lying N-dimensional quantum wave functions by quadrature along a single trajectory. The N-dimensional Schroedinger equation is cast into a series of readily integrable first order ordinary differential equations. Our approach resembles the familiar W.K.B. approximation in one dimension, but is designed to explore the classically forbidden region and has a much wider applicability than W.K.B.. The method also provides a perturbation series expansion and the Green's functions of the wave equation in N-dimension, all by quadratures along a single trajectory. A number of examples are given for illustration, including a simple algorithm to evaluate the Stark effect in closed form to any finite order of the electric field.
Directory of Open Access Journals (Sweden)
S. M. Sadatrasoul
2014-01-01
Full Text Available We introduce some generalized quadrature rules to approximate two-dimensional, Henstock integral of fuzzy-number-valued functions. We also give error bounds for mappings of bounded variation in terms of uniform modulus of continuity. Moreover, we propose an iterative procedure based on quadrature formula to solve two-dimensional linear fuzzy Fredholm integral equations of the second kind (2DFFLIE2, and we present the error estimation of the proposed method. Finally, some numerical experiments confirm the theoretical results and illustrate the accuracy of the method.
Goldstein, M; Haussmann, W; Hayman, W; Rogge, L
1992-01-01
This volume consists of the proceedings of the NATO Advanced Research Workshop on Approximation by Solutions of Partial Differential Equations, Quadrature Formulae, and Related Topics, which was held at Hanstholm, Denmark. These proceedings include the main invited talks and contributed papers given during the workshop. The aim of these lectures was to present a selection of results of the latest research in the field. In addition to covering topics in approximation by solutions of partial differential equations and quadrature formulae, this volume is also concerned with related areas, such as Gaussian quadratures, the Pompelu problem, rational approximation to the Fresnel integral, boundary correspondence of univalent harmonic mappings, the application of the Hilbert transform in two dimensional aerodynamics, finely open sets in the limit set of a finitely generated Kleinian group, scattering theory, harmonic and maximal measures for rational functions and the solution of the classical Dirichlet problem. In ...
Chen, Tianheng; Shu, Chi-Wang
2017-09-01
It is well known that semi-discrete high order discontinuous Galerkin (DG) methods satisfy cell entropy inequalities for the square entropy for both scalar conservation laws (Jiang and Shu (1994) [39]) and symmetric hyperbolic systems (Hou and Liu (2007) [36]), in any space dimension and for any triangulations. However, this property holds only for the square entropy and the integrations in the DG methods must be exact. It is significantly more difficult to design DG methods to satisfy entropy inequalities for a non-square convex entropy, and/or when the integration is approximated by a numerical quadrature. In this paper, we develop a unified framework for designing high order DG methods which will satisfy entropy inequalities for any given single convex entropy, through suitable numerical quadrature which is specific to this given entropy. Our framework applies from one-dimensional scalar cases all the way to multi-dimensional systems of conservation laws. For the one-dimensional case, our numerical quadrature is based on the methodology established in Carpenter et al. (2014) [5] and Gassner (2013) [19]. The main ingredients are summation-by-parts (SBP) operators derived from Legendre Gauss-Lobatto quadrature, the entropy conservative flux within elements, and the entropy stable flux at element interfaces. We then generalize the scheme to two-dimensional triangular meshes by constructing SBP operators on triangles based on a special quadrature rule. A local discontinuous Galerkin (LDG) type treatment is also incorporated to achieve the generalization to convection-diffusion equations. Extensive numerical experiments are performed to validate the accuracy and shock capturing efficacy of these entropy stable DG methods.
Numerical quadrature and operator splitting in finite element methods for cardiac electrophysiology.
Krishnamoorthi, Shankarjee; Sarkar, Mainak; Klug, William S
2013-11-01
We study the numerical accuracy and computational efficiency of alternative formulations of the finite element solution procedure for the monodomain equations of cardiac electrophysiology, focusing on the interaction of spatial quadrature implementations with operator splitting and examining both nodal and Gauss quadrature methods and implementations that mix nodal storage of state variables with Gauss quadrature. We evaluate the performance of all possible combinations of 'lumped' approximations of consistent capacitance and mass matrices. Most generally, we find that quadrature schemes and lumped approximations that produce decoupled nodal ionic equations allow for the greatest computational efficiency, this being afforded through the use of asynchronous adaptive time-stepping of the ionic state variable ODEs. We identify two lumped approximation schemes that exhibit superior accuracy, rivaling that of the most expensive variationally consistent implementations. Finally, we illustrate some of the physiological consequences of discretization error in electrophysiological simulation relevant to cardiac arrhythmia and fibrillation. These results suggest caution with the use of semi-automated free-form tetrahedral and hexahedral meshing algorithms available in most commercially available meshing software, which produce nonuniform meshes having a large distribution of element sizes.
Round-robin differential quadrature phase-shift quantum key distribution
Zhou, Chun; Zhang, Ying-Ying; Bao, Wan-Su; Li, Hong-Wei; Wang, Yang; Jiang, Mu-Sheng
2017-02-01
Recently, a round-robin differential phase-shift (RRDPS) protocol was proposed [Nature 509, 475 (2014)], in which the amount of leakage is bounded without monitoring the signal disturbance. Introducing states of the phase-encoded Bennett–Brassard 1984 protocol (PE-BB84) to the RRDPS, this paper presents another quantum key distribution protocol called round-robin differential quadrature phase-shift (RRDQPS) quantum key distribution. Regarding a train of many pulses as a single packet, the sender modulates the phase of each pulse by one of {0, π/2, π, 3π/2}, then the receiver measures each packet with a Mach–Zehnder interferometer having a phase basis of 0 or π/2. The RRDQPS protocol can be implemented with essential similar hardware to the PE-BB84, so it has great compatibility with the current quantum system. Here we analyze the security of the RRDQPS protocol against the intercept-resend attack and the beam-splitting attack. Results show that the proposed protocol inherits the advantages arising from the simplicity of the RRDPS protocol and is more robust against these attacks than the original protocol. Project supported by the National Natural Science Foundation of China (Grant Nos. 61505261 and 11304397) and the National Basic Research Program of China (Grant No. 2013CB338002)
Sidi, A.; Israeli, M.
1986-01-01
High accuracy numerical quadrature methods for integrals of singular periodic functions are proposed. These methods are based on the appropriate Euler-Maclaurin expansions of trapezoidal rule approximations and their extrapolations. They are used to obtain accurate quadrature methods for the solution of singular and weakly singular Fredholm integral equations. Such periodic equations are used in the solution of planar elliptic boundary value problems, elasticity, potential theory, conformal mapping, boundary element methods, free surface flows, etc. The use of the quadrature methods is demonstrated with numerical examples.
A fast integral equation method for solid particles in viscous flow using quadrature by expansion
Klinteberg, Ludvig af
2016-01-01
Boundary integral methods are advantageous when simulating viscous flow around rigid particles, due to the reduction in number of unknowns and straightforward handling of the geometry. In this work we present a fast and accurate framework for simulating spheroids in periodic Stokes flow, which is based on the completed double layer boundary integral formulation. The framework implements a new method known as quadrature by expansion (QBX), which uses surrogate local expansions of the layer potential to evaluate it to very high accuracy both on and off the particle surfaces. This quadrature method is accelerated through a newly developed precomputation scheme. The long range interactions are computed using the spectral Ewald (SE) fast summation method, which after integration with QBX allows the resulting system to be solved in M log M time, where M is the number of particles. This framework is suitable for simulations of large particle systems, and can be used for studying e.g. porous media models.
Quadrature-free spline method for two-dimensional Navier-Stokes equation
Institute of Scientific and Technical Information of China (English)
HU Xian-liang; HAN Dan-fu
2008-01-01
In this paper,a quadrature-free scheme of spline method for two-dimensional Navier-Stokes equation is derived,which can dramatically improve the efficiency of spline method for fluid problems proposed by Lai and Wenston(2004). Additionally,the explicit formulation for boundary condition with up to second order derivatives is presented. The numerical simulations on several benchmark problems show that the scheme is very efficient.
New uncertainties in QCD-QED rescaling factors using quadrature method
Indian Academy of Sciences (India)
Mahadev Patgiri; N Nimai Singh
2005-12-01
In this paper we briefly outline the quadrature method for estimating uncertainties in a function which depends on several variables, and apply it to estimate the numerical uncertainties in QCD-QED rescaling factors. We employ here the one-loop order in QED and three-loop order in QCD evolution equations of the fermion mass renormalisation. Our present calculation is found to be new and also reliable when compared to the earlier values employed by various authors.
New Adaptive Method for IQ Imbalance Compensation of Quadrature Modulators in Predistortion Systems
Zareian, Hassan; Vakili, Vahid Tabataba
2009-12-01
Imperfections in quadrature modulators (QMs), such as inphase and quadrature (IQ) imbalance, can severely impact the performance of power amplifier (PA) linearization systems, in particular in adaptive digital predistorters (PDs). In this paper, we first analyze the effect of IQ imbalance on the performance of a memory orthogonal polynomials predistorter (MOP PD), and then we propose a new adaptive algorithm to estimate and compensate the unknown IQ imbalance in QM. Unlike previous compensation techniques, the proposed method was capable of online IQ imbalance compensation with faster convergence, and no special calibration or training signals were needed. The effectiveness of the proposed IQ imbalance compensator was validated by simulations. The results clearly show the performance of the MOP PD to be enhanced significantly by adding the proposed IQ imbalance compensator.
New Adaptive Method for IQ Imbalance Compensation of Quadrature Modulators in Predistortion Systems
Directory of Open Access Journals (Sweden)
Hassan Zareian
2009-01-01
Full Text Available Imperfections in quadrature modulators (QMs, such as inphase and quadrature (IQ imbalance, can severely impact the performance of power amplifier (PA linearization systems, in particular in adaptive digital predistorters (PDs. In this paper, we first analyze the effect of IQ imbalance on the performance of a memory orthogonal polynomials predistorter (MOP PD, and then we propose a new adaptive algorithm to estimate and compensate the unknown IQ imbalance in QM. Unlike previous compensation techniques, the proposed method was capable of online IQ imbalance compensation with faster convergence, and no special calibration or training signals were needed. The effectiveness of the proposed IQ imbalance compensator was validated by simulations. The results clearly show the performance of the MOP PD to be enhanced significantly by adding the proposed IQ imbalance compensator.
Directory of Open Access Journals (Sweden)
F. P. Santos
2013-09-01
Full Text Available Direct-quadrature generalized moment based methods were analysed in terms of accuracy, computational cost and robustness for the solution of the population balance problems in the [0,∞ and [0,1] domains. The minimum condition number of the coefficient matrix of their linear system of equations was obtained by global optimization. An heuristic scaling rule from the literature was also evaluated. The results indicate that the methods based on Legendre generalized moments are the most robust for the finite domain problems, while the DQMoM formulation that solves for the abscissas and weights using the heuristic scaling rule is the best for the infinite domain problems.
Directory of Open Access Journals (Sweden)
B. Kuldeep
2015-06-01
Full Text Available Fractional calculus has recently been identified as a very important mathematical tool in the field of signal processing. Digital filters designed by fractional derivatives give more accurate frequency response in the prescribed frequency region. Digital filters are most important part of multi-rate filter bank systems. In this paper, an improved method based on fractional derivative constraints is presented for the design of two-channel quadrature mirror filter (QMF bank. The design problem is formulated as minimization of L2 error of filter bank transfer function in passband, stopband interval and at quadrature frequency, and then Lagrange multiplier method with fractional derivative constraints is applied to solve it. The proposed method is then successfully applied for the design of two-channel QMF bank with higher order filter taps. Performance of the QMF bank design is then examined through study of various parameters such as passband error, stopband error, transition band error, peak reconstruction error (PRE, stopband attenuation (As. It is found that, the good design can be obtained with the change of number and value of fractional derivative constraint coefficients.
A quadrature based method of moments for nonlinear Fokker-Planck equations
Otten, Dustin L.; Vedula, Prakash
2011-09-01
Fokker-Planck equations which are nonlinear with respect to their probability densities and occur in many nonequilibrium systems relevant to mean field interaction models, plasmas, fermions and bosons can be challenging to solve numerically. To address some underlying challenges, we propose the application of the direct quadrature based method of moments (DQMOM) for efficient and accurate determination of transient (and stationary) solutions of nonlinear Fokker-Planck equations (NLFPEs). In DQMOM, probability density (or other distribution) functions are represented using a finite collection of Dirac delta functions, characterized by quadrature weights and locations (or abscissas) that are determined based on constraints due to evolution of generalized moments. Three particular examples of nonlinear Fokker-Planck equations considered in this paper include descriptions of: (i) the Shimizu-Yamada model, (ii) the Desai-Zwanzig model (both of which have been developed as models of muscular contraction) and (iii) fermions and bosons. Results based on DQMOM, for the transient and stationary solutions of the nonlinear Fokker-Planck equations, have been found to be in good agreement with other available analytical and numerical approaches. It is also shown that approximate reconstruction of the underlying probability density function from moments obtained from DQMOM can be satisfactorily achieved using a maximum entropy method.
LC Quadrature Generation in Integrated Circuits
DEFF Research Database (Denmark)
Christensen, Kåre Tais
2001-01-01
Today quadrature signals for IQ demodulation are provided through RC polyphase networks, quadrature oscillators or double frequency VCOs. This paper presents a new method for generating quadrature signals in integrated circuits using only inductors and capacitors. This LC quadrature generation me...
Hasegawa, Takemitsu; Hibino, Susumu; Hosoda, Yohsuke; Ninomiya, Ichizo
2007-08-01
An improvement is made to an automatic quadrature due to Ninomiya (J. Inf. Process. 3:162?170, 1980) of adaptive type based on the Newton?Cotes rule by incorporating a doubly-adaptive algorithm due to Favati, Lotti and Romani (ACM Trans. Math. Softw. 17:207?217, 1991; ACM Trans. Math. Softw. 17:218?232, 1991). We compare the present method in performance with some others by using various test problems including Kahaner?s ones (Computation of numerical quadrature formulas. In: Rice, J.R. (ed.) Mathematical Software, 229?259. Academic, Orlando, FL, 1971).
One-step block method for solving Volterra integro-differential equations
Mohamed, Nurul Atikah binti; Majid, Zanariah Abdul
2015-10-01
One-step block method for solving linear Volterra integro-differential equations (VIDEs) is presented in this paper. In VIDEs, the unknown function appears in the form of derivative and under the integral sign. The popular methods for solving VIDEs are the method of quadrature or quadrature method combined with numerical method. The proposed block method will solve the ordinary differential equations (ODEs) part and Newton-Cotes quadrature rule is applied to calculate the integral part of VIDEs. Numerical problems are presented to illustrate the performance of the proposed method.
Spectral Gauss quadrature method with subspace interpolation for Kohn-Sham Density functional theory
Wang, Xin
Algorithms with linear-scaling ( (N)) computational complexity for Kohn-Sham density functional theory (K-S DFT) is crucial for studying molecular systems beyond thousands of atoms. Of the (N) methods that use a polynomial-based approximation of the density matrix, the linear-scaling spectral Gauss quadrature (LSSGQ) method (Suryanarayana et al., JMPS, 2013) has been shown to exhibit the fastest convergence. The LSSGQ method requires a Lanczos procedure at every node in a real-space mesh, leading to a large computational pre-factor. We propose a new interpolation scheme specific to the LSSGQ method that lift the need to perform a Lanczos procedure at every node in the real-mesh. This interpolation will be referred to as subspace interpolation. The key idea behind subspace interpolation is that there is a large overlap in the Krylov-subspaces produced by the Lanczos procedures of nodes that are close in real-space. The subspace interpolation scheme takes advantage of the block-Lanczos procedure to group the Krylov-subspaces from a few representative nodes to approximate the density matrix over a large collection of nodes. Subspace interpolation outperforms cubic-spline interpolation by several orders of magnitude.
Refinements of some new efficient quadrature rules
Qayyum, A.; Shoaib, M.; Faye, I.; Kashif, A. R.
2016-11-01
In the field of Engineering and Applied Mathematical Sciences, minimizing approximation error is very important task and therefore quadrature rules are investigated regularly. In this paper, using some standard results of theoretical inequalities, e.g. Ostrowski type inequality, some new efficient quadrature rules are introduced for n-times differentiable mappings. These quadrature rules are expected to give better results comparing to the conventional quadrature rules.
Chebfun and numerical quadrature
Hale, Nicholas
2012-07-24
Chebfun is a Matlab-based software system that overloads Matlab\\'s discrete operations for vectors and matrices to analogous continuous operations for functions and operators. We begin by describing Chebfun\\'s fast capabilities for Clenshaw-Curtis and also Gauss-Legendre, -Jacobi, -Hermite, and -Laguerre quadrature, based on algorithms of Waldvogel and Glaser, Liu and Rokhlin. Then we consider how such methods can be applied to quadrature problems including 2D integrals over rectangles, fractional derivatives and integrals, functions defined on unbounded intervals, and the fast computation of weights for barycentric interpolation. © 2012 Science China Press and Springer-Verlag Berlin Heidelberg.
Large eddy simulations of coal jet flame ignition using the direct quadrature method of moments
Pedel, Julien
The Direct Quadrature Method of Moments (DQMOM) was implemented in the Large Eddy Simulation (LES) tool ARCHES to model coal particles. LES coupled with DQMOM was first applied to nonreacting particle-laden turbulent jets. Simulation results were compared to experimental data and accurately modeled a wide range of particle behaviors, such as particle jet waviness, spreading, break up, particle clustering and segregation, in different configurations. Simulations also accurately predicted the mean axial velocity along the centerline for both the gas phase and the solid phase, thus demonstrating the validity of the approach to model particles in turbulent flows. LES was then applied to the prediction of pulverized coal flame ignition. The stability of an oxy-coal flame as a function of changing primary gas composition (CO2 and O2) was first investigated. Flame stability was measured using optical measurements of the flame standoff distance in a 40 kW pilot facility. Large Eddy Simulations (LES) of the facility provided valuable insight into the experimentally observed data and the importance of factors such as heterogeneous reactions, radiation or wall temperature. The effects of three parameters on the flame stand-off distance were studied and simulation predictions were compared to experimental data using the data collaboration method. An additional validation study of the ARCHES LES tool was then performed on an air-fired pulverized coal jet flame ignited by a preheated gas flow. The simulation results were compared qualitatively and quantitatively to experimental observations for different inlet stoichiometric ratios. LES simulations were able to capture the various combustion regimes observed during flame ignition and to accurately model the flame stand-off distance sensitivity to the stoichiometric ratio. Gas temperature and coal burnout predictions were also examined and showed good agreement with experimental data. Overall, this research shows that high
Institute of Scientific and Technical Information of China (English)
高文华
2015-01-01
The total differential quadrature of function of two variables problem was discussed.Analyzed the selection of the path of integration for total differential quadrature of function of two variables through examples.Then total differential quadrature of function of two variables in complex connected domain was explored,the condition for total differential quadrature of function of two variables was generalized.%探讨了高等数学中二元函数全微分的求积问题。按照循序渐进的方式，举例分析二元函数全微分求积时积分路径的选取问题，探究复连通区域内二元函数全微分求积问题，推广了二元函数全微分求积题目的条件。
Sun, Dan; Garmory, Andrew; Page, Gary J.
2017-02-01
For flows where the particle number density is low and the Stokes number is relatively high, as found when sand or ice is ingested into aircraft gas turbine engines, streams of particles can cross each other's path or bounce from a solid surface without being influenced by inter-particle collisions. The aim of this work is to develop an Eulerian method to simulate these types of flow. To this end, a two-node quadrature-based moment method using 13 moments is proposed. In the proposed algorithm thirteen moments of particle velocity, including cross-moments of second order, are used to determine the weights and abscissas of the two nodes and to set up the association between the velocity components in each node. Previous Quadrature Method of Moments (QMOM) algorithms either use more than two nodes, leading to increased computational expense, or are shown here to give incorrect results under some circumstances. This method gives the computational efficiency advantages of only needing two particle phase velocity fields whilst ensuring that a correct combination of weights and abscissas is returned for any arbitrary combination of particle trajectories without the need for any further assumptions. Particle crossing and wall bouncing with arbitrary combinations of angles are demonstrated using the method in a two-dimensional scheme. The ability of the scheme to include the presence of drag from a carrier phase is also demonstrated, as is bouncing off surfaces with inelastic collisions. The method is also applied to the Taylor-Green vortex flow test case and is found to give results superior to the existing two-node QMOM method and is in good agreement with results from Lagrangian modelling of this case.
Correction for quadrature errors
DEFF Research Database (Denmark)
Netterstrøm, A.; Christensen, Erik Lintz
1994-01-01
In high bandwidth radar systems it is necessary to use quadrature devices to convert the signal to/from baseband. Practical problems make it difficult to implement a perfect quadrature system. Channel imbalance and quadrature phase errors in the transmitter and the receiver result in error signal...
Radial Basis Function Based Quadrature over Smooth Surfaces
2016-03-24
Function Interpolation . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.3 Weight calculations...methods: product Gaussian quadrature and finite element integration. The product Gaussian quadrature uses Gauss-Legendre nodes and quadrature weights ...with Gaussian Radial Basis Functions ,” SIAM J. Sci. Comput., vol. 33, pp. 869–892, 2011. 10. B. Fornberg and J. Zuev, “The Runge Phenomenon and
Wright, Douglas L.; McGraw, Robert; Rosner, Daniel E.
2001-04-15
We extendthe application of moment methods to multivariate suspended particle population problems-those for which size alone is insufficient to specify the state of a particle in the population. Specifically, a bivariate extension of the quadrature method of moments (QMOM) (R. McGraw, Aerosol Sci. Technol. 27, 255 (1997)) is presented for efficiently modeling the dynamics of a population of inorganic nanoparticles undergoing simultaneous coagulation and particle sintering. Continuum regime calculations are presented for the Koch-Friedlander-Tandon-Rosner model, which includes coagulation by Brownian diffusion (evaluated for particle fractal dimensions, D(f), in the range 1.8-3) and simultaneous sintering of the resulting aggregates (P. Tandon and D. E. Rosner, J. Colloid Interface Sci. 213, 273 (1999)). For evaluation purposes, and to demonstrate the computational efficiency of the bivariate QMOM, benchmark calculations are carried out using a high-resolution discrete method to evolve the particle distribution function n(nu, a) for short to intermediate times (where nu and a are particle volume and surface area, respectively). Time evolution of a selected set of 36 low-order mixed moments is obtained by integration of the full bivariate distribution and compared with the corresponding moments obtained directly using two different extensions of the QMOM. With the more extensive treatment, errors of less than 1% are obtained over substantial aerosol evolution, while requiring only a few minutes (rather than days) of CPU time. Longer time QMOM simulations lend support to the earlier finding of a self-preserving limit for the dimensionless joint (nu, a) particle distribution function under simultaneous coagulation and sintering (Tandon and Rosner, 1999; D. E. Rosner and S. Yu, AIChE J., 47 (2001)). We demonstrate that, even in the bivariate case, it is possible to use the QMOM to rapidly model the approach to asymptotic behavior, allowing an immediate assessment of
Goto, Nobuo; Miyazaki, Yasumitsu
2014-06-01
Optical switching of high-bit-rate quadrature-phase-shift-keying (QPSK) pulse trains using collinear acousto-optic (AO) devices is theoretically discussed. Since the collinear AO devices have wavelength selectivity, the switched optical pulse trains suffer from distortion when the bandwidth of the pulse train is comparable to the pass bandwidth of the AO device. As the AO device, a sidelobe-suppressed device with a tapered surface-acoustic-wave (SAW) waveguide and a Butterworth-type filter device with a lossy SAW directional coupler are considered. Phase distortion of optical pulse trains at 40 to 100 Gsymbols/s in QPSK format is numerically analyzed. Bit-error-rate performance with additive Gaussian noise is also evaluated by the Monte Carlo method.
Method of differential-phase/absolute-amplitude QAM
Dimsdle, Jeffrey William
2007-07-17
A method of quadrature amplitude modulation involving encoding phase differentially and amplitude absolutely, allowing for a high data rate and spectral efficiency in data transmission and other communication applications, and allowing for amplitude scaling to facilitate data recovery; amplitude scale tracking to track-out rapid and severe scale variations and facilitate successful demodulation and data retrieval; 2.sup.N power carrier recovery; incoherent demodulation where coherent carrier recovery is not possible or practical due to signal degradation; coherent demodulation; multipath equalization to equalize frequency dependent multipath; and demodulation filtering.
Kropf, Pascal; Shmuel, Amir
2016-07-01
Estimation of current source density (CSD) from the low-frequency part of extracellular electric potential recordings is an unstable linear inverse problem. To make the estimation possible in an experimental setting where recordings are contaminated with noise, it is necessary to stabilize the inversion. Here we present a unified framework for zero- and higher-order singular-value-decomposition (SVD)-based spectral regularization of 1D (linear) CSD estimation from local field potentials. The framework is based on two general approaches commonly employed for solving inverse problems: quadrature and basis function expansion. We first show that both inverse CSD (iCSD) and kernel CSD (kCSD) fall into the category of basis function expansion methods. We then use these general categories to introduce two new estimation methods, quadrature CSD (qCSD), based on discretizing the CSD integral equation with a chosen quadrature rule, and representer CSD (rCSD), an even-determined basis function expansion method that uses the problem's data kernels (representers) as basis functions. To determine the best candidate methods to use in the analysis of experimental data, we compared the different methods on simulations under three regularization schemes (Tikhonov, tSVD, and dSVD), three regularization parameter selection methods (NCP, L-curve, and GCV), and seven different a priori spatial smoothness constraints on the CSD distribution. This resulted in a comparison of 531 estimation schemes. We evaluated the estimation schemes according to their source reconstruction accuracy by testing them using different simulated noise levels, lateral source diameters, and CSD depth profiles. We found that ranking schemes according to the average error over all tested conditions results in a reproducible ranking, where the top schemes are found to perform well in the majority of tested conditions. However, there is no single best estimation scheme that outperforms all others under all tested
Efficient Quadrature Operator Using Dual-Perspectives-Fusion Probabilistic Weights
Directory of Open Access Journals (Sweden)
Ashok Sahai
2009-08-01
Full Text Available A new quadrature formula has been proposed which uses weight functions derived using a probabilistic approach, and a rather-ingenious 'Fusion' of two dual perspectives. Unlike the complicatedly structured quadrature formulae of Gauss,Hermite and others of similar type, the proposed quadrature formula only needs the values of integrand at user-defined equidistant points in the interval of integration. The weights are functions of the impugned variable in the integrand, and are not mere constants. The quadrature formula has been compared empirically with the simple classical method of numerical integration using the well-known "Bernstein Operator". The percentage absolute relative errors for the proposed quadrature formula and that with the "Bernstein Operator" have been computed for certain selected functions and with different number of node points in the interval of integration. It has been observed that the proposed quadrature formula produces significantly better results.
A new explicit method for the numerical solution of parabolic differential equations
Satofuka, N.
1983-01-01
A new method is derived for solving parabolic partial differential equations arising in transient heat conduction or in boundary-layer flows. The method is based on a combination of the modified differential quadrature (MDQ) method with the rational Runge-Kutta time-integration scheme. It is fully explicit, requires no matrix inversion, and is stable for any time-step for the heat equations. Burgers equation and the one- and two-dimensional heat equations are solved to demonstrate the accuracy and efficiency of the proposed algorithm. The present method is found to be very accurate and efficient when results are compared with analytic solutions.
Digital quadrature phase detection
Smith, J.A.; Johnson, J.A.
1992-05-26
A system for detecting the phase of a frequency or phase modulated signal that includes digital quadrature sampling of the frequency or phase modulated signal at two times that are one quarter of a cycle of a reference signal apart, determination of the arctangent of the ratio of a first sampling of the frequency or phase modulated signal to the second sampling of the frequency or phase modulated signal, and a determination of quadrant in which the phase determination is increased by 2[pi] when the quadrant changes from the first quadrant to the fourth quadrant and decreased by 2[pi] when the quadrant changes from the fourth quadrant to the first quadrant whereby the absolute phase of the frequency or phase modulated signal can be determined using an arbitrary reference convention. 6 figs.
Multilevel quadrature of elliptic PDEs with log-normal diffusion
Harbrecht, Helmut
2015-01-07
We apply multilevel quadrature methods for the moment computation of the solution of elliptic PDEs with lognormally distributed diffusion coefficients. The computation of the moments is a difficult task since they appear as high dimensional Bochner integrals over an unbounded domain. Each function evaluation corresponds to a deterministic elliptic boundary value problem which can be solved by finite elements on an appropriate level of refinement. The complexity is thus given by the number of quadrature points times the complexity for a single elliptic PDE solve. The multilevel idea is to reduce this complexity by combining quadrature methods with different accuracies with several spatial discretization levels in a sparse grid like fashion.
Tsalamengas, John L.
2016-11-01
We present Gauss-Jacobi quadrature rules in terms of hypergeometric functions for the discretization of weakly singular, strongly singular, hypersingular, and nearly singular integrals that arise in integral equation formulations of potential problems for domains with sharp edges and corners. The rules are tailored to weight functions with algebraic endpoint singularities of a fairly general form, thus allowing one to easily incorporate a wide class of domains into the analysis. Numerical examples illustrate the accuracy and stability of the proposed algorithms; it is shown that the same level of high accuracy can be achieved for any choice of the external variable. The usefulness of the method is exemplified by application to the solution of a singular integral equation that arises in time-harmonic electromagnetic scattering by either closed or open perfectly conducting cylindrical objects with edges and corners, such as polygon cylinders and bent strips. Some practical aspects concerning the role of nearby singularities in achieving a highly accurate solution of singular integral equations are, also, discussed.
DEFF Research Database (Denmark)
Jalaal, M.; Soleimani, Soheil; Domairry, G.
2011-01-01
In this paper the meshless Local Multi Quadrics-based Differential Quadrature (MQ-DQ) method is applied to obtain the electric field distribution for different applicable irregular geometries. This method is the combination of Differential Quadrature approximation of derivatives and function...... with FEM and this fact that MQ-DQ method is an accurate and flexible method in solution of electrostatic equations....
Armas-Pérez, Julio C; Hernández-Ortiz, Juan P; de Pablo, Juan J
2015-12-28
A theoretically informed Monte Carlo method is proposed for Monte Carlo simulation of liquid crystals on the basis of theoretical representations in terms of coarse-grained free energy functionals. The free energy functional is described in the framework of the Landau-de Gennes formalism. A piecewise finite element discretization is used to approximate the alignment field, thereby providing an excellent geometrical representation of curved interfaces and accurate integration of the free energy. The method is suitable for situations where the free energy functional includes highly non-linear terms, including chirality or high-order deformation modes. The validity of the method is established by comparing the results of Monte Carlo simulations to traditional Ginzburg-Landau minimizations of the free energy using a finite difference scheme, and its usefulness is demonstrated in the context of simulations of chiral liquid crystal droplets with and without nanoparticle inclusions.
Directory of Open Access Journals (Sweden)
Jingjun Zhao
2013-01-01
Full Text Available A finite element method (FEM for multiterm fractional partial differential equations (MT-FPDEs is studied for obtaining a numerical solution effectively. The weak formulation for MT-FPDEs and the existence and uniqueness of the weak solutions are obtained by the well-known Lax-Milgram theorem. The Diethelm fractional backward difference method (DFBDM, based on quadrature for the time discretization, and FEM for the spatial discretization have been applied to MT-FPDEs. The stability and convergence for numerical methods are discussed. The numerical examples are given to match well with the main conclusions.
Twelfth degree spline with application to quadrature.
Mohammed, P O; Hamasalh, F K
2016-01-01
In this paper existence and uniqueness of twelfth degree spline is proved with application to quadrature. This formula is in the class of splines of degree 12 and continuity order [Formula: see text] that matches the derivatives up to order 6 at the knots of a uniform partition. Some mistakes in the literature are pointed out and corrected. Numerical examples are given to illustrate the applicability and efficiency of the new method.
2.5-D/3-D resistivity modelling in anisotropic media using Gaussian quadrature grids
Zhou, Bing; Greenhalgh, Mark; Greenhalgh, S. A.
2009-01-01
We present a new numerical scheme for 2.5-D/3-D direct current resistivity modelling in heterogeneous, anisotropic media. This method, named the `Gaussian quadrature grid' (GQG) method, cooperatively combines the solution of the Variational Principle of the partial differential equation, Gaussian quadrature abscissae and local cardinal functions so that it has the main advantages of the spectral element method. The formulation shows that the GQG method is a modification of the spectral element method but does not employ the constant elements or require the mesh generator to match the Earth's surface. This makes it much easier to deal with geological models having a 2-D/3-D complex topography than using traditional numerical methods. The GQG technique can achieve a similar convergence rate to the spectral element method. We show it transforms the 2.5-D/3-D resistivity modelling problem into a sparse and symmetric linear equation system that can be solved by an iterative or matrix inversion method. Comparison with analytic solutions for homogeneous isotropic and anisotropic models shows that the error depends on the Gaussian quadrature order (abscissa number) and the subdomain size. The higher the order or the smaller the subdomain size that is employed, the more accurate are the results obtained. Several other synthetic examples, both homogeneous and inhomogeneous, incorporating sloping, undulating and severe topography, are presented and found to yield results comparable to finite element solutions involving a dense mesh.
A COMPACT QUADRATURE FEEDING CIRCUIT FOR CIRCULARLY POLARIZED ANTENNA
Institute of Scientific and Technical Information of China (English)
Dong Yuliang; Tian Buning; Tang Song
2002-01-01
A novel compact quadrature feeding circuit for a circularly polarized antenna is described. The equivalent circuit method in microwave network theory is used and the conventional directional coupler is converted to a new quadrature feeding circuit. This feeding circuit has the same characteristics as the conventional directional coupler but its size is only about one fourth of that of the latter. The formulas for designing the feeding circuit are given. The optimized results obtained by using the software ENSEMBLE are also reported.
A Jacobi Dual-Petrov-Galerkin Method for Solving Some Odd-Order Ordinary Differential Equations
Directory of Open Access Journals (Sweden)
E. H. Doha
2011-01-01
Full Text Available A Jacobi dual-Petrov-Galerkin (JDPG method is introduced and used for solving fully integrated reformulations of third- and fifth-order ordinary differential equations (ODEs with constant coefficients. The reformulated equation for the Jth order ODE involves n-fold indefinite integrals for n=1,…,J. Extension of the JDPG for ODEs with polynomial coefficients is treated using the Jacobi-Gauss-Lobatto quadrature. Numerical results with comparisons are given to confirm the reliability of the proposed method for some constant and polynomial coefficients ODEs.
Differential equations methods and applications
Said-Houari, Belkacem
2015-01-01
This book presents a variety of techniques for solving ordinary differential equations analytically and features a wealth of examples. Focusing on the modeling of real-world phenomena, it begins with a basic introduction to differential equations, followed by linear and nonlinear first order equations and a detailed treatment of the second order linear equations. After presenting solution methods for the Laplace transform and power series, it lastly presents systems of equations and offers an introduction to the stability theory. To help readers practice the theory covered, two types of exercises are provided: those that illustrate the general theory, and others designed to expand on the text material. Detailed solutions to all the exercises are included. The book is excellently suited for use as a textbook for an undergraduate class (of all disciplines) in ordinary differential equations. .
Directory of Open Access Journals (Sweden)
Ali H. Bhrawy
2014-01-01
Full Text Available The modified generalized Laguerre-Gauss collocation (MGLC method is applied to obtain an approximate solution of fractional neutral functional-differential equations with proportional delays on the half-line. The proposed technique is based on modified generalized Laguerre polynomials and Gauss quadrature integration of such polynomials. The main advantage of the present method is to reduce the solution of fractional neutral functional-differential equations into a system of algebraic equations. Reasonable numerical results are achieved by choosing few modified generalized Laguerre-Gauss collocation points. Numerical results demonstrate the accuracy, efficiency, and versatility of the proposed method on the half-line.
Functional methods in differential equations
Hokkanen, Veli-Matti
2002-01-01
In recent years, functional methods have become central to the study of theoretical and applied mathematical problems. As demonstrated in this Research Note, functional methods can not only provide more generality, but they can also unify results and techniques and lead to better results than those obtained by classical methods. Presenting entirely original results, the authors use functional methods to explore a broad range of elliptic, parabolic, and hyperbolic boundary value problems and various classes of abstract differential and integral equations. They show that while it is crucial to choose an appropriate functional framework, this approach can lead to mathematical models that better describe concrete physical phenomena. In particular, they reach a concordance between the physical sense and the mathematical sense for the solutions of some special models. Beyond its importance as a survey of the primary techniques used in the area, the results illuminated in this volume will prove valuable in a wealth ...
Comparison of two methods for customer differentiation
A.F. Gabor (Adriana); Y. Guang (Yang); S. Axsäter (Sven)
2014-01-01
textabstractIn response to customer specific time guarantee requirements, service providers can offer differentiated ser- vices. However, conventional customer differentiation methods often lead to high holding costs and may have some practical drawbacks. We compare two customer differentiation poli
AN EXTREMAL APPROACH TO BIRKHOFF QUADRATURE FORMULAS
Institute of Scientific and Technical Information of China (English)
Ying-guang Shi
2001-01-01
As we know, a solution of an extremal problem with Hermite interpolation constraints is a system of nodes of corresponding Gaussian Hermite quadrature formula (the so-called Jacobi approach). But this conclusion is violated for a Birkhoff quadrature formula. In this paper an extremal problem with Birkhoff interpolation constraints is discussed, from which a large class of Birkhoff quadrature formulas may be derived.
Institute of Scientific and Technical Information of China (English)
韩海涛; 张铮; 卢子兴
2010-01-01
基于铁木辛柯(Timoshenko)梁理论,建立了含任意脱层的复合梁模型,并利用微分求积DQ(Differential Quadrature)法,研究了含多处任意脱层层合梁的屈曲问题.该复合梁模型给出的含单脱层层合梁的临界屈曲载荷计算结果与相关文献结果一致.此外,以两端固支,含两个任意长度、任意深度贯穿脱层的层合梁为例,分析了脱层长度、深度以及相对位置对屈曲载荷的影响.为工程结构设计和分析提供了一种简单有效的方法,给出了一些有参考价值的结果.
Fast algorithms for Quadrature by Expansion I: Globally valid expansions
Rachh, Manas; Klöckner, Andreas; O'Neil, Michael
2017-09-01
The use of integral equation methods for the efficient numerical solution of PDE boundary value problems requires two main tools: quadrature rules for the evaluation of layer potential integral operators with singular kernels, and fast algorithms for solving the resulting dense linear systems. Classically, these tools were developed separately. In this work, we present a unified numerical scheme based on coupling Quadrature by Expansion, a recent quadrature method, to a customized Fast Multipole Method (FMM) for the Helmholtz equation in two dimensions. The method allows the evaluation of layer potentials in linear-time complexity, anywhere in space, with a uniform, user-chosen level of accuracy as a black-box computational method. Providing this capability requires geometric and algorithmic considerations beyond the needs of standard FMMs as well as careful consideration of the accuracy of multipole translations. We illustrate the speed and accuracy of our method with various numerical examples.
Length Scales in Bayesian Automatic Adaptive Quadrature
Directory of Open Access Journals (Sweden)
Adam Gh.
2016-01-01
Full Text Available Two conceptual developments in the Bayesian automatic adaptive quadrature approach to the numerical solution of one-dimensional Riemann integrals [Gh. Adam, S. Adam, Springer LNCS 7125, 1–16 (2012] are reported. First, it is shown that the numerical quadrature which avoids the overcomputing and minimizes the hidden floating point loss of precision asks for the consideration of three classes of integration domain lengths endowed with specific quadrature sums: microscopic (trapezoidal rule, mesoscopic (Simpson rule, and macroscopic (quadrature sums of high algebraic degrees of precision. Second, sensitive diagnostic tools for the Bayesian inference on macroscopic ranges, coming from the use of Clenshaw-Curtis quadrature, are derived.
Differential operator multiplication method for fractional differential equations
Tang, Shaoqiang; Ying, Yuping; Lian, Yanping; Lin, Stephen; Yang, Yibo; Wagner, Gregory J.; Liu, Wing Kam
2016-08-01
Fractional derivatives play a very important role in modeling physical phenomena involving long-range correlation effects. However, they raise challenges of computational cost and memory storage requirements when solved using current well developed numerical methods. In this paper, the differential operator multiplication method is proposed to address the issues by considering a reaction-advection-diffusion equation with a fractional derivative in time. The linear fractional differential equation is transformed into an integer order differential equation by the proposed method, which can fundamentally fix the aforementioned issues for select fractional differential equations. In such a transform, special attention should be paid to the initial conditions for the resulting differential equation of higher integer order. Through numerical experiments, we verify the proposed method for both fractional ordinary differential equations and partial differential equations.
Solving systems of fractional differential equations using differential transform method
Erturk, Vedat Suat; Momani, Shaher
2008-05-01
This paper presents approximate analytical solutions for systems of fractional differential equations using the differential transform method. The fractional derivatives are described in the Caputo sense. The application of differential transform method, developed for differential equations of integer order, is extended to derive approximate analytical solutions of systems of fractional differential equations. The solutions of our model equations are calculated in the form of convergent series with easily computable components. Some examples are solved as illustrations, using symbolic computation. The numerical results show that the approach is easy to implement and accurate when applied to systems of fractional differential equations. The method introduces a promising tool for solving many linear and nonlinear fractional differential equations.
Quadrature formulas for Fourier coefficients
Bojanov, Borislav
2009-09-01
We consider quadrature formulas of high degree of precision for the computation of the Fourier coefficients in expansions of functions with respect to a system of orthogonal polynomials. In particular, we show the uniqueness of a multiple node formula for the Fourier-Tchebycheff coefficients given by Micchelli and Sharma and construct new Gaussian formulas for the Fourier coefficients of a function, based on the values of the function and its derivatives. © 2009 Elsevier B.V. All rights reserved.
ADAPTIVE CALIBRATION OF I AND Q MISMATCH IN QUADRATURE RECEIVER
Institute of Scientific and Technical Information of China (English)
Yang Xuexian; Hou Zifeng; Zhang Qunying; Ning Yanqing
2002-01-01
The mismatch of in-phase and quadrature channels in quadrature receiver affects and constrains radar detection performance in coherent radar. It is necessary to keep the in-phase and quadrature branches symmetrical. In this letter, an adaptive method to detect imbalance parameters is derived by means of evaluating channel errors from the received signal sequences.No matter how the bias degree of the gain and phase errors in I/Q channels are, the proposed adaptive scheme can obtain good calibration results. And the required calculations are only a few multiplications and additions. No need of a special test signal, the introduced method is simple to implement and easy to operate.
Quadrature formulas for classes of functions with bounded mixed derivative or difference
Institute of Scientific and Technical Information of China (English)
汪和平
1997-01-01
Quadrature formulas are considered for classes of smooth functions Wpr, Bpr,(?) with bounded mixed derivative or difference. For the classes of functions indicated above, the result that quadrature formulas constructed with the help of number-theoretic methods are optimal (in the sense of order) is proved, and the optimal order of the error estimates is obtained.
Abstract methods in partial differential equations
Carroll, Robert W
2012-01-01
Detailed, self-contained treatment examines modern abstract methods in partial differential equations, especially abstract evolution equations. Suitable for graduate students with some previous exposure to classical partial differential equations. 1969 edition.
Analytical Formulae for Two of A. H. Stroud's Quadrature Rules
Peterson, J W
2009-01-01
Analytical formulae for the points and weights of two fifth-order quadrature rules for C_3, the 3-cube, are given. The rules, originally formulated by A. H. Stroud in 1967, are discussed in greater detail in terms of both the setup of the basic equations and the method of obtaining their solutions analytically. The primary purpose of this paper is to better document what we feel is a particularly practical quadrature rule (e.g. in finite element calculations) and one for which we felt comprehensive information was scarce.
Archimedes Quadrature of the Parabola: A Mechanical View
Oster, Thomas J.
2006-01-01
In his famous quadrature of the parabola, Archimedes found the area of the region bounded by a parabola and a chord. His method was to fill the region with infinitely many triangles each of whose area he could calculate. In his solution, he stated, without proof, three preliminary propositions about parabolas that were known in his time, but are…
Archimedes Quadrature of the Parabola: A Mechanical View
Oster, Thomas J.
2006-01-01
In his famous quadrature of the parabola, Archimedes found the area of the region bounded by a parabola and a chord. His method was to fill the region with infinitely many triangles each of whose area he could calculate. In his solution, he stated, without proof, three preliminary propositions about parabolas that were known in his time, but are…
DDCC-Based Quadrature Oscillator with Grounded Capacitors and Resistors
Directory of Open Access Journals (Sweden)
Montree Kumngern
2009-01-01
Full Text Available A new voltage-mode quadrature oscillator using two differential difference current conveyors (DDCCs, two grounded capacitors, and three grounded resistors is presented. The proposed oscillator provides the following advantages: the oscillation condition and oscillation frequency are orthogonally controlled; the oscillation frequency is controlled through a single grounded resistor; the use of only grounded capacitors and resistors makes the proposed circuit ideal for IC implementation; low passive and active sensitivities. Simulation results verifying the theoretical analysis are also included.
Basiri Parsa, A; Rashidi, M M; Anwar Bég, O; Sadri, S M
2013-09-01
In this paper, the semi-numerical techniques known as the optimal homotopy analysis method (HAM) and Differential Transform Method (DTM) are applied to study the magneto-hemodynamic laminar viscous flow of a conducting physiological fluid in a semi-porous channel under a transverse magnetic field. The two-dimensional momentum conservation partial differential equations are reduced to ordinary form incorporating Lorentizian magnetohydrodynamic body force terms. These ordinary differential equations are solved by the homotopy analysis method, the differential transform method and also a numerical method (fourth-order Runge-Kutta quadrature with a shooting method), under physically realistic boundary conditions. The homotopy analysis method contains the auxiliary parameter ℏ, which provides us with a simple way to adjust and control the convergence region of solution series. The differential transform method (DTM) does not require an auxiliary parameter and is employed to compute an approximation to the solution of the system of nonlinear differential equations governing the problem. The influence of Hartmann number (Ha) and transpiration Reynolds number (mass transfer parameter, Re) on the velocity profiles in the channel are studied in detail. Interesting fluid dynamic characteristics are revealed and addressed. The HAM and DTM solutions are shown to both correlate well with numerical quadrature solutions, testifying to the accuracy of both HAM and DTM in nonlinear magneto-hemodynamics problems. Both these semi-numerical techniques hold excellent potential in modeling nonlinear viscous flows in biological systems.
Numerical methods for ordinary differential equations
Butcher, John C
2008-01-01
In recent years the study of numerical methods for solving ordinary differential equations has seen many new developments. This second edition of the author''s pioneering text is fully revised and updated to acknowledge many of these developments. It includes a complete treatment of linear multistep methods whilst maintaining its unique and comprehensive emphasis on Runge-Kutta methods and general linear methods. Although the specialist topics are taken to an advanced level, the entry point to the volume as a whole is not especially demanding. Early chapters provide a wide-ranging introduction to differential equations and difference equations together with a survey of numerical differential equation methods, based on the fundamental Euler method with more sophisticated methods presented as generalizations of Euler. Features of the book includeIntroductory work on differential and difference equations.A comprehensive introduction to the theory and practice of solving ordinary differential equations numeri...
Power flow control using quadrature boosters
Sadanandan, Sandeep N.
A power system that can be controlled within security constraints would be an advantage to power planners and real-time operators. Controlling flows can lessen reliability issues such as thermal limit violations, power stability problems, and/or voltage stability conditions. Control of flows can also mitigate market issues by reducing congestion on some lines and rerouting power to less loaded lines or onto preferable paths. In the traditional control of power flows, phase shifters are often used. More advanced methods include using Flexible AC Transmission System (FACTS) Controllers. Some examples include Thyristor Controlled Series Capacitors, Synchronous Series Static Compensators, and Unified Power Flow Controllers. Quadrature Boosters (QBs) have similar structures to phase-shifters, but allow for higher voltage magnitude during real power flow control. In comparison with other FACTS controllers QBs are not as complex and not as expensive. The present study proposes to use QBs to control power flows on a power system. With the inclusion of QBs, real power flows can be controlled to desired scheduled values. In this thesis, the linearized power flow equations used for power flow analysis were modified for the control problem. This included modifying the Jacobian matrix, the power error vector, and calculating the voltage injected by the quadrature booster for the scheduled real power flow. Two scenarios were examined using the proposed power flow control method. First, the power flow in a line in a 5-bus system was modified with a QB using the method developed in this thesis. Simulation was carried out using Matlab. Second, the method was applied to a 30-bus system and then to a 118-bus system using several QBs. In all the cases, the calculated values of the QB voltages led to desired power flows in the designated line.
Error Analysis of Quadrature Rules. Classroom Notes
Glaister, P.
2004-01-01
Approaches to the determination of the error in numerical quadrature rules are discussed and compared. This article considers the problem of the determination of errors in numerical quadrature rules, taking Simpson's rule as the principal example. It suggests an approach based on truncation error analysis of numerical schemes for differential…
Automatic quadrature control and measuring system
Hamlet, J. F.
1973-01-01
Quadrature is separated from amplified signal by use of phase detector, with phase shifter providing appropriate reference. Output of phase detector is further amplified and filtered by dc amplifier. Output of dc amplifier provides signal to neutralize quadrature component of transducer signal.
Numerical Quadrature of Periodic Singular Integral Equations
DEFF Research Database (Denmark)
Krenk, Steen
1978-01-01
This paper presents quadrature formulae for the numerical integration of a singular integral equation with Hilbert kernel. The formulae are based on trigonometric interpolation. By integration a quadrature formula for an integral with a logarithmic singularity is obtained. Finally...... it is demonstrated how a singular integral equation with infinite support can be solved by use of the preceding formulae....
Comparison of two methods for customer differentiation
Gabor, Adriana; Guang, Yang; Axsäter, Sven
2014-01-01
textabstractIn response to customer specific time guarantee requirements, service providers can offer differentiated ser- vices. However, conventional customer differentiation methods often lead to high holding costs and may have some practical drawbacks. We compare two customer differentiation policies: stock reservation and pipeline stock priority for high priority customers. We derive exact analytical expressions of the waiting time distri- bution of both types of customers for a stock res...
Quadrature frequency generation for wideband wireless applications
Elbadry, Mohammad
2015-01-01
This book describes design techniques for wideband quadrature LO generation for software defined radio transceivers, with frequencies spanning 4GHz to around 80GHz. The authors discuss several techniques that can be used to reduce the cost and/or power consumption of one of the key components of the RF front-end, the quadrature local oscillator. The discussion includes simple and useful insights into quadrature VCOs, along with numerous examples of practical techniques. · Provides a thorough survey of quadrature LO generation; · Offers an intuitive explanation of the different quadrature VCO architectures, and categorization of these architectures based on the intuitive explanations; · Describes a new technique for simultaneous quadrature LO generation for channelized receivers; · Includes simple and detailed explanation of two new quadrature VCO techniques that improve phase-noise performance of QVCOs, while providing a large tuning rang...
Statistical Methods for Stochastic Differential Equations
Kessler, Mathieu; Sorensen, Michael
2012-01-01
The seventh volume in the SemStat series, Statistical Methods for Stochastic Differential Equations presents current research trends and recent developments in statistical methods for stochastic differential equations. Written to be accessible to both new students and seasoned researchers, each self-contained chapter starts with introductions to the topic at hand and builds gradually towards discussing recent research. The book covers Wiener-driven equations as well as stochastic differential equations with jumps, including continuous-time ARMA processes and COGARCH processes. It presents a sp
Angular quadratures for improved transport computations
Energy Technology Data Exchange (ETDEWEB)
Abu-Shumays, I.K.
1999-07-22
This paper introduces new octant-range, composite-type Gauss and mid-point rule angular quadrature formulas for neutron and photon transport computations. A generalization to octant-range quadratures is also introduced in order to allow for discontinuities at material interfaces for two- and three-dimensional transport problems which can be modeled with 60-degree triangular or hexagonal mesh subdivisions in the x-y plane.
Transform methods for solving partial differential equations
Duffy, Dean G
2004-01-01
Transform methods provide a bridge between the commonly used method of separation of variables and numerical techniques for solving linear partial differential equations. While in some ways similar to separation of variables, transform methods can be effective for a wider class of problems. Even when the inverse of the transform cannot be found analytically, numeric and asymptotic techniques now exist for their inversion, and because the problem retains some of its analytic aspect, one can gain greater physical insight than typically obtained from a purely numerical approach. Transform Methods for Solving Partial Differential Equations, Second Edition illustrates the use of Laplace, Fourier, and Hankel transforms to solve partial differential equations encountered in science and engineering. The author has expanded the second edition to provide a broader perspective on the applicability and use of transform methods and incorporated a number of significant refinements: New in the Second Edition: ·...
Orthogonal functions, discrete variable representation, and generalized gauss quadratures
DEFF Research Database (Denmark)
Schneider, B. I.; Nygaard, Nicolai
2002-01-01
The numerical solution of most problems in theoretical chemistry involve either the use of a basis set expansion (spectral method) or a numerical grid. For many basis sets, there is an intimate connection between the spectral form and numerical quadrature. When this connection exists, the distinc......The numerical solution of most problems in theoretical chemistry involve either the use of a basis set expansion (spectral method) or a numerical grid. For many basis sets, there is an intimate connection between the spectral form and numerical quadrature. When this connection exists...... in the original representation. This has been exploited in bound-state, scattering, and time-dependent problems using the so-called, discrete variable representation (DVR). At the core of this approach is the mathematical three-term recursion relationship satisfied by the classical orthogonal functions...
Spectral/quadrature duality: Picard-Vessiot theory and finite-gap potentials
Brezhnev, Yurii V
2010-01-01
In the framework of differential Galois theory we treat classical spectral problem $\\Psi''-u(x)\\Psi=\\lambda\\Psi$ and its finite-gap potentials as exactly solvable in quadratures by Picard-Vessiot without involving special functions (the ideology goes back to works by J. Drach 1919). From this standpoint we inspect known facts and obtain new ones: an important formula for Psi-function, differential properties of Jacobian theta-functions, and Theta-function extension of Picard-Vessiot fields. We show that duality between spectral and quadrature approaches is realized through the Weierstrass permutation theorem for a logarithmic Abelian integral.
Statistical Quadrature Evolution for Continuous-Variable Quantum Key Distribution
Gyongyosi, Laszlo; Imre, Sandor
2016-05-01
We propose a statistical quadrature evolution (SQE) method for multicarrier continuous-variable quantum key distribution (CVQKD). A multicarrier CVQKD protocol utilizes Gaussian subcarrier quantum continuous variables (CV) for information transmission. The SQE framework provides a minimal error estimate of the quadratures of the CV quantum states from the discrete, measured noisy subcarrier variables. We define a method for the statistical modeling and processing of noisy Gaussian subcarrier quadratures. We introduce the terms statistical secret key rate and statistical private classical information, which quantities are derived purely by the statistical functions of our method. We prove the secret key rate formulas for a multiple access multicarrier CVQKD. The framework can be established in an arbitrary CVQKD protocol and measurement setting, and are implementable by standard low-complexity statistical functions, which is particularly convenient for an experimental CVQKD scenario. This work was partially supported by the GOP-1.1.1-11-2012-0092 project sponsored by the EU and European Structural Fund, by the Hungarian Scientific Research Fund - OTKA K-112125, and by the COST Action MP1006.
Fast and Accurate Computation of Gauss--Legendre and Gauss--Jacobi Quadrature Nodes and Weights
Hale, Nicholas
2013-03-06
An efficient algorithm for the accurate computation of Gauss-Legendre and Gauss-Jacobi quadrature nodes and weights is presented. The algorithm is based on Newton\\'s root-finding method with initial guesses and function evaluations computed via asymptotic formulae. The n-point quadrature rule is computed in O(n) operations to an accuracy of essentially double precision for any n ≥ 100. © 2013 Society for Industrial and Applied Mathematics.
Directory of Open Access Journals (Sweden)
Hamed Faghanpour Ganji
2016-09-01
Full Text Available The present study further examines two recent semi-analytic methods, a reduced order of nonlinear differential transformation method (also called RDTM and differential transformation method along with Pade approximation to discuss Jaulent–Miodek and coupled Whitham–Broer–Kaup equations. The basic ideas of these methods are briefly introduced and performance of the proposed methods for above mentioned equations is evaluated via comparing with exact solution. The results illustrate that the so-called DTM method, unlike RDTM, due to the presence of secular terms (similar to perturbation method, cannot be found practical for nonlinear partial differential equations (particularly in Acoustic and Wave propagation problems even through utilizing Pade approximation; meanwhile, RDTM method, despite its simplicity and rapid convergence, assured a significant accuracy and great agreement, and thus it is fair to say that nonlinear problems together with Acoustic application which cannot be solved via Analytical methods, can be studied with reduced order of nonlinear differential transformation method.
Cui, Junning; He, Zhangqiang; Jiu, Yuanwei; Tan, Jiubin; Sun, Tao
2016-09-01
The demand for minimal cyclic nonlinearity error in laser interferometry is increasing as a result of advanced scientific research projects. Research shows that the quadrature phase error is the main effect that introduces cyclic nonlinearity error, and polarization-mixing cross talk during beam splitting is the main error source that causes the quadrature phase error. In this paper, a new homodyne quadrature laser interferometer configuration based on nonpolarization beam splitting and balanced interference between two circularly polarized laser beams is proposed. Theoretical modeling indicates that the polarization-mixing cross talk is elaborately avoided through nonpolarizing and Wollaston beam splitting, with a minimum number of quadrature phase error sources involved. Experimental results show that the cyclic nonlinearity error of the interferometer is up to 0.6 nm (peak-to-valley value) without any correction and can be further suppressed to 0.2 nm with a simple gain and offset correction method.
Numerical Methods for Partial Differential Equations
Guo, Ben-yu
1987-01-01
These Proceedings of the first Chinese Conference on Numerical Methods for Partial Differential Equations covers topics such as difference methods, finite element methods, spectral methods, splitting methods, parallel algorithm etc., their theoretical foundation and applications to engineering. Numerical methods both for boundary value problems of elliptic equations and for initial-boundary value problems of evolution equations, such as hyperbolic systems and parabolic equations, are involved. The 16 papers of this volume present recent or new unpublished results and provide a good overview of current research being done in this field in China.
Two integrator loop quadrature oscillators: A review
Soliman, Ahmed M.
2012-01-01
A review of the two integrator loop oscillator circuits providing two quadrature sinusoidal output voltages is given. All the circuits considered employ the minimum number of capacitors namely two except one circuit which uses three capacitors. The circuits considered are classified to four different classes. The first class includes floating capacitors and floating resistors and the active building blocks realizing these circuits are the Op Amp or the OTRA. The second class employs grounded capacitors and includes floating resistors and the active building blocks realizing these circuits are the DCVC or the unity gain cells or the CFOA. The third class employs grounded capacitors and grounded resistors and the active building blocks realizing these circuits are the CCII. The fourth class employs grounded capacitors and no resistors and the active building blocks realizing these circuits are the TA. Transformation methods showing the generation of different classes from each other is given in details and this is one of the main objectives of this paper. PMID:25685396
Two integrator loop quadrature oscillators: A review
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Ahmed M. Soliman
2013-01-01
Full Text Available A review of the two integrator loop oscillator circuits providing two quadrature sinusoidal output voltages is given. All the circuits considered employ the minimum number of capacitors namely two except one circuit which uses three capacitors. The circuits considered are classified to four different classes. The first class includes floating capacitors and floating resistors and the active building blocks realizing these circuits are the Op Amp or the OTRA. The second class employs grounded capacitors and includes floating resistors and the active building blocks realizing these circuits are the DCVC or the unity gain cells or the CFOA. The third class employs grounded capacitors and grounded resistors and the active building blocks realizing these circuits are the CCII. The fourth class employs grounded capacitors and no resistors and the active building blocks realizing these circuits are the TA. Transformation methods showing the generation of different classes from each other is given in details and this is one of the main objectives of this paper.
Numerical methods for hyperbolic differential functional problems
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Roman Ciarski
2008-01-01
Full Text Available The paper deals with the initial boundary value problem for quasilinear first order partial differential functional systems. A general class of difference methods for the problem is constructed. Theorems on the error estimate of approximate solutions for difference functional systems are presented. The convergence results are proved by means of consistency and stability arguments. A numerical example is given.
Theory of the quadrature elliptic birdcage coil.
Leifer, M C
1997-11-01
This paper presents the theory of the quadrature birdcage coil wound on an elliptic cylindrical former. A conformal transformation of the ellipse to a circular geometry is used to derive the optimal sampling of the continuous surface current distribution to produce uniform magnetic fields within an elliptic cylinder. The analysis is rigorous for ellipses of any aspect ratio and shows how to produce quadrature operation of the elliptic birdcage with a conventional hybrid combiner. Insight gained from the transformation is also used to analyze field homogeneity, find the optimal RF shield shape, and specify component values to produce the correct current distribution in practice. Measurements and images from a 16-leg elliptic birdcage coil at both low and high frequencies show good quadrature performance, homogeneity, and sensitivity.
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Murat Osmanoglu
2013-01-01
Full Text Available We have considered linear partial differential algebraic equations (LPDAEs of the form , which has at least one singular matrix of . We have first introduced a uniform differential time index and a differential space index. The initial conditions and boundary conditions of the given system cannot be prescribed for all components of the solution vector here. To overcome this, we introduced these indexes. Furthermore, differential transform method has been given to solve LPDAEs. We have applied this method to a test problem, and numerical solution of the problem has been compared with analytical solution.
Adaptive grid methods for partial differential equations
Anderson, D. A.
1983-01-01
A number of techniques for constructing adaptive mesh generators for use in solving partial differential equations are reviewed in this paper. Techniques reviewed include methods based on steady grid generation schemes and those which are explicitly designed to determine grid speeds in a time-dependent or space-marching problem. Results for candidate methods are included and suggestions for areas of future research are suggested.
Summation Paths in Clenshaw-Curtis Quadrature
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Adam S.
2016-01-01
Full Text Available Two topics concerning the use of Clenshaw-Curtis quadrature within the Bayesian automatic adaptive quadrature approach to the numerical solution of Riemann integrals are considered. First, it is found that the efficient floating point computation of the coefficients of the Chebyshev series expansion of the integrand is to be done within a mathematical structure consisting of the union of coefficient families ordered into complete binary trees. Second, the scrutiny of the decay rates of the involved even and odd rank Chebyshev expansion coefficients with the increase of their rank labels enables the definition of Bayesian decision paths for the advancement to the numerical output.
Numerical Quadratures for Hadamard Hypersingular Integrals
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
In this paper, we develop Gaussian quadrature formulas for the Hadamard finite part integrals. In our formulas, the classical orthogonal polynomials such as Legendre and Chebyshev polynomials are used to approximate the density function f(x) so that the Gaussian quadrature formulas have degree n - 1. The error estimates of the formulas are obtained. It is found from the numerical examples that the convergence rate and the accuracy of the approximation results are satisfactory. Moreover, the rate and the accuracy can be improved by choosing appropriate weight functions.
Numerical methods for nonlinear partial differential equations
Bartels, Sören
2015-01-01
The description of many interesting phenomena in science and engineering leads to infinite-dimensional minimization or evolution problems that define nonlinear partial differential equations. While the development and analysis of numerical methods for linear partial differential equations is nearly complete, only few results are available in the case of nonlinear equations. This monograph devises numerical methods for nonlinear model problems arising in the mathematical description of phase transitions, large bending problems, image processing, and inelastic material behavior. For each of these problems the underlying mathematical model is discussed, the essential analytical properties are explained, and the proposed numerical method is rigorously analyzed. The practicality of the algorithms is illustrated by means of short implementations.
Composite Gauss-Legendre Quadrature with Error Control
Prentice, J. S. C.
2011-01-01
We describe composite Gauss-Legendre quadrature for determining definite integrals, including a means of controlling the approximation error. We compare the form and performance of the algorithm with standard Newton-Cotes quadrature. (Contains 1 table.)
Composite Gauss-Legendre Quadrature with Error Control
Prentice, J. S. C.
2011-01-01
We describe composite Gauss-Legendre quadrature for determining definite integrals, including a means of controlling the approximation error. We compare the form and performance of the algorithm with standard Newton-Cotes quadrature. (Contains 1 table.)
ON QUADRATURE FORMULAE FOR SINGULAR INTEGRALS OF ARBITRARY ORDER
Institute of Scientific and Technical Information of China (English)
杜金元
2004-01-01
Some quadrature formulae for the numerical evaluation of singular integrals of arbitrary order are established and both the estimate of remainder and the convergence of each quadrature formula derived here are also given.
Quadrature representation of finite element variational forms
DEFF Research Database (Denmark)
Ølgaard, Kristian Breum; Wells, Garth N.
2012-01-01
This chapter addresses the conventional run-time quadrature approach for the numerical integration of local element tensors associated with finite element variational forms, and in particular automated optimizations that can be performed to reduce the number of floating point operations...
Integrated source of broadband quadrature squeezed light
DEFF Research Database (Denmark)
Hoff, Ulrich Busk; Nielsen, Bo Melholt; Andersen, Ulrik Lund
2015-01-01
An integrated silicon nitride resonator is proposed as an ultracompact source of bright single-mode quadrature squeezed light at 850 nm. Optical properties of the device are investigated and tailored through numerical simulations, with particular attention paid to loss associated with interfacing...
Asymptotic Properties of Unbounded Quadrature Domains in the Plane
Karp, Lavi
2013-01-01
We prove that if $\\Omega$ is a simply connected quadrature domain for a distribution with compact support and the infinity point belongs the boundary, then the boundary has an asymptotic curve that is either a straight line or a parabola or an infinite ray. In other words, unbounded quadrature domains in the plane are perturbations of null quadrature domains.
MULTISCALE DIFFERENTIAL METHOD FOR DIGITAL IMAGE SHARPENING
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Vitaly V. Bezzubik
2014-11-01
Full Text Available We have proposed and tested a novel method for digital image sharpening. The method is based on multi-scale image analysis, calculation of differential responses of image brightness in different spatial scales, and the subsequent calculation of a restoration function, which sharpens the image by simple subtraction of its brightness values from those of the original image. The method features spatial transposition of the restoration function elements, its normalization, and taking into account the sign of the brightness differential response gradient close to the object edges. The calculation algorithm for the proposed method makes use of integer arithmetic that significantly reduces the computation time. The paper shows that for the images containing small amount of the blur due to the residual aberrations of an imaging system, only the first two scales are needed for the calculation of the restoration function. Similar to the blind deconvolution, the method requires no a priori information about the nature and magnitude of the blur kernel, but it is computationally inexpensive and is much easier in practical implementation. The most promising applications of the method are machine vision and surveillance systems based on real-time intelligent pattern recognition and decision making.
Extrapolation methods for dynamic partial differential equations
Turkel, E.
1978-01-01
Several extrapolation procedures are presented for increasing the order of accuracy in time for evolutionary partial differential equations. These formulas are based on finite difference schemes in both the spatial and temporal directions. On practical grounds the methods are restricted to schemes that are fourth order in time and either second, fourth or sixth order in space. For hyperbolic problems the second order in space methods are not useful while the fourth order methods offer no advantage over the Kreiss-Oliger method unless very fine meshes are used. Advantages are first achieved using sixth order methods in space coupled with fourth order accuracy in time. Computational results are presented confirming the analytic discussions.
Automatic quadrature control and measuring system. [using optical coupling circuitry
Hamlet, J. F. (Inventor)
1974-01-01
A quadrature component cancellation and measuring system comprising a detection system for detecting the quadrature component from a primary signal, including reference circuitry to define the phase of the quadrature component for detection is described. A Raysistor optical coupling control device connects an output from the detection system to a circuit driven by a signal based upon the primary signal. Combining circuitry connects the primary signal and the circuit controlled by the Raysistor device to subtract quadrature components. A known current through the optically sensitive element produces a signal defining the magnitude of the quadrature component.
Differential temperature sensor system and method
Savchenkov, Anatoliy A. (Inventor); Yu, Nan (Inventor); Maleki, Lute (Inventor); Iltchenko, Vladimir S. (Inventor); Matsko, Andrey B. (Inventor); Strekalov, Dmitry V. (Inventor)
2010-01-01
A differential temperature sensor system and method of determining a temperature shift of an optical resonator and its surroundings are provided. The differential temperature sensor system includes a light generating device capable of generating a beam having a carrier frequency, a modulator capable of modulating the beam with a sideband frequency, and an optical resonator capable of supporting an ordinary mode and an extraordinary mode. The system includes an ordinary mode-lock setup capable of locking the carrier frequency of the beam to the ordinary mode of the optical resonator and an extraordinary mode-lock setup capable of locking the sideband frequency of the beam to the extraordinary mode of the optical resonator by providing a specific radio frequency to the modulator substantially corresponding to a frequency shift between the ordinary mode and the extraordinary mode of the optical resonator resulting from a temperature change of the optical resonator. A processor precisely calculates the differential temperature based upon the frequency shift between the ordinary mode and extraordinary mode of the optical resonator.
Adaptive finite element methods for differential equations
Bangerth, Wolfgang
2003-01-01
These Lecture Notes discuss concepts of `self-adaptivity' in the numerical solution of differential equations, with emphasis on Galerkin finite element methods. The key issues are a posteriori error estimation and it automatic mesh adaptation. Besides the traditional approach of energy-norm error control, a new duality-based technique, the Dual Weighted Residual method for goal-oriented error estimation, is discussed in detail. This method aims at economical computation of arbitrary quantities of physical interest by properly adapting the computational mesh. This is typically required in the design cycles of technical applications. For example, the drag coefficient of a body immersed in a viscous flow is computed, then it is minimized by varying certain control parameters, and finally the stability of the resulting flow is investigated by solving an eigenvalue problem. `Goal-oriented' adaptivity is designed to achieve these tasks with minimal cost. At the end of each chapter some exercises are posed in order ...
Principles and improvements of quadrature-based QKD
Hu, Wenhao; Shu, Di; Wang, Daqing; Liu, Yu
2010-11-01
An overview of quadrature-based quantum key distribution is provided. Beginning from the comparison between single-photon schema and continuous variable schema, the article focuses on the classical and state-of-art protocols. Protocols' main procedures and security analysis are introduced, which includes the methods under individual attack and collective attack. Then recent development of unconditional security proof is introduced including the optimality of Gaussian attack and de Finetti theorem. Introduction towards discrete modulated schemas' security proof is also made. At last, the article discusses experimental realization of various protocols and the main trend in this field.
Design and Application of Quadrature Compensation Patterns in Bulk Silicon Micro-Gyroscopes
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Yunfang Ni
2014-10-01
Full Text Available This paper focuses on the detailed design issues of a peculiar quadrature reduction method named system stiffness matrix diagonalization, whose key technology is the design and application of quadrature compensation patterns. For bulk silicon micro-gyroscopes, a complete design and application case was presented. The compensation principle was described first. In the mechanical design, four types of basic structure units were presented to obtain the basic compensation function. A novel layout design was proposed to eliminate the additional disturbing static forces and torques. Parameter optimization was carried out to maximize the available compensation capability in a limited layout area. Two types of voltage loading methods were presented. Their influences on the sense mode dynamics were analyzed. The proposed design was applied on a dual-mass silicon micro-gyroscope developed in our laboratory. The theoretical compensation capability of a quadrature equivalent angular rate no more than 412 °/s was designed. In experiments, an actual quadrature equivalent angular rate of 357 °/s was compensated successfully. The actual compensation voltages were a little larger than the theoretical ones. The correctness of the design and the theoretical analyses was verified. They can be commonly used in planar linear vibratory silicon micro-gyroscopes for quadrature compensation purpose.
Partial differential equations with numerical methods
Larsson, Stig
2003-01-01
The book is suitable for advanced undergraduate and beginning graduate students of applied mathematics and engineering. The main theme is the integration of the theory of linear PDEs and the numerical solution of such equations. For each type of PDE, elliptic, parabolic, and hyperbolic, the text contains one chapter on the mathematical theory of the differential equation, followed by one chapter on finite difference methods and one on finite element methods. As preparation, the two-point boundary value problem and the initial-value problem for ODEs are discussed in separate chapters. There is also one chapter on the elliptic eigenvalue problem and eigenfunction expansion. The presentation does not presume a deep knowledge of mathematical and functional analysis. Some background on linear functional analysis and Sobolev spaces, and also on numerical linear algebra, is reviewed in two appendices.
On some quadrature rules with Gregory end corrections
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Bogusław Bożek
2009-01-01
Full Text Available How can one compute the sum of an infinite series \\(s := a_1 + a_2 + \\ldots\\? If the series converges fast, i.e., if the term \\(a_n\\ tends to \\(0\\ fast, then we can use the known bounds on this convergence to estimate the desired sum by a finite sum \\(a_1 + a_2 + \\ldots + a_n\\. However, the series often converges slowly. This is the case, e.g., for the series \\(a_n = n^{-t}\\ that defines the Riemann zeta-function. In such cases, to compute \\(s\\ with a reasonable accuracy, we need unrealistically large values \\(n\\, and thus, a large amount of computation. Usually, the \\(n\\-th term of the series can be obtained by applying a smooth function \\(f(x\\ to the value \\(n\\: \\(a_n = f(n\\. In such situations, we can get more accurate estimates if instead of using the upper bounds on the remainder infinite sum \\(R = f(n + 1 + f(n + 2 + \\ldots\\, we approximate this remainder by the corresponding integral \\(I\\ of \\(f(x\\ (from \\(x = n + 1\\ to infinity, and find good bounds on the difference \\(I - R\\. First, we derive sixth order quadrature formulas for functions whose 6th derivative is either always positive or always negative and then we use these quadrature formulas to get good bounds on \\(I - R\\, and thus good approximations for the sum \\(s\\ of the infinite series. Several examples (including the Riemann zeta-function show the efficiency of this new method. This paper continues the results from [W. Solak, Z. Szydełko, Quadrature rules with Gregory-Laplace end corrections, Journal of Computational and Applied Mathematics 36 (1991, 251–253] and [W. Solak, A remark on power series estimation via boundary corrections with parameter, Opuscula Mathematica 19 (1999, 75–80].
Quadrature effects on the accuracy of flux calculations in realistic atmospheres.
Box, M. A.; Trautmann, T.; Loughlin, P. E.
1993-12-01
The authors have investigated the accuracy of five different quadrature methods - equal steps in θ, equal steps in cos θ, Gaussian, double Gaussian and Gauss-Lobatto - on the accuracy of fluxes in realistic aerosol atmospheres, using the Gauss-Seidel method. In addition, a range of Gaussian quadrature stream numbers from two to 32 were compared. The atmospheric models considered are those recently presented by Lenoble, with the exception that the authors have used Henyey-Greenstein phase functions in place of Mie. The results should be easily reproduceable by any other workers interested in similar realistic atmospheres. A table of Gauss-Lobatto weights and points is provided as an appendix.
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L. Jones Tarcius Doss
2012-01-01
Full Text Available A quadrature-based mixed Petrov-Galerkin finite element method is applied to a fourth-order linear ordinary differential equation. After employing a splitting technique, a cubic spline trial space and a piecewise linear test space are considered in the method. The integrals are then replaced by the Gauss quadrature rule in the formulation itself. Optimal order a priori error estimates are obtained without any restriction on the mesh.
Numerical Methods for Stochastic Partial Differential Equations
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Sharp, D.H.; Habib, S.; Mineev, M.B.
1999-07-08
This is the final report of a Laboratory Directed Research and Development (LDRD) project at the Los Alamos National laboratory (LANL). The objectives of this proposal were (1) the development of methods for understanding and control of spacetime discretization errors in nonlinear stochastic partial differential equations, and (2) the development of new and improved practical numerical methods for the solutions of these equations. The authors have succeeded in establishing two methods for error control: the functional Fokker-Planck equation for calculating the time discretization error and the transfer integral method for calculating the spatial discretization error. In addition they have developed a new second-order stochastic algorithm for multiplicative noise applicable to the case of colored noises, and which requires only a single random sequence generation per time step. All of these results have been verified via high-resolution numerical simulations and have been successfully applied to physical test cases. They have also made substantial progress on a longstanding problem in the dynamics of unstable fluid interfaces in porous media. This work has lead to highly accurate quasi-analytic solutions of idealized versions of this problem. These may be of use in benchmarking numerical solutions of the full stochastic PDEs that govern real-world problems.
Log-Domain Current-mode Quadrature Sinusoidal Oscillator
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P. Prommee
2011-09-01
Full Text Available A log-domain current-mode quadrature sinusoidal oscillator based on lossless integrators is presented. The circuit is a direct realization of a first-order differential equation for obtaining the lossy and lossless integrators. Each of the log-domain lossless integrators is realized by using only NPN transistors and a grounded capacitor for achieving low-power and fast response. The proposed oscillator uses two-lossless integrator loop which can be electronically tuned through bias currents. A validated BJT model which is used in SPICE simulation operated from a single power supply as low as 2.5V. The oscillation frequency is controlled over four decades of frequency. The total harmonic distortions for two-phases QSO (12MHz is obtained around 0.93% which enables fully integrated in telecommunication systems. The proposed circuit is also suitable for high-frequency applications. Nonideality studies are included and PSpice simulation results confirm the theoretical results.
Quadrature phase interferometer for high resolution force spectroscopy
Paolino, Pierdomenico; Bellon, Ludovic
2013-01-01
In this article, we present a deflection measurement setup for Atomic Force Microscopy (AFM). It is based on a quadrature phase differential interferometer: we measure the optical path difference between a laser beam reflecting above the cantilever tip and a reference beam reflecting on the static base of the sensor. A design with very low environmental susceptibility and another allowing calibrated measurements on a wide spectral range are described. Both enable a very high resolution (down to $2.5E-15 m/sqrt{Hz}$), illustrated by a thermal noise measurement on an AFM cantilever. A quick review shows that our precision is equaling or outperforming the best results reported in the literature, but for a much larger deflection range, up to a few microns.
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Hossein Jafari
2016-04-01
Full Text Available The non-differentiable solution of the linear and non-linear partial differential equations on Cantor sets is implemented in this article. The reduced differential transform method is considered in the local fractional operator sense. The four illustrative examples are given to show the efficiency and accuracy features of the presented technique to solve local fractional partial differential equations.
Some Numerical Quadrature Schemes of a Non-conforming Quadrilateral Finite Element
Institute of Scientific and Technical Information of China (English)
Xiao-fei GUAN; Ming-xia LI; Shao-chun CHEN
2012-01-01
Numerical quadrature schemes of a non-conforming finite element method for general second order elliptic problems in two dimensional (2-D) and three dimensional (3-D) space are discussed in this paper.We present and analyze some optimal numerical quadrature schemes. One of the schemes contains only three sampling points,which greatly improves the efficiency of numerical computations.The optimal error estimates are derived by using some traditional approaches and techniques.Lastly,some numerical results are provided to verify our theoretical analysis.
Integrated source of broadband quadrature squeezed light
DEFF Research Database (Denmark)
Hoff, Ulrich Busk; Nielsen, Bo Melholt; Andersen, Ulrik Lund
2015-01-01
An integrated silicon nitride resonator is proposed as an ultracompact source of bright single-mode quadrature squeezed light at 850 nm. Optical properties of the device are investigated and tailored through numerical simulations, with particular attention paid to loss associated with interfacing...... squeezing spectrum for intra-cavity pump self-phase modulation. Subject to standard material loss and detection efficiencies, we find that the device holds promises for generating substantial quantum noise squeezing over a bandwidth exceeding 1 GHz. In the low-propagation loss regime, approximately -6 d...
Introduction to numerical methods for time dependent differential equations
Kreiss, Heinz-Otto
2014-01-01
Introduces both the fundamentals of time dependent differential equations and their numerical solutions Introduction to Numerical Methods for Time Dependent Differential Equations delves into the underlying mathematical theory needed to solve time dependent differential equations numerically. Written as a self-contained introduction, the book is divided into two parts to emphasize both ordinary differential equations (ODEs) and partial differential equations (PDEs). Beginning with ODEs and their approximations, the authors provide a crucial presentation of fundamental notions, such as the t
A Birkhoff-Noether method of solving differential equations
Institute of Scientific and Technical Information of China (English)
Shang Mei; Guo Yong-Xin; Mei Feng-Xiang
2007-01-01
In this paper, a Birkhoff-Noether method of solving ordinary differential equations is presented. The differential equations can be expressed in terms of Birkhoff's equations. The first integrals for differential equations can be found by using the Noether theory for Birkhoffian systems. Two examples are given to illustrate the application of the method.
Multipole-preserving quadratures for discretization of functions
Genovese, Luigi
2015-01-01
Discretizing an analytic function on a uniform real-space grid is often done via a straightforward collocation method. This is ubiquitous in all areas of computational physics and quantum chemistry. An example in Density Functional Theory is given by the local external potential describing the interaction between ions and electrons. Also notable examples are given by the analytic functions defining compensation charges for range-separated electrostatic treatments. The accuracy of the collocation method used is therefore very important for the reliability of subsequent treatments like self-consistent field solutions of the electronic structure problems. When the real-space grid is too coarse, the collocation method introduces numerical artifacts typical of real-space treatments, like the so-called egg-box error, that may spoil the numerical stability of the description. We present in this paper a new quadrature scheme that is able to exactly preserve the multipoles of a given analytic function for a wide range...
17th century arguments for the impossibility of the indefinite and the definite circle quadrature
DEFF Research Database (Denmark)
Lützen, Jesper
2014-01-01
The classical problem of the quadrature (or equivalently the rectification) of the circle enjoyed a renaissance in the second half of the 17th century. The new analytic methods provided the means for the discovery of infinite expressions of and for the first attempts to prove impossibility statem...
An unified framework for the computation of polynomial quadrature weights and errors
Graça, Mário M
2012-01-01
For the class of polynomial quadrature rules we show that conveniently chosen bases allow to compute both the weights and the theoretical error expression of a $n$-point rule via the undetermined coefficients method. As an illustration, the framework is applied to some classical rules such as Newton-Cotes, Adams-Bashforth, Adams-Moulton and Gaussian rules.
Nonlinear analysis of a cross-coupled quadrature harmonic oscillator
DEFF Research Database (Denmark)
Djurhuus, Torsten; Krozer, Viktor; Vidkjær, Jens;
2005-01-01
The dynamic equations governing the cross-coupled quadrature harmonic oscillator are derived assuming quasi-sinusoidal operation. This allows for an investigation of the previously reported tradeoff between close-to-carrier phase noise and quadrature precision. The results explain how nonlinearit...
Quadrature Formula of Singular Integral Based on Rational Interpolation
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
We construct a quadrature formula of the singular integral with the Chebyshev weight of the second kind by using Lagrange interpolation based on the rational system {1/(x-a1),1/(x-a2),...}, and both the remainder and convergence of the quadrature formula established here are discussed. Our results extend some classical ones.
Single-quadrature continuous-variable quantum key distribution
DEFF Research Database (Denmark)
Gehring, Tobias; Jacobsen, Christian Scheffmann; Andersen, Ulrik Lund
2016-01-01
Most continuous-variable quantum key distribution schemes are based on the Gaussian modulation of coherent states followed by continuous quadrature detection using homodyne detectors. In all previous schemes, the Gaussian modulation has been carried out in conjugate quadratures thus requiring two...... commercialization of continuous-variable quantum key distribution, provided that the low noise requirement can be achieved....
Quadrature measurements of a bright squeezed state via sideband swapping
DEFF Research Database (Denmark)
Schneider, J.; Glockl, O.; Leuchs, G.
2009-01-01
The measurement of an arbitrary quadrature of a bright quantum state of light is a commonly requested action in many quantum information protocols, but it is experimentally challenging with previously proposed schemes. We suggest that the quadrature be measured at a specific sideband frequency...
Quadrature rules and distribution of points on manifolds
Brandolini, Luca; Colzani, Leonardo; Gigante, Giacomo; Seri, Raffaello; Travaglini, Giancarlo
2010-01-01
We study the error in quadrature rules on a compact manifold. As in the Koksma-Hlawka inequality, we consider a discrepancy of the sampling points and a generalized variation of the function. In particular, we give sharp quantitative estimates for quadrature rules of functions in Sobolev classes.
Nonlinear Analysis of a Cross-Coupled Quadrature Harmonic Oscillator
DEFF Research Database (Denmark)
Djurhuus, Torsten; Krozer, Viktor; Vidkjær, Jens;
2004-01-01
We derive the dynamic equations governing the cross-coupled quadrature oscillator leading to an expression for the trade-off between signal quadrature and close-in phase noise. The theory shows that nonlinearity in the coupling transconductance results in AM-PM noise close to the carrier, which...
A time-variant analysis of the 1/f^(2) phase noise in CMOS parallel LC-Tank quadrature oscillators
DEFF Research Database (Denmark)
Andreani, Pietro
2006-01-01
This paper presents a study of 1/f2 phase noise in quadrature oscillators built by connecting two differential LC-tank oscillators in a parallel fashion. The analysis clearly demonstrates the necessity of adopting a time-variant theory of phase noise, where a more simplistic, time......-invariant approach fails to explain numerical simulation results even at the qualitative level. Two topologies of 5-GHz parallel quadrature oscillators are considered, and compact but nevertheless highly general, closed-form formulas are derived for the phase noise caused by the losses in the LC...
A Method for Image Decontamination Based on Partial Differential Equation
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Hou Junping
2015-01-01
Full Text Available This paper will introduce the method to apply partial differential equations for the decontamination processing of images. It will establish continuous partial differential mathematical models for image information and use specific solving methods to conduct decontamination processing to images during the process of solving partial differential equations, such as image noise reduction, image denoising and image segmentation. This paper will study the uniqueness of solution for the partial differential equations and the monotonicity that functional constrain has on multipliers by making analysis of the ROF model in the partial differential mathematical model.
Modified Chebyshev Collocation Method for Solving Differential Equations
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M Ziaul Arif
2015-05-01
Full Text Available This paper presents derivation of alternative numerical scheme for solving differential equations, which is modified Chebyshev (Vieta-Lucas Polynomial collocation differentiation matrices. The Scheme of modified Chebyshev (Vieta-Lucas Polynomial collocation method is applied to both Ordinary Differential Equations (ODEs and Partial Differential Equations (PDEs cases. Finally, the performance of the proposed method is compared with finite difference method and the exact solution of the example. It is shown that modified Chebyshev collocation method more effective and accurate than FDM for some example given.
Analytical solution of linear ordinary differential equations by differential transfer matrix method
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Sina Khorasani
2003-08-01
Full Text Available We report a new analytical method for finding the exact solution of homogeneous linear ordinary differential equations with arbitrary order and variable coefficients. The method is based on the definition of jump transfer matrices and their extension into limiting differential form. The approach reduces the $n$th-order differential equation to a system of $n$ linear differential equations with unity order. The full analytical solution is then found by the perturbation technique. The important feature of the presented method is that it deals with the evolution of independent solutions, rather than its derivatives. We prove the validity of method by direct substitution of the solution in the original differential equation. We discuss the general properties of differential transfer matrices and present several analytical examples, showing the applicability of the method.
On averaging methods for partial differential equations
Verhulst, F.
2001-01-01
The analysis of weakly nonlinear partial differential equations both qualitatively and quantitatively is emerging as an exciting eld of investigation In this report we consider specic results related to averaging but we do not aim at completeness The sections and contain important material which
ALGEBRAIC METHODS IN PARTIAL DIFFERENTIAL OPERATORS
Institute of Scientific and Technical Information of China (English)
Djilali Behloul
2005-01-01
In this paper we build a class of partial differential operators L having the following property: if u is a meromorphic function in Cn and Lu is a rational function A/q, with q homogenous, then u is also a rational function.
Methods from Differential Geometry in Polytope Theory
Adiprasito, Karim Alexander
2014-01-01
The purpose of this thesis is to study classical combinatorial objects, such as polytopes, polytopal complexes, and subspace arrangements, using tools that have been developed in combinatorial topology, especially those tools developed in connection with (discrete) differential geometry, geometric group theory and low-dimensional topology.
Serbes, Gorkem; Aydin, Nizamettin
2014-01-01
Quadrature signals are dual-channel signals obtained from the systems employing quadrature demodulation. Embolic Doppler ultrasound signals obtained from stroke-prone patients by using Doppler ultrasound systems are quadrature signals caused by emboli, which are particles bigger than red blood cells within circulatory system. Detection of emboli is an important step in diagnosing stroke. Most widely used parameter in detection of emboli is embolic signal-to-background signal ratio. Therefore, in order to increase this ratio, denoising techniques are employed in detection systems. Discrete wavelet transform has been used for denoising of embolic signals, but it lacks shift invariance property. Instead, dual-tree complex wavelet transform having near-shift invariance property can be used. However, it is computationally expensive as two wavelet trees are required. Recently proposed modified dual-tree complex wavelet transform, which reduces the computational complexity, can also be used. In this study, the denoising performance of this method is extensively evaluated and compared with the others by using simulated and real quadrature signals. The quantitative results demonstrated that the modified dual-tree-complex-wavelet-transform-based denoising outperforms the conventional discrete wavelet transform with the same level of computational complexity and exhibits almost equal performance to the dual-tree complex wavelet transform with almost half computational cost.
Differential Transformation Method for Temperature Distribution in a Radiating Fin
DEFF Research Database (Denmark)
Rahimi, M.; Hosseini, M. J.; Barari, Amin
2011-01-01
Radiating extended surfaces are widely used to enhance heat transfer between a primary surface and the environment. In this paper, the differential transformation method (DTM) is proposed for solving nonlinear differential equation of temperature distribution in a heat radiating fin. The concept...... of differential transformation is briefly introduced, and then we employed it to derive solutions of two nonlinear equations. The results obtained by DTM are compared with those derived from the analytical solution to verify the accuracy of the proposed method....
Hamilton Jacobi method for solving ordinary differential equations
Mei, Feng-Xiang; Wu, Hui-Bin; Zhang, Yong-Fa
2006-08-01
The Hamilton-Jacobi method for solving ordinary differential equations is presented in this paper. A system of ordinary differential equations of first order or second order can be expressed as a Hamilton system under certain conditions. Then the Hamilton-Jacobi method is used in the integration of the Hamilton system and the solution of the original ordinary differential equations can be found. Finally, an example is given to illustrate the application of the result.
Induced polarization of volcanic rocks. 1Surface versus quadrature conductivity
Revil, A.; Breton, M. Le; Niu, Q.; Wallin, E.; Haskins, E.; Thomas, D. M.
2016-11-01
We performed complex conductivity measurements on 28 core samples from the hole drilled for the Humu´ula Groundwater Research Project (Hawai´i Island, HI, USA). The complex conductivity measurements were performed at 4 different pore water conductivities (0.07, 0.5, 1.0 or 2.0, and 10 S m-1 prepared with NaCl) over the frequency range 1 mHz to 45 kHz at 22 ± 1°C. The in-phase conductivity data are plotted against the pore water conductivity to determine, sample by sample, the intrinsic formation factor and the surface conductivity. The intrinsic formation factor is related to porosity by Archie's law with an average value of the cementation exponent m of 2.45, indicating that only a small fraction of the connected pore space controls the transport properties. Both the surface and quadrature conductivities are found to be linearly related to the cation exchange capacity of the material, which was measured with the cobalt hexamine chloride method. Surface and quadrature conductivities are found to be proportional to each other like for sedimentary siliclastic rocks. A Stern layer polarization model is used to explain these experimental results. Despite the fact that the samples contain some magnetite (up to 5% wt.), we were not able to identify the effect of this mineral on the complex conductivity spectra. These results are very encouraging in showing that galvanometric induced polarization measurements can be used in volcanic areas to separate the bulk from the surface conductivity and therefore to define some alteration attributes. Such a goal cannot be achieved with resistivity alone.
Induced polarization of volcanic rocks - 1. Surface versus quadrature conductivity
Revil, A.; Le Breton, M.; Niu, Q.; Wallin, E.; Haskins, E.; Thomas, D. M.
2017-02-01
We performed complex conductivity measurements on 28 core samples from the hole drilled for the Humu'ula Groundwater Research Project (Hawai'i Island, HI, USA). The complex conductivity measurements were performed at 4 different pore water conductivities (0.07, 0.5, 1.0 or 2.0, and 10 S m-1 prepared with NaCl) over the frequency range 1 mHz to 45 kHz at 22 ± 1 °C. The in-phase conductivity data are plotted against the pore water conductivity to determine, sample by sample, the intrinsic formation factor and the surface conductivity. The intrinsic formation factor is related to porosity by Archie's law with an average value of the cementation exponent m of 2.45, indicating that only a small fraction of the connected pore space controls the transport properties. Both the surface and quadrature conductivities are found to be linearly related to the cation exchange capacity of the material, which was measured with the cobalt hexamine chloride method. Surface and quadrature conductivities are found to be proportional to each other like for sedimentary siliclastic rocks. A Stern layer polarization model is used to explain these experimental results. Despite the fact that the samples contain some magnetite (up to 5 per cent wt.), we were not able to identify the effect of this mineral on the complex conductivity spectra. These results are very encouraging in showing that galvanometric induced polarization measurements can be used in volcanic areas to separate the bulk from the surface conductivity and therefore to define some alteration attributes. Such a goal cannot be achieved with resistivity alone.
Auxiliary equation method for solving nonlinear partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Sirendaoreji,; Jiong, Sun
2003-03-31
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.
Field Method for Integrating the First Order Differential Equation
Institute of Scientific and Technical Information of China (English)
JIA Li-qun; ZHENG Shi-wang; ZHANG Yao-yu
2007-01-01
An important modern method in analytical mechanics for finding the integral, which is called the field-method, is used to research the solution of a differential equation of the first order. First, by introducing an intermediate variable, a more complicated differential equation of the first order can be expressed by two simple differential equations of the first order, then the field-method in analytical mechanics is introduced for solving the two differential equations of the first order. The conclusion shows that the field-method in analytical mechanics can be fully used to find the solutions of a differential equation of the first order, thus a new method for finding the solutions of the first order is provided.
Introduction to partial differential equations and Hilbert space methods
Gustafson, Karl E
1997-01-01
Easy-to-use text examines principal method of solving partial differential equations, 1st-order systems, computation methods, and much more. Over 600 exercises, with answers for many. Ideal for a 1-semester or full-year course.
Modern methods in partial differential equations
Schechter, Martin
2013-01-01
Upon its initial 1977 publication, this volume made recent accomplishments in its field available to advanced undergraduates and beginning graduate students of mathematics. Requiring only some familiarity with advanced calculus and rudimentary complex function theory, it covered discoveries of the previous three decades, a particularly fruitful era. Now it remains a permanent, much-cited contribution to the ever-expanding literature on partial differential equations. Author Martin Schechter chose subjects that will motivate students and introduce them to techniques with wide applicability to p
Approximate Method for Solving the Linear Fuzzy Delay Differential Equations
Directory of Open Access Journals (Sweden)
S. Narayanamoorthy
2015-01-01
Full Text Available We propose an algorithm of the approximate method to solve linear fuzzy delay differential equations using Adomian decomposition method. The detailed algorithm of the approach is provided. The approximate solution is compared with the exact solution to confirm the validity and efficiency of the method to handle linear fuzzy delay differential equation. To show this proper features of this proposed method, numerical example is illustrated.
Wavelet operational matrix method for solving the Riccati differential equation
Li, Yuanlu; Sun, Ning; Zheng, Bochao; Wang, Qi; Zhang, Yingchao
2014-03-01
A Haar wavelet operational matrix method (HWOMM) was derived to solve the Riccati differential equations. As a result, the computation of the nonlinear term was simplified by using the Block pulse function to expand the Haar wavelet one. The proposed method can be used to solve not only the classical Riccati differential equations but also the fractional ones. The capability and the simplicity of the proposed method was demonstrated by some examples and comparison with other methods.
Spectral methods for partial differential equations
Hussaini, M. Y.; Streett, C. L.; Zang, T. A.
1984-01-01
Origins of spectral methods, especially their relation to the Method of Weighted Residuals, are surveyed. Basic Fourier, Chebyshev, and Legendre spectral concepts are reviewed, and demonstrated through application to simple model problems. Both collocation and tau methods are considered. These techniques are then applied to a number of difficult, nonlinear problems of hyperbolic, parabolic, elliptic, and mixed type. Fluid-dynamical applications are emphasized.
Hilbert space methods for partial differential equations
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Ralph E. Showalter
1994-09-01
Full Text Available This book is an outgrowth of a course which we have given almost periodically over the last eight years. It is addressed to beginning graduate students of mathematics, engineering, and the physical sciences. Thus, we have attempted to present it while presupposing a minimal background: the reader is assumed to have some prior acquaintance with the concepts of ``linear'' and ``continuous'' and also to believe $L^2$ is complete. An undergraduate mathematics training through Lebesgue integration is an ideal background but we dare not assume it without turning away many of our best students. The formal prerequisite consists of a good advanced calculus course and a motivation to study partial differential equations.
Cui, Junning; He, Zhangqiang; Tan, Jiubin; Sun, Tao
2016-10-03
The deviation of wave plates' optical axes from their intended angles, which may result from either instability or assembly error, is the main cause of quadrature phase error in homodyne quadrature laser interferometers (HQLIs). The quadrature phase error sensitivity to wave plate angle deviations, which is an effective measure of HQLI robustness, is further amplified by beam splitter imperfections. In this paper, a new HQLI design involving non-polarization beam splitting is presented, and a method of making this HQLI robust by yawing the wave plates in the measurement and reference arms is proposed. The theoretical analysis results indicate that ultra-low quadrature phase error sensitivities to wave plate angle deviations can be realized and that non-polarizing beam splitter imperfections can be adequately compensated for. The experimental results demonstrate that the proposed method can reduce the quadrature phase error sensitivity by more than 1 order of magnitude, from a theoretical value of 1.4°/1° to 0.05°/1°.
Farshid Mirzaee; Mohammad Komak Yari
2016-01-01
In this paper, we introduce three-dimensional fuzzy differential transform method and we utilize it to solve fuzzy partial differential equations. This technique is a successful method because of reducing such problems to solve a system of algebraic equations; so, the problem can be solved directly. A considerable advantage of this method is to obtain the analytical solutions if the equation has an exact solution that is a polynomial function. Numerical examples are included to demonstrate th...
Researching on quadrature conversion structures for an UWB demonstrative receiver
Institute of Scientific and Technical Information of China (English)
Zhu Canyan; Wang Yiming; Yang Huibao; Liu Jiasheng
2006-01-01
Some structures of digital quadrature AD conversion for software-defined radio (SDR) systems are studied. Their performances and affections on the SDR systems are also analyzed. Two generalized quadrature AD schemes are proposed. In one of them, the AD sampling speed can be reduced by 2 times; and in the other both the output data rate of every channel and AD sampling speed can be lowered by paralleling the digital quadrature filtering structure. These structures can be also easily implemented into modules, and the polyphase filters can be flexibly realized by VHDL language based one chip of FPGA. To assess the proposed schemes, their applications to a particular ultra wideband (UWB) demonstrative receiver system are introduced. Some experimental results are also given. It is shown that the generalized quadrature AD structures are reliable and feasible for its module design, and performances are improved obviously for its better performance to price ratio.
Differential Thermostimulated Discharge Current Method for Studying Electrets
Mekishev, G. A.; Yovcheva, T. A.; Viraneva, A. P.; Gencheva, E. A.
2010-01-01
The thermostimulated discharge current method (TSDC) is widely used for the study of charge storage mechanisms in electrets. A new discharged technique, called differential, which consists in discharging a charged sample through an otherwise identical but uncharged one, has been proposed by J.-P. Reboul and A. Toureille. In the present paper a new version of the differential thermostimulated discharge current method is advanced. In contrast to the differential technique described earlier, the measuring cell allows to realize typical differential technique. In this case the measuring system records the difference of the thermostimulated currents of two samples which have been preliminary charged (or thermally treated) under the same or different conditions. Samples of 0.85 mm thick polymethylmethacrylate are used to demonstrate an operation of the developed differential TSDC method.
Polyphase Structure Based Eigen Design of Two-Channel Quadrature Mirror Filter Bank
Directory of Open Access Journals (Sweden)
S. K. Agrawal
2014-09-01
Full Text Available This paper presents a method for the design of two-channel quadrature mirror filter (QMF banks with linear phase in frequency domain. Low-pass prototype filter of the QMF bank is implemented using polyphase decomposition. Prototype filter coefficients are optimized to minimize an objective function using eigenvalue-eigenvector approach without matrix inversion. The objective function is formulated as a weighted sum of four terms, pass-band error and stop-band residual energy of low-pass analysis filter, the square error of the overall transfer function at the quadrature frequency and amplitude distortion of the filter bank. The simulation results clearly show that the proposed method requires less computational efforts in comparison to the other state-of-art existing design methods.
Electronically Tunable Quadrature Oscillator Using Translinear Conveyors and Grounded Capacitors
Sudhanshu Maheshwari
2003-01-01
A new electronically tunable current-mode sinusoidal oscillator with three quadrature outputs is presented. The proposed circuit employs three translinear conveyors and two grounded capacitors to realize three quadrature outputs with independent frequency control. The circuit requires no resistors and the frequency of the oscillator can be varied over a wide range by external current control. RSPICE simulation results using the bipolar implementation of translinear conveyors are given to s...
Exact and Approximate Quadratures for Curvature Tensor Estimation
Langer, Torsten; Belyaev, Alexander; Seidel, Hans-Peter; Greiner, Günther; Hornegger, Joachim; Niemann, Heinrich; Stamminger, Marc
2005-01-01
Accurate estimations of geometric properties of a surface from its discrete approximation are important for many computer graphics and geometric modeling applications. In this paper, we derive exact quadrature formulae for mean curvature, Gaussian curvature, and the Taubin integral representation of the curvature tensor. The exact quadratures are then used to obtain reliable estimates of the curvature tensor of a smooth surface approximated by a dense triangle me...
Noncritical quadrature squeezing through spontaneous polarization symmetry breaking
Garcia-Ferrer, Ferran V; de Valcárcel, Germán J; Roldán, Eugenio
2010-01-01
We discuss the possibility of generating noncritical quadrature squeezing by spontaneous polarization symmetry breaking. We consider first type-II frequency-degenerate optical parametric oscillators, but discard them for a number of reasons. Then we propose a four-wave mixing cavity in which the polarization of the output mode is always linear but has an arbitrary orientation. We show that in such a cavity complete noise suppression in a quadrature of the output field occurs, irrespective of the parameter values.
Solving Generalised Riccati Differential Equations by Homotopy Analysis Method
Directory of Open Access Journals (Sweden)
J. Vahidi
2013-07-01
Full Text Available In this paper, the quadratic Riccati differential equation is solved by means of an analytic technique, namely the homotopy analysis method (HAM. Comparisons are made between Adomian’s decomposition method (ADM and the exact solution and the homotopy analysis method. The results reveal that the proposed method is very effective and simple.
Quadrature mixture LO suppression via DSW DAC noise dither
Dubbert, Dale F.; Dudley, Peter A.
2007-08-21
A Quadrature Error Corrected Digital Waveform Synthesizer (QECDWS) employs frequency dependent phase error corrections to, in effect, pre-distort the phase characteristic of the chirp to compensate for the frequency dependent phase nonlinearity of the RF and microwave subsystem. In addition, the QECDWS can employ frequency dependent correction vectors to the quadrature amplitude and phase of the synthesized output. The quadrature corrections cancel the radars' quadrature upconverter (mixer) errors to null the unwanted spectral image. A result is the direct generation of an RF waveform, which has a theoretical chirp bandwidth equal to the QECDWS clock frequency (1 to 1.2 GHz) with the high Spurious Free Dynamic Range (SFDR) necessary for high dynamic range radar systems such as SAR. To correct for the problematic upconverter local oscillator (LO) leakage, precision DC offsets can be applied over the chirped pulse using a pseudo-random noise dither. The present dither technique can effectively produce a quadrature DC bias which has the precision required to adequately suppress the LO leakage. A calibration technique can be employed to calculate both the quadrature correction vectors and the LO-nulling DC offsets using the radar built-in test capability.
Directory of Open Access Journals (Sweden)
M. Raghunadh Acharya
2009-12-01
Full Text Available A new quadrature formula has been proposed which uses modified weight functions derived from those of ‘Bernstein Polynomial’ using a ‘Two-Phase Modification’ therein. The quadrature formula has been compared empirically with the simple method of numerical integration using the well-known “Bernstein Operator”. The percentage absolute relative errors for the proposed quadrature formula and that with the “Bernstein Operator” have been computed for certain selected functions, with different number of usual equidistant node-points in the interval of integration~ [0, 1]. It has been observed that both of the proposed modified quadrature formulae, respectively after the ‘Phase-I’ and after the ‘Phases-I & II’ of these modifications, produce significantly better results than that using, simply, the “Bernstein Operator”. Inasmuch as the proposed “Two-Phase Improvement” is available iteratively again-and-again at the end of the current iteration, the proposed improvement algorithm, which is ‘Computerizable’, is an “Iterative-Algorithm”, leading to more-and-more efficient “Quadrature-Operator”, till we are pleased!
Directory of Open Access Journals (Sweden)
F. Z. Geng
2012-01-01
Full Text Available We introduce a new method for solving Riccati differential equations, which is based on reproducing kernel method and quasilinearization technique. The quasilinearization technique is used to reduce the Riccati differential equation to a sequence of linear problems. The resulting sets of differential equations are treated by using reproducing kernel method. The solutions of Riccati differential equations obtained using many existing methods give good approximations only in the neighborhood of the initial position. However, the solutions obtained using the present method give good approximations in a larger interval, rather than a local vicinity of the initial position. Numerical results compared with other methods show that the method is simple and effective.
Entropy methods for diffusive partial differential equations
Jüngel, Ansgar
2016-01-01
This book presents a range of entropy methods for diffusive PDEs devised by many researchers in the course of the past few decades, which allow us to understand the qualitative behavior of solutions to diffusive equations (and Markov diffusion processes). Applications include the large-time asymptotics of solutions, the derivation of convex Sobolev inequalities, the existence and uniqueness of weak solutions, and the analysis of discrete and geometric structures of the PDEs. The purpose of the book is to provide readers an introduction to selected entropy methods that can be found in the research literature. In order to highlight the core concepts, the results are not stated in the widest generality and most of the arguments are only formal (in the sense that the functional setting is not specified or sufficient regularity is supposed). The text is also suitable for advanced master and PhD students and could serve as a textbook for special courses and seminars.
Energy Technology Data Exchange (ETDEWEB)
Pozar, Tomaz; Gregorcic, Peter; Mozina, Janez
2011-03-20
We present the influence of alignment and the real properties of optical components on the performance of a two-detector homodyne displacement-measuring quadrature laser interferometer. An experimental method, based on the optimization of visibility and sensitivity, was established and theoretically described to assess the performance and stability of the interferometer. We show that the optimal performance of such interferometers is achieved with the iterative alignment procedure described.
A parallel method for numerical solution of delay differential equations
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
A parallel diagonally-iterated Runge-Kutta (PDIRK) method is constructed to solve stiff initial value problems for delay differential equations. The order and stability of this PDIRK method has been analyzed, and the iteration parameters of the method are tuned in such a way that fast convergence to the value of corrector is achieved.
Directory of Open Access Journals (Sweden)
Farshid Mirzaee
2016-06-01
Full Text Available In this paper, we introduce three-dimensional fuzzy differential transform method and we utilize it to solve fuzzy partial differential equations. This technique is a successful method because of reducing such problems to solve a system of algebraic equations; so, the problem can be solved directly. A considerable advantage of this method is to obtain the analytical solutions if the equation has an exact solution that is a polynomial function. Numerical examples are included to demonstrate the validity and applicability of the method.
Energy Technology Data Exchange (ETDEWEB)
Ravi Kanth, A.S.V. [Applied Mathematics Division, School of Science and Humanities, V.I.T. University, Vellore-632 014, Tamil Nadu (India)], E-mail: asvravikanth@yahoo.com; Aruna, K. [Applied Mathematics Division, School of Science and Humanities, V.I.T. University, Vellore-632 014, Tamil Nadu (India)
2008-11-17
In this Letter, we propose a reliable algorithm to develop exact and approximate solutions for the linear and non-linear systems of partial differential 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 non-linear 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.
A Parameter Robust Method for Singularly Perturbed Delay Differential Equations
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Erdogan Fevzi
2010-01-01
Full Text Available Uniform finite difference methods are constructed via nonstandard finite difference methods for the numerical solution of singularly perturbed quasilinear initial value problem for delay differential equations. A numerical method is constructed for this problem which involves the appropriate Bakhvalov meshes on each time subinterval. The method is shown to be uniformly convergent with respect to the perturbation parameter. A numerical example is solved using the presented method, and the computed result is compared with exact solution of the problem.
Reproducing Kernel Method for Fractional Riccati Differential Equations
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X. Y. Li
2014-01-01
Full Text Available This paper is devoted to a new numerical method for fractional Riccati differential equations. The method combines the reproducing kernel method and the quasilinearization technique. Its main advantage is that it can produce good approximations in a larger interval, rather than a local vicinity of the initial position. Numerical results are compared with some existing methods to show the accuracy and effectiveness of the present method.
Directory of Open Access Journals (Sweden)
L. O. Fichte
2006-01-01
Full Text Available Boundary Integral Equation formulations can be used to describe electromagnetic shielding problems. Yet, this approach frequently leads to integrals which contain a singularity and an oscillating part. Those integrals are difficult to handle when integrated naivly using standard integration techniques, and in some cases even a very high number of integration nodes will not lead to precise results. We present a method for the numerical quadrature of an integral with a logarithmic singularity and a cosine oscillator: a modified Filon-Lobatto quadrature for the oscillating parts and an integral transformation based on the error function for the singularity. Since this integral can be solved analytically, we are in a position to verify the results of our investigations, with a focus on precision and computation time.
Information entropy of Gegenbauer polynomials and Gaussian quadrature
Sánchez-Ruiz, J
2003-01-01
In a recent paper (Buyarov V S, Lopez-Artes P, Martinez-Finkelshtein A and Van Assche W 2000 J. Phys. A: Math. Gen. 33 6549-60), an efficient method was provided for evaluating in closed form the information entropy of the Gegenbauer polynomials C sup ( suplambda sup ) sub n (x) in the case when lambda = l element of N. For given values of n and l, this method requires the computation by means of recurrence relations of two auxiliary polynomials, P(x) and H(x), of degrees 2l - 2 and 2l - 4, respectively. Here it is shown that P(x) is related to the coefficients of the Gaussian quadrature formula for the Gegenbauer weights w sub l (x) = (1 - x sup 2) sup l sup - sup 1 sup / sup 2 , and this fact is used to obtain the explicit expression of P(x). From this result, an explicit formula is also given for the polynomial S(x) = lim sub n sub-> subinfinity P(1 - x/(2n sup 2)), which is relevant to the study of the asymptotic (n -> infinity with l fixed) behaviour of the entropy.
An introduction to neural network methods for differential equations
Yadav, Neha; Kumar, Manoj
2015-01-01
This book introduces a variety of neural network methods for solving differential equations arising in science and engineering. The emphasis is placed on a deep understanding of the neural network techniques, which has been presented in a mostly heuristic and intuitive manner. This approach will enable the reader to understand the working, efficiency and shortcomings of each neural network technique for solving differential equations. The objective of this book is to provide the reader with a sound understanding of the foundations of neural networks, and a comprehensive introduction to neural network methods for solving differential equations together with recent developments in the techniques and their applications. The book comprises four major sections. Section I consists of a brief overview of differential equations and the relevant physical problems arising in science and engineering. Section II illustrates the history of neural networks starting from their beginnings in the 1940s through to the renewed...
Robust fractional order differentiators using generalized modulating functions method
Liu, Dayan
2015-02-01
This paper aims at designing a fractional order differentiator for a class of signals satisfying a linear differential equation with unknown parameters. A generalized modulating functions method is proposed first to estimate the unknown parameters, then to derive accurate integral formulae for the left-sided Riemann-Liouville fractional derivatives of the studied signal. Unlike the improper integral in the definition of the left-sided Riemann-Liouville fractional derivative, the integrals in the proposed formulae can be proper and be considered as a low-pass filter by choosing appropriate modulating functions. Hence, digital fractional order differentiators applicable for on-line applications are deduced using a numerical integration method in discrete noisy case. Moreover, some error analysis are given for noise error contributions due to a class of stochastic processes. Finally, numerical examples are given to show the accuracy and robustness of the proposed fractional order differentiators.
Wang, Dongdong; Li, Xiwei; Pan, Feixu
2016-11-01
A simple and unified finite element formulation is presented for superconvergent eigenvalue computation of wave equations ranging from 1D to 3D. In this framework, a general method based upon the so called α mass matrix formulation is first proposed to effectively construct 1D higher order mass matrices for arbitrary order elements. The finite elements discussed herein refer to the Lagrangian type of Lobatto elements that take the Lobatto points as nodes. Subsequently a set of quadrature rules that exactly integrate the 1D higher order mass matrices are rationally derived, which are termed as the superconvergent quadrature rules. More importantly, in 2D and 3D cases, it is found that the employment of these quadrature rules via tensor product simultaneously for the mass and stiffness matrix integrations of Lobatto elements produces a unified superconvergent formulation for the eigenvalue or frequency computation without wave propagation direction dependence, which usually is a critical issue for the multidimensional higher order mass matrix formulation. Consequently the proposed approach is capable of computing arbitrary frequencies in a superconvergent fashion. Meanwhile, numerical implementation of the proposed method for multidimensional problems is trivial. The effectiveness of the proposed methodology is systematically demonstrated by a series of numerical examples. Numerical results revealed that a superconvergence with 2(p+1)th order of frequency accuracy is achieved by the present unified formulation for the pth order Lobatto element.
International Conference on Multiscale Methods and Partial Differential Equations.
Energy Technology Data Exchange (ETDEWEB)
Thomas Hou
2006-12-12
The International Conference on Multiscale Methods and Partial Differential Equations (ICMMPDE for short) was held at IPAM, UCLA on August 26-27, 2005. The conference brought together researchers, students and practitioners with interest in the theoretical, computational and practical aspects of multiscale problems and related partial differential equations. The conference provided a forum to exchange and stimulate new ideas from different disciplines, and to formulate new challenging multiscale problems that will have impact in applications.
GHM method for obtaining rationalsolutions of nonlinear differential equations.
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.
Modified Homotopy Analysis Method for Nonlinear Fractional Partial Differential Equations
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D. Ziane
2017-05-01
Full Text Available In this paper, a combined form of natural transform with homotopy analysis method is proposed to solve nonlinear fractional partial differential equations. This method is called the fractional homotopy analysis natural transform method (FHANTM. The FHANTM can easily be applied to many problems and is capable of reducing the size of computational work. The fractional derivative is described in the Caputo sense. The results show that the FHANTM is an appropriate method for solving nonlinear fractional partial differentia equation.
Numerical Evaluation of CPV Boundary Integrals with Symmetrical Quadrature Schemes
Institute of Scientific and Technical Information of China (English)
马杭; 徐凯宇
2003-01-01
Stemming from the definition of the Cauchy principal values (CPV) integrals, a newly developed symmetrical quadrature scheme was proposed in the paper for the accurate numerical evaluation of the singular boundary integrals in the sense of CPV encountered in the boundary element method. In the case of inner-element singularities, the CPV integrals could be evaluated in a straightforward way by dividing the element into the symmetrical part and the remainder(s). And in the case of end-singularities, the CPV integrals could be evaluated simply by taking a tangential distance transformation of the integrand after cutting out a symmetrical tiny zone around the singular point. In both cases, the operations are no longer necessary before the numerical implementation, which involves the dull routine work to separate out singularities from the integral kernels. Numerical examples were presented for both the two-and the three-dimensional boundary integrals in elasticity. Comparing the numerical results with those by other approaches demonstrates the feasibility and the effectiveness of the proposed scheme.
ADAPTIVE INTERVAL WAVELET PRECISE INTEGRATION METHOD FOR PARTIAL DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
MEI Shu-li; LU Qi-shao; ZHANG Sen-wen; JIN Li
2005-01-01
The quasi-Shannon interval wavelet is constructed based on the interpolation wavelet theory, and an adaptive precise integration method, which is based on extrapolation method is presented for nonlinear ordinary differential equations (ODEs). And then, an adaptive interval wavelet precise integration method (AIWPIM) for nonlinear partial differential equations(PDEs) is proposed. The numerical results show that the computational precision of AIWPIM is higher than that of the method constructed by combining the wavelet and the 4th Runge-Kutta method, and the computational amounts of these two methods are almost equal. For convenience, the Burgers equation is taken as an example in introducing this method, which is also valid for more general cases.
Nonlinear ordinary differential equations analytical approximation and numerical methods
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...
Solution of partial differential equations using a gridless method
Energy Technology Data Exchange (ETDEWEB)
Syms, G.F. [National Research Council of Canada, Inst. for Aerospace Research, Ottawa, Ontario (Canada)]. E-mail: Jerry.Syms@nrc-cnrc.gc.ca
2004-07-01
A set of algorithms to solve linear and nonlinear partial differential evolution equations in one dimension using a gridless method was developed. The potential flexibility of the method is connected to the fact that the points in the grid are not. In the gridless method, the spatial derivatives are computed from the analytic differentiation of a local approximation to the function while the temporal integration is carried out using standard ordinary differential equation techniques. Clouds of points were used to determine the local function approximation. Two sets of basis functions were implemented: ordinary polynomials, x{sup j}, and focus-centred polynomials, (x - x{sup (i)}){sup j}. Overdetermined matrix systems defining the polynomial coefficients were solved through a linear least-squares procedure using either the normal equations or orthogonal triangulation. It was found that the choice of the basis functions and solution procedure could greatly affect the matrix condition number and thus the accuracy of the function reconstruction. The ability of the gridless method to solve partial differential equations was demonstrated by applying the method to the linear convection-diffusion equation and the nonlinear Burger's equation. The stability of the method was found to be negatively affected when reconstructions from over-determined systems were used. (author)
Lattice quantum chromodynamics equation of state: A better differential method
Indian Academy of Sciences (India)
Rajiv V Gavai; Sourendu Gupta; Swagato Mukherjee
2008-09-01
We propose a better differential method for the computation of the equation of state of QCD from lattice simulations. In contrast to the earlier differential method, our technique yields positive pressure for all temperatures including the temperatures in the transition region. Employing it on temporal lattices of 8, 10 and 12 sites and by extrapolating to zero lattice spacing we obtained the pressure, energy density, entropy density, specific heat and speed of sound in quenched QCD for 0.9 ≤ /c ≤ 3. At high temperatures comparisons of our results are made with those from the dimensional reduction approach and also with those from a conformal symmetric theory.
Stability analysis of linear multistep methods for delay differential equations
Directory of Open Access Journals (Sweden)
V. L. Bakke
1986-01-01
Full Text Available Stability properties of linear multistep methods for delay differential equations with respect to the test equation y′(t=ay(λt+by(t, t≥0,0<λ<1, are investigated. It is known that the solution of this equation is bounded if and only if |a|<−b and we examine whether this property is inherited by multistep methods with Lagrange interpolation and by parametrized Adams methods.
Multigrid methods for space fractional partial differential equations
Jiang, Yingjun; Xu, Xuejun
2015-12-01
We propose some multigrid methods for solving the algebraic systems resulting from finite element approximations of space fractional partial differential equations (SFPDEs). It is shown that our multigrid methods are optimal, which means the convergence rates of the methods are independent of the mesh size and mesh level. Moreover, our theoretical analysis and convergence results do not require regularity assumptions of the model problems. Numerical results are given to support our theoretical findings.
Spectral methods for time dependent partial differential equations
Gottlieb, D.; Turkel, E.
1983-01-01
The theory of spectral methods for time dependent partial differential equations is reviewed. When the domain is periodic Fourier methods are presented while for nonperiodic problems both Chebyshev and Legendre methods are discussed. The theory is presented for both hyperbolic and parabolic systems using both Galerkin and collocation procedures. While most of the review considers problems with constant coefficients the extension to nonlinear problems is also discussed. Some results for problems with shocks are presented.
Bell's inequality for systems with quadrature phase coherence
Tan, S. M.; Holland, M. J.; Walls, D. F.
1990-07-01
We show that a violation of Bell's inequalities by quadrature phase measurements is not due to the interference of the two photons in a photon pair state. Rather the violation predicted by Grangier et al. for a parametric down-converter is due to the interference of the photon pair state with the vacuum. We propose new sources which violate the quadrature phase Bell's inequalities, including one which employs squeezed light and another which demonstrates the non-local properties of a single photon state.
Numerical methods for stochastic partial differential equations with white noise
Zhang, Zhongqiang
2017-01-01
This book covers numerical methods for stochastic partial differential equations with white noise using the framework of Wong-Zakai approximation. The book begins with some motivational and background material in the introductory chapters and is divided into three parts. Part I covers numerical stochastic ordinary differential equations. Here the authors start with numerical methods for SDEs with delay using the Wong-Zakai approximation and finite difference in time. Part II covers temporal white noise. Here the authors consider SPDEs as PDEs driven by white noise, where discretization of white noise (Brownian motion) leads to PDEs with smooth noise, which can then be treated by numerical methods for PDEs. In this part, recursive algorithms based on Wiener chaos expansion and stochastic collocation methods are presented for linear stochastic advection-diffusion-reaction equations. In addition, stochastic Euler equations are exploited as an application of stochastic collocation methods, where a numerical compa...
Differential and difference equations a comparison of methods of solution
Maximon, Leonard C
2016-01-01
This book, intended for researchers and graduate students in physics, applied mathematics and engineering, presents a detailed comparison of the important methods of solution for linear differential and difference equations - variation of constants, reduction of order, Laplace transforms and generating functions - bringing out the similarities as well as the significant differences in the respective analyses. Equations of arbitrary order are studied, followed by a detailed analysis for equations of first and second order. Equations with polynomial coefficients are considered and explicit solutions for equations with linear coefficients are given, showing significant differences in the functional form of solutions of differential equations from those of difference equations. An alternative method of solution involving transformation of both the dependent and independent variables is given for both differential and difference equations. A comprehensive, detailed treatment of Green’s functions and the associat...
Coherent Detection of Optical Quadrature Phase-Shift Keying Signals With Carrier Phase Estimation
Ly-Gagnon, Dany-Sebastien; Tsukamoto, Satoshi; Katoh, Kazuhiro; Kikuchi, Kazuro
2006-01-01
This paper describes a coherent optical receiver for demodulating optical quadrature phase-shift keying (QPSK) signals. At the receiver, a phase-diversity homodyne detection scheme is employed without locking the phase of the local oscillator (LO). To handle the carrier phase drift, the carrier phase is estimated with digital signal processing (DSP) on the homodyne-detected signal. Such a scheme presents the following major advantages over the conventional optical differential detection. First, its bit error rate (BER) performance is better than that of differential detection. This higher sensitivity can extend the reach of unrepeated transmission systems and reduce crosstalk between multiwavelength channels. Second, the optoelectronic conversion process is linear, so that the whole optical signal information can be postprocessed in the electrical domain. Third, this scheme is applicable to multilevel modulation formats such as M-array PSK and quadrature amplitude modulation (QAM). The performance of the receiver is evaluated through various simulations and experiments. As a result, an unrepeated transmission over 210 km with a 20-Gb/s optical QPSK signal is achieved. Moreover, in wavelength-division multiplexing (WDM) environment, coherent detection allows the filtering of a desired wavelength channel to reside entirely in the electrical domain, taking advantage of the sharp cutoff characteristics of electrical filters. The experiments show the feasibility to transmit polarization-multiplexed 40-Gb/s QPSK signals over 200 km with channel spacing of 16 GHz, leading to a spectral efficiency as high as 2.5 b/s/Hz.
Hyperbolic function method for solving nonlinear differential-different equations
Institute of Scientific and Technical Information of China (English)
Zhu Jia-Min
2005-01-01
An algorithm is devised to obtained exact travelling wave solutions of differential-different equations by means of hyperbolic function. For illustration, we apply the method to solve the discrete nonlinear (2+1)-dimensional Toda lattice equation and the discretized nonlinear mKdV lattice equation, and successfully constructed some explicit and exact travelling wave solutions.
Using Mixed Methods to Interpret Differential Item Functioning
Benítez, Isabel; Padilla, José-Luis; Hidalgo Montesinos, María Dolores; Sireci, Stephen G.
2016-01-01
Analysis of differential item functioning (DIF) is often used to determine if cross-lingual assessments are equivalent across languages. However, evidence on the causes of cross-lingual DIF is still evasive. Expert appraisal is a qualitative method useful for obtaining detailed information about problematic elements in the different linguistic…
Splitting methods for partial Volterra integro-differential equations
Brunner, H.; Houwen, P.J. van der; Sommeijer, B.P.
1999-01-01
The spatial discretization of initial-value problems for (nonlinear) parabolic or hyperbolic PDEs with memory terms leads to (large) systems of Volterra integro-differential equations (VIDEs). In this paper we study the efficient numerical solution of such systems by methods based on linear multiste
Perturbative methods for inverse problems on degenerate differential equations
Directory of Open Access Journals (Sweden)
Angelo Favini
2012-12-01
Full Text Available Pertubation results for linear relations satisfying a resolvent condition of weak parabolic type are established. Such results are applied to solve some inverse problems for degenerate differential equations, supplying a new method which avoids any fixed-point argument and essentially consists in reducing the original inverse problem to an auxiliary direct one.
On a perturbation method for partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Fernandez, Francisco M. [CEQUINOR (Conicet), Departamento de Quimica, Facultad de Ciencias Exactas, Universidad Nacional de la Plata, La Plata (Argentina)]. E-mail: framfer@isis.unlp.edu.ar
2001-06-08
We show that a recently developed perturbation method for partial differential equations can be rewritten in the form of an interaction picture. In this way it is possible to compare this approach with others such as the standard perturbation theory and a straightforward temporal expansion of the evolution operator. We choose a simple, exactly solvable model as an illustrative example. (author)
Euler-Chebyshev methods for integro-differential equations
Houwen, P.J. van der; Sommeijer, B.P.
1996-01-01
We construct and analyse explicit methods for solving initial value problems for systems of differential equations with expensive righthand side functions whose Jacobian has its stiff eigenvalues along the negative axis. Such equations arise after spatial discretization of parabolic integro-differen
Homotopy-based methods for fractional differential equations
Ateş, Inan
2017-01-01
The intention of this thesis is two-fold. The first aim is to describe and apply, series-based, numerical methods to fractional differential equation models. For this, it is needed to distinguish between space-fractional and time-fractional derivatives. The second goal of this thesis is to give a
Electrodynamics, Differential Forms and the Method of Images
Low, Robert J.
2011-01-01
This paper gives a brief description of how Maxwell's equations are expressed in the language of differential forms and use this to provide an elegant demonstration of how the method of images (well known in electrostatics) also works for electrodynamics in the presence of an infinite plane conducting boundary. The paper should be accessible to an…
A RATIONAL SEPCTRAL METHOD FOR SINGULAR DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
王中庆; 王立联; 郭本瑜
2003-01-01
An orthogonal system of rational functions is derived from the mapped Laguerre polynomials,which is used for numerical solution of singular differential equations.A model problem is considered.A multiple-step algorithm is developed to implement this method.Numerical results show the efficiency of this new approach.
Evaluation of Chebyshev pseudospectral methods for third order differential equations
Renaut, Rosemary; Su, Yi
1997-03-01
When the standard Chebyshev collocation method is used to solve a third order differential equation with one Neumann boundary condition and two Dirichlet boundary conditions, the resulting differentiation matrix has spurious positive eigenvalues and extreme eigenvalue already reaching O(N 5 for N = 64. Stable time-steps are therefore very small in this case. A matrix operator with better stability properties is obtained by using the modified Chebyshev collocation method, introduced by Kosloff and Tal Ezer [3]. By a correct choice of mapping and implementation of the Neumann boundary condition, the matrix operator has extreme eigenvalue less than O(N 4. The pseudospectral and modified pseudospectral methods are implemented for the solution of one-dimensional third-order partial differential equations and the accuracy of the solutions compared with those by finite difference techniques. The comparison verifies the stability analysis and the modified method allows larger time-steps. Moreover, to obtain the accuracy of the pseudospectral method the finite difference methods are substantially more expensive. Also, for the small N tested, N ? 16, the modified pseudospectral method cannot compete with the standard approach.
A Synthetic Quadrature Phase Detector/Demodulator for Fourier Transform Transform Spectrometers
Campbell, Joel
2008-01-01
A method is developed to demodulate (velocity correct) Fourier transform spectrometer (FTS) data that is taken with an analog to digital converter that digitizes equally spaced in time. This method makes it possible to use simple low cost, high resolution audio digitizers to record high quality data without the need for an event timer or quadrature laser hardware, and makes it possible to use a metrology laser of any wavelength. The reduced parts count and simplicity implementation makes it an attractive alternative in space based applications when compared to previous methods such as the Brault algorithm.
Optimal Variational Asymptotic Method for Nonlinear Fractional Partial Differential Equations.
Baranwal, Vipul K; Pandey, Ram K; Singh, Om P
2014-01-01
We propose optimal variational asymptotic method to solve time fractional nonlinear partial differential equations. In the proposed method, an arbitrary number of auxiliary parameters γ 0, γ 1, γ 2,… and auxiliary functions H 0(x), H 1(x), H 2(x),… are introduced in the correction functional of the standard variational iteration method. The optimal values of these parameters are obtained by minimizing the square residual error. To test the method, we apply it to solve two important classes of nonlinear partial differential equations: (1) the fractional advection-diffusion equation with nonlinear source term and (2) the fractional Swift-Hohenberg equation. Only few iterations are required to achieve fairly accurate solutions of both the first and second problems.
A Collocation Method for Solving Fractional Riccati Differential Equation
Directory of Open Access Journals (Sweden)
Yalçın Öztürk
2013-01-01
Full Text Available We have introduced a Taylor collocation method, which is based on collocation method for solving fractional Riccati differential equation with delay term. This method is based on first taking the truncated Taylor expansions of the solution function in the fractional Riccati differential equation and then substituting their matrix forms into the equation. Using collocation points, we have the system of nonlinear algebraic equation. Then, we solve the system of nonlinear algebraic equation using Maple 13, and we have the coefficients of the truncated Taylor sum. In addition, illustrative examples are presented to demonstrate the effectiveness of the proposed method. Comparing the methodology with some known techniques shows that the present approach is relatively easy and highly accurate.
Extended Trial Equation Method for Nonlinear Partial Differential Equations
Gepreel, Khaled A.; Nofal, Taher A.
2015-04-01
The main objective of this paper is to use the extended trial equation method to construct a series of some new solutions for some nonlinear partial differential equations (PDEs) in mathematical physics. We will construct the solutions in many different functions such as hyperbolic function solutions, trigonometric function solutions, Jacobi elliptic function solutions, and rational functional solutions for the nonlinear PDEs when the balance number is a real number via the Zhiber-Shabat nonlinear differential equation. The balance number of this method is not constant as we shown in other methods, but it is changed by changing the trial equation derivative definition. This method allowed us to construct many new types of solutions. It is shown by using the Maple software package that all obtained solutions satisfy the original PDEs.
Directory of Open Access Journals (Sweden)
Brajesh Kumar Singh
2016-01-01
Full Text Available This paper deals with an analytical solution of an initial value system of time dependent linear and nonlinear partial differential equations by implementing reduced differential transform (RDT method. The effectiveness and the convergence of RDT method are tested by means of five test problems, which indicates the validity and great potential of the reduced differential transform method for solving system of partial differential equations.
Workshop on Numerical Methods for Ordinary Differential Equations
Gear, Charles; Russo, Elvira
1989-01-01
Developments in numerical initial value ode methods were the focal topic of the meeting at L'Aquila which explord the connections between the classical background and new research areas such as differental-algebraic equations, delay integral and integro-differential equations, stability properties, continuous extensions (interpolants for Runge-Kutta methods and their applications, effective stepsize control, parallel algorithms for small- and large-scale parallel architectures). The resulting proceedings address many of these topics in both research and survey papers.
Exp-function method for solving fractional partial differential equations.
Zheng, Bin
2013-01-01
We extend the Exp-function method to fractional partial differential equations in the sense of modified Riemann-Liouville derivative based on nonlinear fractional complex transformation. For illustrating the validity of this method, we apply it to the space-time fractional Fokas equation and the nonlinear fractional Sharma-Tasso-Olver (STO) equation. As a result, some new exact solutions for them are successfully established.
Certified reduced basis methods for parametrized partial differential equations
Hesthaven, Jan S; Stamm, Benjamin
2016-01-01
This book provides a thorough introduction to the mathematical and algorithmic aspects of certified reduced basis methods for parametrized partial differential equations. Central aspects ranging from model construction, error estimation and computational efficiency to empirical interpolation methods are discussed in detail for coercive problems. More advanced aspects associated with time-dependent problems, non-compliant and non-coercive problems and applications with geometric variation are also discussed as examples.
16-QAM Field-Quadrature Decomposition using Polarization-Assisted Phase Sensitive Amplification
DEFF Research Database (Denmark)
Kjøller, Niels-Kristian; Piels, Molly; Da Ros, Francesco
2016-01-01
Simultaneous I and Q extraction for 16-QAM is experimentally demonstrated through field-quadrature decomposition using a polarization-assisted phase sensitive amplifier. The quadrature components are successfully received and performance is evaluated through bit-error-ratio testing.......Simultaneous I and Q extraction for 16-QAM is experimentally demonstrated through field-quadrature decomposition using a polarization-assisted phase sensitive amplifier. The quadrature components are successfully received and performance is evaluated through bit-error-ratio testing....
From Lobatto Quadrature to the Euler Constant "e"
Khattri, Sanjay Kumar
2010-01-01
Based on the Lobatto quadrature, we develop several new closed form approximations to the mathematical constant "e." For validating effectiveness of our approximations, a comparison of our results to the existing approximations is also presented. Another objective of our work is to inspire students to formulate other better approximations by using…
Self-calibrating quadrature mixing front-end for SDR
CSIR Research Space (South Africa)
De Witt, JJ
2008-01-01
Full Text Available A quadrature mixing front-end is well-suited toward software define radio (SDR) applications, due to its low complexity and the inherent flexibility that it affords the radio front-end. Its performance is, however, severely affected by gain...
Entropy of phase measurement quantum phase via quadrature measurement
My, R; My, Robert; Uni, Palacky
1995-01-01
The content of phase information of an arbitrary phase--sensitive measurement is evaluated using the maximum likelihood estimation. The phase distribution is characterized by the relative entropy--a nonlinear functional of input quantum state. As an explicit example the multiple measurement of quadrature operator is interpreted as quantum phase detection achieving the ultimate resolution predicted by the Fisher information.
Quantum correlations induced by multiple scattering of quadrature squeezed light
DEFF Research Database (Denmark)
Lodahl, Peter
2006-01-01
Propagating quadrature squeezed light through a multiple scattering random medium is found to induce pronounced spatial quantum correlations that have no classical analogue. The correlations are revealed in the number of photons transported through the sample that can be measured from the intensity...
Fully Digital Chaotic Differential Equation-based Systems And Methods
Radwan, Ahmed Gomaa Ahmed
2012-09-06
Various embodiments are provided for fully digital chaotic differential equation-based systems and methods. In one embodiment, among others, a digital circuit includes digital state registers and one or more digital logic modules configured to obtain a first value from two or more of the digital state registers; determine a second value based upon the obtained first values and a chaotic differential equation; and provide the second value to set a state of one of the plurality of digital state registers. In another embodiment, a digital circuit includes digital state registers, digital logic modules configured to obtain outputs from a subset of the digital shift registers and to provide the input based upon a chaotic differential equation for setting a state of at least one of the subset of digital shift registers, and a digital clock configured to provide a clock signal for operating the digital shift registers.
Improved stochastic approximation methods for discretized parabolic partial differential equations
Guiaş, Flavius
2016-12-01
We present improvements of the stochastic direct simulation method, a known numerical scheme based on Markov jump processes which is used for approximating solutions of ordinary differential equations. This scheme is suited especially for spatial discretizations of evolution partial differential equations (PDEs). By exploiting the full path simulation of the stochastic method, we use this first approximation as a predictor and construct improved approximations by Picard iterations, Runge-Kutta steps, or a combination. This has as consequence an increased order of convergence. We illustrate the features of the improved method at a standard benchmark problem, a reaction-diffusion equation modeling a combustion process in one space dimension (1D) and two space dimensions (2D).
Arshad, Muhammad; Lu, Dianchen; Wang, Jun
2017-07-01
In this paper, we pursue the general form of the fractional reduced differential transform method (DTM) to (N+1)-dimensional case, so that fractional order partial differential equations (PDEs) can be resolved effectively. The most distinct aspect of this method is that no prescribed assumptions are required, and the huge computational exertion is reduced and round-off errors are also evaded. We utilize the proposed scheme on some initial value problems and approximate numerical solutions of linear and nonlinear time fractional PDEs are obtained, which shows that the method is highly accurate and simple to apply. The proposed technique is thus an influential technique for solving the fractional PDEs and fractional order problems occurring in the field of engineering, physics etc. Numerical results are obtained for verification and demonstration purpose by using Mathematica software.
Fast methods for static Hamilton-Jacobi Partial Differential Equations
Energy Technology Data Exchange (ETDEWEB)
Vladimirsky, Alexander Boris
2001-05-01
The authors develop a family of fast methods approximating the solution to a wide class of static Hamilton-Jacobi partial differential equations. These partial differential equations are considered in the context of control-theoretic and front-propagation problems. In general, to produce a numerical solution to such a problem, one has to solve a large system of coupled non-linear discretized equations. The techniques use partial information about the characteristic directions to de-couple the system. Previously known fast methods, available for isotropic problems, are discussed in detail. They introduce a family of new Ordered Upwinding Methods (OUM) for general (anisotropic) problems and prove convergence to the viscosity solution of the corresponding Hamilton-Jacobi partial differential equation. The hybrid methods introduced here are based on the analysis of the role played by anisotropy in the context of front propagation and optimal trajectory problems. The performance of the methods is analyzed and compared to that of several other numerical approaches to these problems. Computational experiments are performed using test problems from control theory, computational geometry and seismology.
Fast methods for static Hamilton-Jacobi Partial Differential Equations
Energy Technology Data Exchange (ETDEWEB)
Vladimirsky, Alexander Boris [Univ. of California, Berkeley, CA (United States)
2001-01-01
The authors develop a family of fast methods approximating the solution to a wide class of static Hamilton-Jacobi partial differential equations. These partial differential equations are considered in the context of control-theoretic and front-propagation problems. In general, to produce a numerical solution to such a problem, one has to solve a large system of coupled non-linear discretized equations. The techniques use partial information about the characteristic directions to de-couple the system. Previously known fast methods, available for isotropic problems, are discussed in detail. They introduce a family of new Ordered Upwinding Methods (OUM) for general (anisotropic) problems and prove convergence to the viscosity solution of the corresponding Hamilton-Jacobi partial differential equation. The hybrid methods introduced here are based on the analysis of the role played by anisotropy in the context of front propagation and optimal trajectory problems. The performance of the methods is analyzed and compared to that of several other numerical approaches to these problems. Computational experiments are performed using test problems from control theory, computational geometry and seismology.
The Finite Element Method An Introduction with Partial Differential Equations
Davies, A J
2011-01-01
The finite element method is a technique for solving problems in applied science and engineering. The essence of this book is the application of the finite element method to the solution of boundary and initial-value problems posed in terms of partial differential equations. The method is developed for the solution of Poisson's equation, in a weighted-residual context, and then proceeds to time-dependent and nonlinear problems. The relationship with the variational approach is alsoexplained. This book is written at an introductory level, developing all the necessary concepts where required. Co
Methods of mathematical modelling continuous systems and differential equations
Witelski, Thomas
2015-01-01
This book presents mathematical modelling and the integrated process of formulating sets of equations to describe real-world problems. It describes methods for obtaining solutions of challenging differential equations stemming from problems in areas such as chemical reactions, population dynamics, mechanical systems, and fluid mechanics. Chapters 1 to 4 cover essential topics in ordinary differential equations, transport equations and the calculus of variations that are important for formulating models. Chapters 5 to 11 then develop more advanced techniques including similarity solutions, matched asymptotic expansions, multiple scale analysis, long-wave models, and fast/slow dynamical systems. Methods of Mathematical Modelling will be useful for advanced undergraduate or beginning graduate students in applied mathematics, engineering and other applied sciences.
A new efficient method for solving delay differential equations and a comparison with other methods
Bildik, Necdet; Deniz, Sinan
2017-01-01
In this paper, a new analytical technique, namely the optimal perturbation iteration method, is presented and applied to delay differential equations to find an efficient algorithm for their approximate solutions. Effectiveness of this method is tested by various examples of linear and nonlinear problems of delay differential equations. Obtained results reveal that optimal perturbation iteration algorithm is very effective, easy to use and simple to perform.
Quadrature-based Lattice Boltzmann Model for Relativistic Flows
Blaga, Robert
2016-01-01
A quadrature-based finite-difference lattice Boltzmann model is developed that is suitable for simulating relativistic flows of massless particles. We briefly review the relativistc Boltzmann equation and present our model. The quadrature is constructed such that the stress-energy tensor is obtained as a second order moment of the distribution function. The results obtained with our model are presented for a particular instance of the Riemann problem (the Sod shock tube). We show that the model is able to accurately capture the behavior across the whole domain of relaxation times, from the hydrodynamic to the ballistic regime. The property of the model of being extendable to arbitrarily high orders is shown to be paramount for the recovery of the analytical result in the ballistic regime.
Observation of Localized Multi-Spatial-Mode Quadrature Squeezing
Directory of Open Access Journals (Sweden)
C. S. Embrey
2015-07-01
Full Text Available Quantum states of light can improve imaging whenever the image quality and resolution are limited by the quantum noise of the illumination. In the case of a bright illumination, quantum enhancement is obtained for a light field composed of many squeezed transverse modes. A possible realization of such a multi-spatial-mode squeezed state is a field which contains a transverse plane in which the local electric field displays reduced quantum fluctuations at all locations, on any one quadrature. Using a traveling-wave amplifier, we have generated a multi-spatial-mode squeezed state and showed that it exhibits localized quadrature squeezing at any point of its transverse profile, in regions much smaller than its size. We observe 75 independently squeezed regions. The amplification relies on nondegenerate four-wave mixing in a hot vapor and produces a bichromatic squeezed state. The result confirms the potential of this technique for producing illumination suitable for practical quantum imaging.
Quadrature-dependent Bogoliubov transformations and multiphoton squeezed states
De Siena, S; Illuminati, F; Siena, Silvio De; Lisi, Antonio Di; Illuminati, Fabrizio
2001-01-01
We introduce a linear, canonical transformation of the fundamental single--mode field operators $a$ and $a^{\\dagger}$ that generalizes the linear Bogoliubov transformation familiar in the construction of the harmonic oscillator squeezed states. This generalization is obtained by adding to the linear transformation a nonlinear function of any of the fundamental quadrature operators $X_{1}$ and $X_{2}$, making the original Bogoliubov transformation quadrature--dependent. Remarkably, the conditions of canonicity do not impose any constraint on the form of the nonlinear function, and lead to a set of nontrivial algebraic relations between the $c$--number coefficients of the transformation. We examine in detail the structure and the properties of the new quantum states defined as eigenvectors of the transformed annihilation operator $b$. These eigenvectors define a class of multiphoton squeezed states. The structure of the uncertainty products and of the quasiprobability distributions in phase space shows that bes...
Orthogonal functions, discrete variable representation, and generalized gauss quadratures
DEFF Research Database (Denmark)
Schneider, B. I.; Nygaard, Nicolai
2002-01-01
, the basis of the generalized weight functions. We review these ideas below and apply then to the generation of the points and weights of the Rys polynomials which have proven useful in the evaluation of multicenter integrals, using Gaussian basis sets in quantum chemistry. In contrast to some approaches....... This three-term recursion can be used to generate the orthogonal functions as well as to generate the points and weights of Gauss quadratures on the basis of these functions. For the classical orthogonal functions, the terms in the three-term recursion are known analytically. For more general weight...... functions, this is not the case. However, they may be computed in a stable numerical fashion, via the recursion. In essence, this is an application of the well-known Lanczos recursion approach. Once the recursion coefficients are known, it is possible to compute the points and weights of quadratures on...
Energy Technology Data Exchange (ETDEWEB)
Abdel-Halim Hassan, I.H. [Department of Mathematics, Faculty of Science, Zagazig University, Zagazig (Egypt)], E-mail: ismhalim@hotmail.com
2008-04-15
In this paper, we will compare the differential transformation method DTM and Adomian decomposition method ADM to solve partial differential equations (PDEs). The definition and operations of differential transform method was introduced by Zhou [Zhou JK. Differential transformation and its application for electrical circuits. Wuuhahn, China: Huarjung University Press; 1986 [in Chinese
Quadrature Uncertainty and Information Entropy of Quantum Elliptical Vortex States
Banerji, Anindya; Panigrahi, Prasanta. K.; Singh, Ravindra Pratap; Chowdhury, Saurav; Bandyopadhyay, Abir
2012-01-01
We study the quadrature uncertainty of the quantum elliptical vortex state using the associated Wigner function. Deviations from the minimum uncertainty states were observed due to the absence of the Gaussian nature. In our study of the entropy, we noticed that with increasing vorticity, entropy increases for both the modes. We further observed that, there exists an optimum value of ellipticity which gives rise to maximum entanglement of the two modes of the quantum elliptical vortex states. ...
Electronically Tunable Current-Mode Quadrature Oscillator Using Single MCDTA
Directory of Open Access Journals (Sweden)
Y. Li
2010-12-01
Full Text Available This paper presents a modified current differencing transconductance amlpifier (MCDTA and the MCDTA based quadrature oscillator. The oscillator is current-mode and provides current output from high output impedance terminals. The circuit uses only one MCDTA and two grounded capacitors, and is easy to be integrated. Its oscillation frequency can be tuned electronically by tuning bias currents of MCDTA. Finally, frequency error is analyzed. The results of circuit simulations are in agreement with theory.
A Simple Current-Mode Quadrature Oscillator Using Single CDTA
Directory of Open Access Journals (Sweden)
D. Biolek
2008-12-01
Full Text Available This article presents a simple current-mode quadrature oscillator using a single Current Differencing Transconductance Amplifier (CDTA as the active element. The oscillation condition and oscillation frequency can be electronically controlled. The circuit structure is very simple, consisting of merely one CDTA, one resistor and two capacitors. The proposed circuit is suitable for IC architecture. The PSpice simulation and experimental results are shown, and the results agree well with the theoretical assumptions.
Quadrature two-dimensional correlation spectroscopy (Q-2DCOS)
Noda, Isao
2016-11-01
Quadrature 2D correlation spectroscopy (Q-2DCOS) is introduced. The technique incorporates the effect of the perturbation into the traditional 2DCOS analysis by building a multivariate model, merging the information of the perturbation variable and spectral responses. By employing factors which are 90° out of phase with each other, pertinent coincidental and sequential spectral intensity variations are adequately captured for the subsequent 2D correlation analysis. Almost complete replication of the original 2DCOS results based on such a simple rank 2 model of experimental spectra suggests that only the dominant spectral intensity variation patterns in combination with its quadrature counterpart seems to be utilized in 2DCOS analysis. Using the linear perturbation variable itself as the basis for generating the primary score vector is equivalent to the least squares fitting of a quadratic polynomial with spectral intensity variations. Q-2DCOS analysis may be displayed in terms of a graphical plot on a phase plane in the vector space, so that coincidental and sequential matching of the patterns of spectral intensity variations is represented simply by the phase angle difference between two vectors. Q-2DCOS analysis is closely related to other established ideas and practices in the 2D correlation spectroscopy field, such as dynamic 2D IR dichroism, PCA 2D, quadrature orthogonal signal correction (Q-OSC), and perturbation correlation moving window (PCMW) analyses.
Beyond pressureless gas dynamics : Quadrature-based velocity moment models
Chalons, Christophe; Massot, Marc
2010-01-01
Following the seminal work of F. Bouchut on zero pressure gas dynamics which has been extensively used for gas particle-flows, the present contribution investigates quadrature-based velocity moments models for kinetic equations in the framework of the infinite Knudsen number limit, that is, for dilute clouds of small particles where the collision or coalescence probability asymptotically approaches zero. Such models define a hierarchy based on the number of moments and associated quadrature nodes, the first level of which leads to pressureless gas dynamics. We focus in particular on the four moment model where the flux closure is provided by a two-node quadrature in the velocity phase space and provide the right framework for studying both smooth and singular solutions. The link with both the kinetic underlying equation as well as with zero pressure gas dynamics is provided and we define the notion of measure solutions as well as the mathematical structure of the resulting system of four PDEs. We exhibit a fa...
Testing the Empirical Shock Arrival Model using Quadrature Observations
Gopalswamy, N; Xie, H; Yashiro, S
2013-01-01
The empirical shock arrival (ESA) model was developed based on quadrature data from Helios (in-situ) and P-78 (remote-sensing) to predict the Sun-Earth travel time of coronal mass ejections (CMEs) [Gopalswamy et al. 2005a]. The ESA model requires earthward CME speed as input, which is not directly measurable from coronagraphs along the Sun-Earth line. The Solar Terrestrial Relations Observatory (STEREO) and the Solar and Heliospheric Observatory (SOHO) were in quadrature during 2010 - 2012, so the speeds of Earth-directed CMEs were observed with minimal projection effects. We identified a set of 20 full halo CMEs in the field of view of SOHO that were also observed in quadrature by STEREO. We used the earthward speed from STEREO measurements as input to the ESA model and compared the resulting travel times with the observed ones from L1 monitors. We find that the model predicts the CME travel time within about 7.3 hours, which is similar to the predictions by the ENLIL model. We also find that CME-CME and CME...
Optimal method for exoplanet detection by angular differential imaging.
Mugnier, Laurent M; Cornia, Alberto; Sauvage, Jean-François; Rousset, Gérard; Fusco, Thierry; Védrenne, Nicolas
2009-06-01
We propose a novel method for the efficient direct detection of exoplanets from the ground using angular differential imaging. The method combines images appropriately, then uses the combined images jointly in a maximum-likelihood framework to estimate the position and intensity of potential planets orbiting the observed star. It takes into account the mixture of photon and detector noises and a positivity constraint on the planet's intensity. A reasonable detection criterion is also proposed based on the computation of the noise propagation from the images to the estimated intensity of the potential planet. The implementation of this method is tested on simulated data that take into account static aberrations before and after the coronagraph, residual turbulence after adaptive optics correction, and noise.
[Series: Utilization of Differential Equations and Methods for Solving Them in Medical Physics (2)].
Murase, Kenya
2015-01-01
In this issue, symbolic methods for solving differential equations were firstly introduced. Of the symbolic methods, Laplace transform method was also introduced together with some examples, in which this method was applied to solving the differential equations derived from a two-compartment kinetic model and an equivalent circuit model for membrane potential. Second, series expansion methods for solving differential equations were introduced together with some examples, in which these methods were used to solve Bessel's and Legendre's differential equations. In the next issue, simultaneous differential equations and various methods for solving these differential equations will be introduced together with some examples in medical physics.
Differential correction method applied to measurement of the FAST reflector
Li, Xin-Yi; Zhu, Li-Chun; Hu, Jin-Wen; Li, Zhi-Heng
2016-08-01
The Five-hundred-meter Aperture Spherical radio Telescope (FAST) adopts an active deformable main reflector which is composed of 4450 triangular panels. During an observation, the illuminated area of the reflector is deformed into a 300-m diameter paraboloid and directed toward a source. To achieve accurate control of the reflector shape, positions of 2226 nodes distributed around the entire reflector must be measured with sufficient precision within a limited time, which is a challenging task because of the large scale. Measurement of the FAST reflector makes use of stations and node targets. However, in this case the effect of the atmosphere on measurement accuracy is a significant issue. This paper investigates a differential correction method for total stations measurement of the FAST reflector. A multi-benchmark differential correction method, including a scheme for benchmark selection and weight assignment, is proposed. On-site evaluation experiments show there is an improvement of 70%-80% in measurement accuracy compared with the uncorrected measurement, verifying the effectiveness of the proposed method.
Eigenvalues of singular differential operators by finite difference methods. II.
Baxley, J. V.
1972-01-01
Note is made of an earlier paper which defined finite difference operators for the Hilbert space L2(m), and gave the eigenvalues for these operators. The present work examines eigenvalues for higher order singular differential operators by using finite difference methods. The two self-adjoint operators investigated are defined by a particular value in the same Hilbert space, L2(m), and are strictly positive with compact inverses. A class of finite difference operators is considered, with the idea of application to the theory of Toeplitz matrices. The approximating operators consist of a good approximation plus a perturbing operator.
Shoupeng, Song; Zhou, Jiang
2017-03-01
Converting ultrasonic signal to ultrasonic pulse stream is the key step of finite rate of innovation (FRI) sparse sampling. At present, ultrasonic pulse-stream-forming techniques are mainly based on digital algorithms. No hardware circuit that can achieve it has been reported. This paper proposes a new quadrature demodulation (QD) based circuit implementation method for forming an ultrasonic pulse stream. Elaborating on FRI sparse sampling theory, the process of ultrasonic signal is explained, followed by a discussion and analysis of ultrasonic pulse-stream-forming methods. In contrast to ultrasonic signal envelope extracting techniques, a quadrature demodulation method (QDM) is proposed. Simulation experiments were performed to determine its performance at various signal-to-noise ratios (SNRs). The circuit was then designed, with mixing module, oscillator, low pass filter (LPF), and root of square sum module. Finally, application experiments were carried out on pipeline sample ultrasonic flaw testing. The experimental results indicate that the QDM can accurately convert ultrasonic signal to ultrasonic pulse stream, and reverse the original signal information, such as pulse width, amplitude, and time of arrival. This technique lays the foundation for ultrasonic signal FRI sparse sampling directly with hardware circuitry.
Furihata, Daisuke
2010-01-01
Nonlinear Partial Differential Equations (PDEs) have become increasingly important in the description of physical phenomena. Unlike Ordinary Differential Equations, PDEs can be used to effectively model multidimensional systems. The methods put forward in Discrete Variational Derivative Method concentrate on a new class of ""structure-preserving numerical equations"" which improves the qualitative behaviour of the PDE solutions and allows for stable computing. The authors have also taken care to present their methods in an accessible manner, which means that the book will be useful to engineer
Scalable nonlinear iterative methods for partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Cai, X-C
2000-10-29
We conducted a six-month investigation of the design, analysis, and software implementation of a class of singularity-insensitive, scalable, parallel nonlinear iterative methods for the numerical solution of nonlinear partial differential equations. The solutions of nonlinear PDEs are often nonsmooth and have local singularities, such as sharp fronts. Traditional nonlinear iterative methods, such as Newton-like methods, are capable of reducing the global smooth nonlinearities at a nearly quadratic convergence rate but may become very slow once the local singularities appear somewhere in the computational domain. Even with global strategies such as line search or trust region the methods often stagnate at local minima of {parallel}F{parallel}, especially for problems with unbalanced nonlinearities, because the methods do not have built-in machinery to deal with the unbalanced nonlinearities. To find the same solution u* of F(u) = 0, we solve, instead, an equivalent nonlinearly preconditioned system G(F(u*)) = 0 whose nonlinearities are more balanced. In this project, we proposed and studied a nonlinear additive Schwarz based parallel nonlinear preconditioner and showed numerically that the new method converges well even for some difficult problems, such as high Reynolds number flows, when a traditional inexact Newton method fails.
Final Report: Symposium on Adaptive Methods for Partial Differential Equations
Energy Technology Data Exchange (ETDEWEB)
Pernice, M.; Johnson, C.R.; Smith, P.J.; Fogelson, A.
1998-12-10
OAK-B135 Final Report: Symposium on Adaptive Methods for Partial Differential Equations. Complex physical phenomena often include features that span a wide range of spatial and temporal scales. Accurate simulation of such phenomena can be difficult to obtain, and computations that are under-resolved can even exhibit spurious features. While it is possible to resolve small scale features by increasing the number of grid points, global grid refinement can quickly lead to problems that are intractable, even on the largest available computing facilities. These constraints are particularly severe for three dimensional problems that involve complex physics. One way to achieve the needed resolution is to refine the computational mesh locally, in only those regions where enhanced resolution is required. Adaptive solution methods concentrate computational effort in regions where it is most needed. These methods have been successfully applied to a wide variety of problems in computational science and engineering. Adaptive methods can be difficult to implement, prompting the development of tools and environments to facilitate their use. To ensure that the results of their efforts are useful, algorithm and tool developers must maintain close communication with application specialists. Conversely it remains difficult for application specialists who are unfamiliar with the methods to evaluate the trade-offs between the benefits of enhanced local resolution and the effort needed to implement an adaptive solution method.
Statistical methods for detecting differentially methylated loci and regions
Directory of Open Access Journals (Sweden)
Mark D Robinson
2014-09-01
Full Text Available DNA methylation, the reversible addition of methyl groups at CpG dinucleotides, represents an important regulatory layer associated with gene expression. Changed methylation status has been noted across diverse pathological states, including cancer. The rapid development and uptake of microarrays and large scale DNA sequencing has prompted an explosion of data analytic methods for processing and discovering changes in DNA methylation across varied data types. In this mini-review, we present a compact and accessible discussion of many of the salient challenges, such as experimental design, statistical methods for differential methylation detection, critical considerations such as cell type composition and the potential confounding that can arise from batch effects. From a statistical perspective, our main interests include the use of empirical Bayes or hierarchical models, which have proved immensely powerful in genomics, and the procedures by which false discovery control is achieved.
Cubature Methods For Stochastic (Partial) Differential Equations In Weighted Spaces
Doersek, Philipp; Veluscek, Dejan
2012-01-01
The cubature on Wiener space method, a high-order weak approximation scheme, is established for SPDEs in the case of unbounded characteristics and unbounded payoffs. We first introduce a recently described flexible functional analytic framework, so called weighted spaces, where Feller-like properties hold. A refined analysis of vector fields on weighted spaces then yields optimal convergence rates of cubature methods for stochastic partial differential equations of Da Prato-Zabczyk type. The ubiquitous stability for the local approximation operator within the functional analytic setting is proved for SPDEs, however, in the infinite dimensional case we need a newly introduced assumption on weak symmetry of the cubature formula. In finite dimensions, we use the UFG condition to obtain optimal rates of convergence on non-uniform meshes for nonsmooth payoffs with exponential growth.
Reduced basis methods for partial differential equations an introduction
Quarteroni, Alfio; Negri, Federico
2016-01-01
This book provides a basic introduction to reduced basis (RB) methods for problems involving the repeated solution of partial differential equations (PDEs) arising from engineering and applied sciences, such as PDEs depending on several parameters and PDE-constrained optimization. The book presents a general mathematical formulation of RB methods, analyzes their fundamental theoretical properties, discusses the related algorithmic and implementation aspects, and highlights their built-in algebraic and geometric structures. More specifically, the authors discuss alternative strategies for constructing accurate RB spaces using greedy algorithms and proper orthogonal decomposition techniques, investigate their approximation properties and analyze offline-online decomposition strategies aimed at the reduction of computational complexity. Furthermore, they carry out both a priori and a posteriori error analysis. The whole mathematical presentation is made more stimulating by the use of representative examp...
A contribution to continuous-time quadrature bandpass sigma-delta modulators for low-IF receivers
Kim, Song-Bok
2009-01-01
This work presents the implementation of the continuous-time quadrature bandpass sigma-delta modulators (CT-QBP SDMs). CT-QBP SDMs is well suited for low-IF receivers due to some significant advantages over other implementations. Firstly, the possible design methodologies have been defined and compared. The proposed inverse method is desirable for the design of CT-QBP SDM. Starting from CT loop filter optimization, the equivalent noise shaping transfer function is finally calculated and its s...
Ambruş, Victor Eugen; Sofonea, Victor
2014-04-01
The Gauss-Laguerre quadrature method is used on the Cartesian semiaxes in the momentum space to construct a family of lattice Boltzmann models. When all quadrature orders Qx, Qy, Qz equal N+1, the Laguerre lattice Boltzmann model LLB(Qx,Qy,Qz) exactly recovers all moments up to order N of the Maxwell-Boltzmann equilibrium distribution function f(eq), calculated over any Cartesian octant of the three-dimensional momentum space. Results of Couette flow simulations at Kn=0.1, 0.5, 1.0 and in the ballistic regime are reported. Specific microfluidic effects (velocity slip, temperature jump, longitudinal heat flux) are well captured up to Kn=0.5, as demonstrated by comparison to direct simulation Monte Carlo results. Excellent agreement with analytic results is obtained in the ballistic regime.
Directory of Open Access Journals (Sweden)
Nicola Ponara
2012-11-01
Full Text Available Regularized Heaviside and Dirac delta function are used in several fields of computational physics and mechanics. Hence the issue of the quadrature of integrals of discontinuous and singular functions arises. In order to avoid ad-hoc quadrature procedures, regularization of the discontinuous and the singular fields is often carried out. In particular, weight functions of the signed distance with respect to the discontinuity interface are exploited. Tornberg and Engquist (Journal of Scientific Computing, 2003, 19: 527–552 proved that the use of compact support weight function is not suitable because it leads to errors that do not vanish for decreasing mesh size. They proposed the adoption of non-compact support weight functions. In the present contribution, the relationship between the Fourier transform of the weight functions and the accuracy of the regularization procedure is exploited. The proposed regularized approach was implemented in the eXtended Finite Element Method. As a three-dimensional example, we study a slender solid characterized by an inclined interface across which the displacement is discontinuous. The accuracy is evaluated for varying position of the discontinuity interfaces with respect to the underlying mesh. A procedure for the choice of the regularization parameters is proposed.
Explicit Gaussian quadrature rules for C^1 cubic splines with symmetrically stretched knot sequence
Ait-Haddou, Rachid
2015-06-19
We provide explicit expressions for quadrature rules on the space of C^1 cubic splines with non-uniform, symmetrically stretched knot sequences. The quadrature nodes and weights are derived via an explicit recursion that avoids an intervention of any numerical solver and the rule is optimal, that is, it requires minimal number of nodes. Numerical experiments validating the theoretical results and the error estimates of the quadrature rules are also presented.
Savoye, Philippe
2009-01-01
In recent years, I started covering difference equations and z transform methods in my introductory differential equations course. This allowed my students to extend the "classical" methods for (ordinary differential equation) ODE's to discrete time problems arising in many applications.
Directory of Open Access Journals (Sweden)
R. Nandi
2009-01-01
Full Text Available A new dual-input differential input active integrator using a current differencing buffered amplifier (CDBA is proposed. A multiplier element is appropriately used in the circuit whose control voltage (Vc tunes the integrator time constant (τ electronically. The design of a voltage controlled quadrature oscillator (VCQO based on the proposed integrator had been satisfactorily implemented. A new type of measurement for the tuning error of the oscillator based on the Nyquist plot is presented that shows an error of only 2% at fo≈ 1 MHz with Total Harmonic Distortion (THD less than 3%.
Study of rat neuronal genes with ordered differential display method
Institute of Scientific and Technical Information of China (English)
KANG; Jiansheng; (
2001-01-01
［1］Wang, Y., Du, Z. W., eds., Neurobiology and Molecular Biology, Beijing: People's Medical Publishing House, 1997, 184-207, 244-248.［2］Liang, P., Pardee, A., Differential display of eukaryotic messenger RNA by means of the polymerase chain reaction, Science, 1992, 257: 967-971.［3］Michiels, L., Van Leuven, F., van den Oord, J. J. et al., Representational difference analysis using minute quantities of DNA, Nucleic Acids Res., 1998, 26(15): 3608-3610.［4］Diatchenko, L., Lau, Y. F., Campbell, A. P. et al., Suppression subtractive hybridization: a method for generating differentially regulated or tissue-specific cDNA probes and libraries, Proc. Natl. Acad. Sci. USA, 1996, 93(12): 6025-6030.［5］Matz, M., Lukyanov, S., Different strategies of differential display: areas of application, Nucleic Acids Res., 1998, 26: 5537-5543.［6］Matz, M., Usman, N., Shagin, D. et al., Ordered differential display: a simple method for systematic comparison of gene expression profiles, Nucleic Acids Res, 1997, 25: 2541-2542.［7］Chen, X. X., Guan, L. C., Bao, S. M. et al., Comparison and study of memory and open field behavior of four different mouse strain, Psychological Science, 1994, 17(1): 39-41.［8］Chapman, C. R., Casey, K. L., Dubner, R. et al., Pain measurement: an overview, Pain, 1985, 22: 1-31.［9］Mitchell, .D., Hellon, R. F., Neuronal and behavioral responses in rats during noxious stimulation of the tail, Proc. R. Soc. Lond., 1977, 197: 169-194.［10］Shen, Y., Yan, Y. S., eds., Medical Statistics, Shanghai: Shanghai Medical University Press, 1999, 39-44.［11］Kang, J. S., Li, R. X., Du, Y. C., Ordered differential display, Chemistry of Life, 1999, 19(6): 282-283.［12］Mou, L., Miller, H., Li, J. et al., Improvements to the differential display method for gene analysis, Biochem. Biophys. Res. Commun., 1994, 199: 564-569.［13］Lee, H. N., Weinstock, K. G., Kirkness, E. F. et al., Comparative expressed-sequence-tag analysis of differential gene
Method and apparatus for calibrating a linear variable differential transformer
Pokrywka, Robert J.
2005-01-18
A calibration apparatus for calibrating a linear variable differential transformer (LVDT) having an armature positioned in au LVDT armature orifice, and the armature able to move along an axis of movement. The calibration apparatus includes a heating mechanism with an internal chamber, a temperature measuring mechanism for measuring the temperature of the LVDT, a fixture mechanism with an internal chamber for at least partially accepting the LVDT and for securing the LVDT within the heating mechanism internal chamber, a moving mechanism for moving the armature, a position measurement mechanism for measuring the position of the armature, and an output voltage measurement mechanism. A method for calibrating an LVDT, including the steps of: powering the LVDT; heating the LVDT to a desired temperature; measuring the position of the armature with respect to the armature orifice; and measuring the output voltage of the LVDT.
Null quadrature domains and a free boundary problem for the Laplacian
Karp, Lavi
2010-01-01
Null quadrature domains are unbounded domains in $\\R^n$ ($n \\geq 2$) with external gravitational force zero in some generalized sense. In this paper we prove a quadratic growth estimate of the Schwarz potential of a null quadrature domain and conclude by a theorem of Caffarelli, Karp and Shahgolian that any null quadrature domain is the complement of a convex set with analytic boundary. Using this result we prove that a null quadrature domain with a non-zero upper Lebesgue density at infinity is half-space.
The best quadrature formula based on Hermite information for the class KW2[a,b
Institute of Scientific and Technical Information of China (English)
WANG; Xinghua; MI; Xiangjiang
2005-01-01
The best quadrature formula has been found in the following sense: for a function whose norm of the second derivative is bounded by a given constant and the best quadrature formula for the approximate evaluation of integration of that function can minimize the worst possible error if the values of the function and its derivative at certain nodes are known.The best interpolation formula used to get the quadrature formula above is also found.Moreover,we compare the best quadrature formula with the open compound corrected trapezoidal formula by theoretical analysis and stochastic experiments.
Gaussian quadrature rules for C 1 quintic splines with uniform knot vectors
Bartoň, Michael
2017-03-21
We provide explicit quadrature rules for spaces of C1C1 quintic splines with uniform knot sequences over finite domains. The quadrature nodes and weights are derived via an explicit recursion that avoids numerical solvers. Each rule is optimal, that is, requires the minimal number of nodes, for a given function space. For each of nn subintervals, generically, only two nodes are required which reduces the evaluation cost by 2/32/3 when compared to the classical Gaussian quadrature for polynomials over each knot span. Numerical experiments show fast convergence, as nn grows, to the “two-third” quadrature rule of Hughes et al. (2010) for infinite domains.
Planar quadrature coil design using shielded-loop resonators
DEFF Research Database (Denmark)
Stensgaard, A
1997-01-01
The shielded-loop resonator is known to have a low capacitive sample loss due to a perfect balancing. In this paper, it is demonstrated that shielded-loop technology also can be used to improve design of planar quadrature coils. Both a dual-loop circuit and especially a dual-mode circuit may...... benefit from use of shielded-loop resonators. Observations in measurements agree with theory for both a dual-loop coil and a dual-mode coil. The coils were designed for use as transmit/receive coil for 1H imaging and spectroscopy at 4.7 T in rat brain....
An automatically controlled predistorter for multilevel quadrature amplitude modulation
Namiki, J.
1983-05-01
In digital microwave transmission, the nonlinear characteristics in a high power amplifier, such as a TWT (traveling-wave tube), inhibit efficient output use. This note introduces a new predistorter control technique, and assesses the nonlinear compensation capability of a third-order predistorter incorporating this technique. Concerning 16-QAM (quadrature amplitude modulation), a 10 dB reduction in out-of-band emission and larger than 8 dB C/N improvement with respect to symbol error rate can be achieved at 3 dB TWT average output power backoff.
Photoacoustic Tomography using a Michelson Interferometer with Quadrature Phase Detection
Speirs, Rory W
2013-01-01
We present a pressure sensor based on a Michelson interferometer, for use in photoacoustic tomography. Quadrature phase detection is employed allowing measurement at any point on the mirror surface without having to retune the interferometer, as is typically required by Fabry-Perot type detectors. This opens the door to rapid full surface detection, which is necessary for clinical applications. Theory relating acoustic pressure to detected acoustic particle displacements is used to calculate the detector sensitivity, which is validated with measurement. Proof-of-concept tomographic images of blood vessel phantoms have been taken with sub-millimeter resolution at depths of several millimeters.
In-phase and quadrature imbalance modeling, estimation, and compensation
Li, Yabo
2013-01-01
This book provides a unified IQ imbalance model and systematically reviews the existing estimation and compensation schemes. It covers the different assumptions and approaches that lead to many models of IQ imbalance. In wireless communication systems, the In-phase and Quadrature (IQ) modulator and demodulator are usually used as transmitter (TX) and receiver (RX), respectively. For Digital-to-Analog Converter (DAC) and Analog-to-Digital Converter (ADC) limited systems, such as multi-giga-hertz bandwidth millimeter-wave systems, using analog modulator and demodulator is still a low power and l
Bearing diagnostics: A method based on differential geometry
Tian, Ye; Wang, Zili; Lu, Chen; Wang, Zhipeng
2016-12-01
The structures around bearings are complex, and the working environment is variable. These conditions cause the collected vibration signals to become nonlinear, non-stationary, and chaotic characteristics that make noise reduction, feature extraction, fault diagnosis, and health assessment significantly challenging. Thus, a set of differential geometry-based methods with superiorities in nonlinear analysis is presented in this study. For noise reduction, the Local Projection method is modified by both selecting the neighborhood radius based on empirical mode decomposition and determining noise subspace constrained by neighborhood distribution information. For feature extraction, Hessian locally linear embedding is introduced to acquire manifold features from the manifold topological structures, and singular values of eigenmatrices as well as several specific frequency amplitudes in spectrograms are extracted subsequently to reduce the complexity of the manifold features. For fault diagnosis, information geometry-based support vector machine is applied to classify the fault states. For health assessment, the manifold distance is employed to represent the health information; the Gaussian mixture model is utilized to calculate the confidence values, which directly reflect the health status. Case studies on Lorenz signals and vibration datasets of bearings demonstrate the effectiveness of the proposed methods.
Novel determination of differential-equation solutions: universal approximation method
Leephakpreeda, Thananchai
2002-09-01
In a conventional approach to numerical computation, finite difference and finite element methods are usually implemented to determine the solution of a set of differential equations (DEs). This paper presents a novel approach to solve DEs by applying the universal approximation method through an artificial intelligence utility in a simple way. In this proposed method, neural network model (NNM) and fuzzy linguistic model (FLM) are applied as universal approximators for any nonlinear continuous functions. With this outstanding capability, the solutions of DEs can be approximated by the appropriate NNM or FLM within an arbitrary accuracy. The adjustable parameters of such NNM and FLM are determined by implementing the optimization algorithm. This systematic search yields sub-optimal adjustable parameters of NNM and FLM with the satisfactory conditions and with the minimum residual errors of the governing equations subject to the constraints of boundary conditions of DEs. The simulation results are investigated for the viability of efficiently determining the solutions of the ordinary and partial nonlinear DEs.
Hooked differential mobility spectrometry apparatus and method therefore
Shvartsburg, Alexandre A [Richland, WA; Tang, Keqi [Richland, WA; Ibrahim, Yehia M [Richland, WA; Smith, Richard D [Richland, WA
2009-02-17
Disclosed are a device and method for improved interfacing of differential mobility spectrometry (DMS) or field asymmetric waveform ion mobility spectrometry (FAIMS) analyzers of substantially planar geometry to subsequent or preceding instrument stages. Interfacing is achieved using curved DMS elements, where a thick ion beam emitted by planar DMS analyzers or injected into them for ion filtering is compressed to the gap median by DMS ion focusing effect in a spatially inhomogeneous electric field. Resulting thinner beams are more effectively transmitted through necessarily constrained conductance limit apertures to subsequent instrument stages operated at a pressure lower than DMS, and/or more effectively injected into planar DMS analyzers. The technology is synergetic with slit apertures, slit aperture/ion funnels, and high-pressure ion funnel interfaces known in the art which allow for increasing cross-sectional area of MS inlets. The invention may be used in integrated analytical platforms, including, e.g., DMS/MS, LC/DMS/MS, and DMS/IMS/MS that could replace and/or enhance current LC/MS methods, e.g., for proteomics research.
Energy Technology Data Exchange (ETDEWEB)
Wunschel, David S.; Melville, Angela M.; Ehrhardt, Christopher J.; Colburn, Heather A.; Victry, Kristin D.; Antolick, Kathryn C.; Wahl, Jon H.; Wahl, Karen L.
2012-05-17
The investigation of crimes involving chemical or biological agents is infrequent, but presents unique analytical challenges. The protein toxin ricin is encountered more frequently than other agents and is found in the seeds of the castor plant Ricinus communis. Typically, the toxin is extracted from castor seeds utilizing a variety of different recipes that result in varying purity of the toxin. Moreover, these various purification steps can also leave or differentially remove a variety of exogenous and endogenous residual components with the toxin that may indicate the type and number of purification steps involved. We have applied three gas chromatographic - mass spectrometric (GC-MS) based analytical methods to measure the variation in seed carbohydrates and castor oil ricinoleic acid as well as the presence of solvents used for purification. These methods were applied to the same samples prepared using four previously identified toxin preparation methods starting from four varieties of castor seeds. The individual data sets for seed carbohydrate profiles, ricinoleic acid or acetone amount each provided information capable of differentiating different types of toxin preparations across seed types. However, the integration of the data sets using multivariate factor analysis provided a clear distinction of all samples based on the preparation method and independent of the seed source. In particular the abundance of mannose, arabinose, fucose, ricinoleic acid and acetone were shown to be important differentiating factors. These complementary tools provide a more confident determination of the method of toxin preparation.
Energy Technology Data Exchange (ETDEWEB)
Rafiq, Arif [Department of Mathematics, COMSATS Institute of Information Technology, Islamabad (Pakistan)], E-mail: arafiq@comsats.edu.pk; Ahmed, Munshoor [Department of Mathematics, COMSATS Institute of Information Technology, Islamabad (Pakistan)], E-mail: ahmed.manshoor@gmail.com; Hussain, Sifat [CASPAM, Bahauddin Zakariya University, Multan (Pakistan)], E-mail: siffat2002@gmail.com
2008-07-21
Homotopy perturbation method is used to solve specific second order ordinary differential equations and tested for different examples. The results obtained demonstrate efficiency of the proposed method.
Electrostatic stiffness correction for quadrature error in decoupled dual-mass MEMS gyroscope
Li, Hongsheng; Cao, Huiliang; Ni, Yunfang
2014-07-01
This paper proposes an electrostatic stiffness correction method for the quadrature error (QUER) in a decoupled dual-mass gyroscope structure. The QUER is caused by the imperfections during the structure manufacturing process, and the two masses usually have different QUERs. The harm contribution to the Coriolis signal is analyzed and quantified. The generating forms of QUER motion in both masses are analyzed, the correction electrodes' working principle is introduced, and a single mass individual correction method is proposed. The QUER stiffness correction system is designed based on a PI controller, and the experiments are arranged to verify the theoretical analysis. The bias stability decreases from 2.06 to 0.64 deg/h after the QUER correction, and the parameters of scale factor such as nonlinearly, asymmetry, and repeatability, reduce from 143, 557, and 210 ppm to 84, 242, and 175 ppm, respectively.
Rivera-Ortega, Uriel; Meneses-Fabian, Cruz; Rodriguez-Zurita, Gustavo; Robledo-Sanchez, Carlos
2014-04-01
An alternative method for phase retrieval based on spatial and binary non-quadrature amplitude modulation (NQAM) is presented. This proposal is based on the superposition of a probe beam with a reference beam modulated in phase and amplitude (PAM) by NQAM, which is implemented by two neutral density filters (NDF) in a three-beam Mach-Zehnder interferometer (MZI). The principal advantage of this proposal lies in an analytical relationship between the variations of phase and visibility in an interferogram with the variations in the amplitudes of the reference beams used to implement NQAM; thus, the interferograms can be normalized and their introduced phase variations can be known from the measured intensities. Consequently it is possible to successfully retrieve the object phase. It is worthy to note that this method is capable of accepting that the phase and visibility variations in the interferograms could be spatial functions.
Hadjesfandiari, Ali R
2010-01-01
A boundary element formulation is developed to determine the complex stress intensity factors associated with cracks on the interface between dissimilar materials. This represents an extension of the methodology developed previously by the authors for determination of free-edge generalized stress intensity factors on bi-material interfaces, which employs displacements and weighted tractions as primary variables. However, in the present work, the characteristic oscillating stress singularity is addressed through the introduction of complex weighting functions for both displacements and tractions, along with corresponding non-standard numerical quadrature formulas. As a result, this boundary-only approach provides extremely accurate mesh-independent solutions for a range of two-dimensional interface crack problems. A number of computational examples are considered to assess the performance of the method in comparison with analytical solutions and previous work on the subject. As a final application, the method ...
Solving Fractional Partial Differential Equations with Corrected Fourier Series Method
Directory of Open Access Journals (Sweden)
Nor Hafizah Zainal
2014-01-01
Full Text Available The corrected Fourier series (CFS is proposed for solving partial differential equations (PDEs with fractional time derivative on a finite domain. In the previous work, we have been solving partial differential equations by using corrected Fourier series. The fractional derivatives are described in Riemann sense. Some numerical examples are presented to show the solutions.
Solvability of a Lie algebra of vector fields implies their integrability by quadratures
Cariñena, J. F.; Falceto, F.; Grabowski, J.
2016-10-01
We present a substantial generalisation of a classical result by Lie on integrability by quadratures. Namely, we prove that all vector fields in a finite-dimensional transitive and solvable Lie algebra of vector fields on a manifold can be integrated by quadratures.
The Nature of the Nodes, Weights and Degree of Precision in Gaussian Quadrature Rules
Prentice, J. S. C.
2011-01-01
We present a comprehensive proof of the theorem that relates the weights and nodes of a Gaussian quadrature rule to its degree of precision. This level of detail is often absent in modern texts on numerical analysis. We show that the degree of precision is maximal, and that the approximation error in Gaussian quadrature is minimal, in a…
Novel IQ imbalance and offset compensation techniques for quadrature mixing radio transceivers
CSIR Research Space (South Africa)
De Witt, JJ
2006-09-01
Full Text Available Despite the advantages that quadrature mixing offers to radio front-ends, its practical use has been limited due to its sensitivity towards gain and phase mismatches between its in-phase and quadrature channels. DC offsets are also a problem when a...
Development of Galerkin Method for Solving the Generalized Burger's-Huxley Equation
Directory of Open Access Journals (Sweden)
M. El-Kady
2013-01-01
Full Text Available Numerical treatments for the generalized Burger's—Huxley GBH equation are presented. The treatments are based on cardinal Chebyshev and Legendre basis functions with Galerkin method. Gauss quadrature formula and El-gendi method are used to convert the problem into a system of ordinary differential equations. The numerical results are compared with the literatures to show efficiency of the proposed methods.
Differential Mobility Spectrometer with Spatial Ion Detector and Methods Related Thereto
Duong, Tuan A. (Inventor); Kanik, Isik (Inventor); Duong, Vu A. (Inventor)
2013-01-01
Differential mobility spectrometer with spatial ion detector and methods related thereto are disclosed. The use of one or more spatial detector within differential mobility spectrometry can provide for the identification and separation of ions with similar mobility and mass.
Ismail, Azman; Ahmad, Rokiah Rozita; Din, Ummul Khair Salma; Hamid, Mohd Rosli A.
2014-09-01
This study is based on third order multistep method using interpolation formula. The coefficients of new formula are produced using modification on interpolation. This method is tested on ordinary differential equations. Comparisons are between the modified method and the classical Adams Bashforth. Mathematica software is used to determine the new coefficients. The methods was found to be efficient when tested on ordinary differential equation.
Energy Technology Data Exchange (ETDEWEB)
Zhao Xiqiang [Department of Mathematics, Ocean University of China, Qingdao Shandong 266071 (China)] e-mail: zhaodss@yahoo.com.cn; Wang Limin [Shandong University of Technology, Zibo Shandong 255049 (China); Sun Weijun [Shandong University of Technology, Zibo Shandong 255049 (China)
2006-04-01
In this letter, a new method, called the repeated homogeneous balance method, is proposed for seeking the traveling wave solutions of nonlinear partial differential equations. The Burgers-KdV equation is chosen to illustrate our method. It has been confirmed that more traveling wave solutions of nonlinear partial differential equations can be effectively obtained by using the repeated homogeneous balance method.
Parallel-quadrature phase-shifting digital holographic microscopy using polarization beam splitter.
Das, Bhargab; Yelleswarapu, Chandra S; Rao, Dvgln
2012-11-01
We present a digital holography microscopy technique based on parallel-quadrature phase-shifting method. Two π/2 phase-shifted holograms are recorded simultaneously using polarization phase-shifting principle, slightly off-axis recording geometry, and two identical CCD sensors. The parallel phase-shifting is realized by combining circularly polarized object beam with a 45° degree polarized reference beam through a polarizing beam splitter. DC term is eliminated by subtracting the two holograms from each other and the object information is reconstructed after selecting the frequency spectrum of the real image. Both amplitude and phase object reconstruction results are presented. Simultaneous recording eliminates phase errors caused by mechanical vibrations and air turbulences. The slightly off-axis recording geometry with phase-shifting allows a much larger dimension of the spatial filter for reconstruction of the object information. This leads to better reconstruction capability than traditional off-axis holography.
Quadrature Slotted Surface Coil Pair for Magnetic Resonance Imaging at 4 Tesla: Phantom Study
Directory of Open Access Journals (Sweden)
Solis S.E.
2012-01-01
Full Text Available A coil array was composed of two slotted surface coils forming a structure with two plates at 900, each one having 6 circular slots and is introduced in this paper. Numerical simulations of the magnetic field of this coil array were performed at 170 MHz using the finite element method to study its behaviour. This coil array was developed for brain magnetic resonance imaging to be operated at the resonant frequency of 170 MHz in the transceiver mode and quadrature driven. Numerical simulations demonstrated that electromagnetic interaction between the coil elements is negligible, and that the magnetic field showed a good uniformity. Phantom images were acquired with our coil array and standard pulse sequences on a research-dedicated 4 Tesla scanner. In vitro images showed the feasibility of this coil array for standard pulses and high field magnetic resonance imaging.
Utilizing Gauss-Hermite Quadrature to Evaluate Uncertainty in Dynamic System Response
Energy Technology Data Exchange (ETDEWEB)
Field, R.V.; Paez, T.L.; Red-Horse, J.R.
1998-11-17
Probabilistic uncertainty is a phenomenon that occurs to a certain degree in many engineering!~ applications. The effects that the uncertainty has upon a given system response is a matter of some concern. Techniques which provide insight to these effects will be required as modeling and prediction become a more vital tool in the engineering design process. As might be expected, this is a difficult proposition and the focus of many research efforts. The purpose of this paper is to outline a procedure to evaluate uncertainty in dynamic system response exploiting Gauss-Hermite numerical quadrature. Specifically numerical integration techniques are utilized in conjunction with the Advanced Mean Value method to efficiently and accurately estimate moments of the response process. A numerical example illustrating the use of this analytical tool in a practical framework is presented.
Utilizing Gauss-Hermite Quadrature to Evaluate Uncertainty in Dynamic System Response
Energy Technology Data Exchange (ETDEWEB)
Field, R.V.; Paez, T.L.; Red-Horse, J.R.
1998-11-17
Probabilistic uncertainty is a phenomenon that occurs to a certain degree in many engineering!~ applications. The effects that the uncertainty has upon a given system response is a matter of some concern. Techniques which provide insight to these effects will be required as modeling and prediction become a more vital tool in the engineering design process. As might be expected, this is a difficult proposition and the focus of many research efforts. The purpose of this paper is to outline a procedure to evaluate uncertainty in dynamic system response exploiting Gauss-Hermite numerical quadrature. Specifically numerical integration techniques are utilized in conjunction with the Advanced Mean Value method to efficiently and accurately estimate moments of the response process. A numerical example illustrating the use of this analytical tool in a practical framework is presented.
The numerical solution of differential-algebraic systems by Runge-Kutta methods
Hairer, Ernst; Lubich, Christian
1989-01-01
The term differential-algebraic equation was coined to comprise differential equations with constraints (differential equations on manifolds) and singular implicit differential equations. Such problems arise in a variety of applications, e.g. constrained mechanical systems, fluid dynamics, chemical reaction kinetics, simulation of electrical networks, and control engineering. From a more theoretical viewpoint, the study of differential-algebraic problems gives insight into the behaviour of numerical methods for stiff ordinary differential equations. These lecture notes provide a self-contained and comprehensive treatment of the numerical solution of differential-algebraic systems using Runge-Kutta methods, and also extrapolation methods. Readers are expected to have a background in the numerical treatment of ordinary differential equations. The subject is treated in its various aspects ranging from the theory through the analysis to implementation and applications.
Method for HEPA filter leak scanning with differentiating aerosol detector
Energy Technology Data Exchange (ETDEWEB)
Kovach, B.J.; Banks, E.M.; Wikoff, W.O. [NUCON International, Inc., Columbus, OH (United States)
1997-08-01
While scanning HEPA filters for leaks with {open_quotes}Off the Shelf{close_quote} aerosol detection equipment, the operator`s scanning speed is limited by the time constant and threshold sensitivity of the detector. This is based on detection of the aerosol density, where the maximum signal is achieved when the scanning probe resides over the pinhole longer than several detector time-constants. Since the differential value of the changing signal can be determined by observing only the first small fraction of the rising signal, using a differentiating amplifier will speed up the locating process. The other advantage of differentiation is that slow signal drift or zero offset will not interfere with the process of locating the leak, since they are not detected. A scanning hand-probe attachable to any NUCON{reg_sign} Aerosol Detector displaying the combination of both aerosol density and differentiated signal was designed. 3 refs., 1 fig.
Directory of Open Access Journals (Sweden)
Shaheed N. Huseen
2013-01-01
Full Text Available A modified q-homotopy analysis method (mq-HAM was proposed for solving nth-order nonlinear differential equations. This method improves the convergence of the series solution in the nHAM which was proposed in (see Hassan and El-Tawil 2011, 2012. The proposed method provides an approximate solution by rewriting the nth-order nonlinear differential equation in the form of n first-order differential equations. The solution of these n differential equations is obtained as a power series solution. This scheme is tested on two nonlinear exactly solvable differential equations. The results demonstrate the reliability and efficiency of the algorithm developed.
Design of an MRI quadrature-data acquisition card
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
A design of a quadrature-data acquisition card based on peripheral component interconnect (PCI) bus for mini-type magnetic resonance imaging (MRI) system is reported. It uses two high speed analog-to-digital converters (ADCs) to sample the MRI signals and two static random access memories (SRAMs) to store the data which will be read to the computer by PCI bus after sampling. All the logic control signals on the card are generated by the field programmable gate array (FPGA). The software Foundation3.1 is used to design the FPGA and achieve useful result after simulating and implementing. The card has some merits that normal commercial cards do not have. For example, the sampling parameters can be varied according to different pulse sequences.
Increasing the Reliability of Adaptive Quadrature Using Explicit Interpolants
Gonnet, Pedro
2010-01-01
We present two new adaptive quadrature routines. Both routines differ from previously published algorithms in many aspects, most significantly in how they represent the integrand, how they treat non-numerical values of the integrand, how they deal with improper divergent integrals and how they estimate the integration error. The main focus of these improvements is to increase the reliability of the algorithms without significantly impacting their efficiency. Both algorithms are implemented in Matlab and tested using both the ``families'' suggested by Lyness and Kaganove and the battery test used by Gander and Gautschi and Kahaner. They are shown to be more reliable, albeit in some cases less efficient, than other commonly-used adaptive integrators.
Two-step greedy algorithm for reduced order quadratures
Antil, Harbir; Herrmann, Frank; Nochetto, Ricardo H; Tiglio, Manuel
2012-01-01
We present an algorithm to generate application-specific, global reduced order quadratures (ROQ) for multiple fast evaluations of weighted inner products between parameterized functions. If a reduced basis (RB) or any other projection-based model reduction technique is applied, the dimensionality of integrands is reduced dramatically; however, the cost of evaluating the reduced integrals still scales as the size of the original problem. In contrast, using discrete empirical interpolation (DEIM) points as ROQ nodes leads to a computational cost which depends linearly on the dimension of the reduced space. Generation of a reduced basis via a greedy procedure requires a training set, which for products of functions can be very large. Since this direct approach can be impractical in many applications, we propose instead a two-step greedy targeted towards approximation of such products. We present numerical experiments demonstrating the accuracy and the efficiency of the two-step approach. The presented ROQ are ex...
Single mode quadrature entangled light from room temperature atomic vapour
Wasilewski, W; Jensen, K; Madsen, L S; Krauter, H; Polzik, E S
2009-01-01
We analyse a novel squeezing and entangling mechanism which is due to correlated Stokes and anti-Stokes photon forward scattering in a multi-level atom vapour. Following the proposal we present an experimental demonstration of 3.5 dB pulsed frequency nondegenerate squeezed (quadrature entangled) state of light using room temperature caesium vapour. The source is very robust and requires only a few milliwatts of laser power. The squeezed state is generated in the same spatial mode as the local oscillator and in a single temporal mode. The two entangled modes are separated by twice the Zeeman frequency of the vapour which can be widely tuned. The narrow-band squeezed light generated near an atomic resonance can be directly used for atom-based quantum information protocols. Its single temporal mode characteristics make it a promising resource for quantum information processing.
Quadrature Uncertainty and Information Entropy of Quantum Elliptical Vortex States
Banerji, Anindya; Singh, Ravindra Pratap; Chowdhury, Saurav; Bandyopadhyay, Abir
2013-01-01
We study the quadrature uncertainty of the quantum elliptical vortex state using the associated Wigner function. Deviations from the minimum uncertainty states were observed due to the absence of the Gaussian nature. In our study of the entropy, we noticed that with increasing vorticity, entropy increases for both the modes. We further observed that, there exists an optimum value of ellipticity which gives rise to maximum entanglement of the two modes of the quantum elliptical vortex states. A further increase in ellipticity reduces the entropy thereby resulting in a loss of information carrying capacity. We check the validity of the entropic inequality relations, namely the subaddivity and the Araki-Lieb inequality. The later was satisfied only for a very small range of the ellipticity of the vortex while the former seemed to be valid at all values.
An integrated source of broadband quadrature squeezed light
Hoff, Ulrich B; Andersen, Ulrik L
2015-01-01
An integrated silicon nitride resonator is proposed as an ultra-compact source of bright single-mode quadrature squeezed light at 850 nm. Optical properties of the device are investigated and tailored through numerical simulations, with particular attention paid to loss associated with interfacing the device. An asymmetric double layer stack waveguide geometry with inverse vertical tapers is proposed for efficient and robust fibre-chip coupling, yielding a simulated total loss of -0.75 dB/facet. We assess the feasibility of the device through a full quantum noise analysis and derive the output squeezing spectrum for intra-cavity pump self-phase modulation. Subject to standard material loss and detection efficiencies, we find that the device holds promises for generating substantial quantum noise squeezing over a bandwidth exceeding 1 GHz. In the low-propagation loss regime, approximately -7 dB squeezing is predicted for a pump power of only 50 mW.
Institute of Scientific and Technical Information of China (English)
黄思训; 杜华栋; 韩威
2004-01-01
The generalized variational data assimilation for non-differential dynamical systems is studied.There is no tangent linear model for non-differential systems and thus the general adjoint model can not be derived in the traditional way.The weak form of the original system was introduced, and then the generalized adjoint model was derived. The generalized variational data assimilation methods were developed for non-differential low dimensional system and non-differential high dimensional system with global and local observations. Furthermore, ideas in inverse problems are introduced to 4DVAR (Four-dimensional variational) of non-differential partial differential system with local observations.
Method of the Logistic Function for Finding Analytical Solutions of Nonlinear Differential Equations
Kudryashov, N. A.
2015-01-01
The method of the logistic function is presented for finding exact solutions of nonlinear differential equations. The application of the method is illustrated by using the nonlinear ordinary differential equation of the fourth order. Analytical solutions obtained by this method are presented. These solutions are expressed via exponential functions.logistic function, nonlinear wave, nonlinear ordinary differential equation, Painlev´e test, exact solution
Asymptotic stability properties of θ-methods for delay differential equations
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Deals with the asymptotic stability properties of θ- methods for the pantograph equation and the linear delay differential-algebraic equation with emphasis on the linear θ- methods with variable stepsize schemes for the pantograph equation, proves that asymptotic stability is obtained if and only if θ ＞ 1/2, and studies further the one-leg θ- method for the linear delay differential-algebraic equation and establishes the sufficient asymptotic-ally differential-algebraic stable condition θ = 1.
Solving linear fractional-order differential equations via the enhanced homotopy perturbation method
Energy Technology Data Exchange (ETDEWEB)
Naseri, E; Ghaderi, R; Sadati, J; Mahmoudian, M; Hosseinnia, S H [Intelligent System Research Group, Babol, Noushirvani University of Technology, Faculty of Electrical and Computer Engineering, PO Box 47135-484, Babol (Iran, Islamic Republic of); Ranjbar N, A [Golestan University, Gorgan (Iran, Islamic Republic of); Momani, S [Mutah University, PO Box 7, Al-Karak (Jordan)], E-mail: h.hoseinnia@stu.nit.ac.ir, E-mail: a.ranjbar@nit.ac.ir, E-mail: shahermm@yahoo.com
2009-10-15
The linear fractional differential equation is solved using the enhanced homotopy perturbation method (EHPM). In this method, the convergence has been provided by selecting a stabilizing linear part. The most significant features of this method are its simplicity and its excellent accuracy and convergence for the whole range of fractional-order differential equations.
Solving linear fractional-order differential equations via the enhanced homotopy perturbation method
Naseri, E.; Ghaderi, R.; Ranjbar N, A.; Sadati, J.; Mahmoudian, M.; Hosseinnia, S. H.; Momani, S.
2009-10-01
The linear fractional differential equation is solved using the enhanced homotopy perturbation method (EHPM). In this method, the convergence has been provided by selecting a stabilizing linear part. The most significant features of this method are its simplicity and its excellent accuracy and convergence for the whole range of fractional-order differential equations.
A SPECTRAL METHOD FOR PANTOGRAPH-TYPE DELAY DIFFERENTIAL EQUATIONS AND ITS CONVERGENCE ANALYSIS
Institute of Scientific and Technical Information of China (English)
Ishtiaq Ali; Hermann Brunner; Tao Tang
2009-01-01
We propose a novel numerical approach for delay differential equations with vanishing proportional delays based on spectral methods. A Legendre-collocation method is employed to obtain highly accurate numerical approximations to the exact solution. It is proved theoretically and demonstrated numerically that the proposed method converges exponentially provided that the data in the given pantograph delay differential equation are smooth.
Gaussian quadrature for splines via homotopy continuation: Rules for C2 cubic splines
Barton, Michael
2015-10-24
We introduce a new concept for generating optimal quadrature rules for splines. To generate an optimal quadrature rule in a given (target) spline space, we build an associated source space with known optimal quadrature and transfer the rule from the source space to the target one, while preserving the number of quadrature points and therefore optimality. The quadrature nodes and weights are, considered as a higher-dimensional point, a zero of a particular system of polynomial equations. As the space is continuously deformed by changing the source knot vector, the quadrature rule gets updated using polynomial homotopy continuation. For example, starting with C1C1 cubic splines with uniform knot sequences, we demonstrate the methodology by deriving the optimal rules for uniform C2C2 cubic spline spaces where the rule was only conjectured to date. We validate our algorithm by showing that the resulting quadrature rule is independent of the path chosen between the target and the source knot vectors as well as the source rule chosen.
Adaptive quadrature-polybinary detection in super-Nyquist WDM systems.
Chen, Sai; Xie, Chongjin; Zhang, Jie
2015-03-23
We propose an adaptive detection technique in super-Nyquist wavelength-division-multiplexed (WDM) polarization-division-multiplexed quadrature-phase-shift-keying (PDM-QPSK) systems, where a QPSK signal is digitally converted to a quadrature n-level polybinary signal followed by a MLSE detector at the receiver, and study the performance of quadrature-duobinary and quadrature four-level polybinary signals using this detection technique. We change the level of the quadrature-polybinary modulation at the coherent receiver according to the channel spacing of a super-Nyquist system. Numerical studies show that the best performance can be achieved by choosing different modulation levels at the receiver in adaption to the channel spacing. In the experiment, we demonstrate the transmission of 3-channel 112-Gbit/s PDM-QPSK signals at a 20-GHz channel spacing, which is detected as a quadrature four-level polybinary signal, with performance comparable to PDM 16-ary quadrature-amplitude modulation (16QAM) at the same bit rate.
Solution of (3+1-Dimensional Nonlinear Cubic Schrodinger Equation by Differential Transform Method
Directory of Open Access Journals (Sweden)
Hassan A. Zedan
2012-01-01
Full Text Available Four-dimensional differential transform method has been introduced and fundamental theorems have been defined for the first time. Moreover, as an application of four-dimensional differential transform, exact solutions of nonlinear system of partial differential equations have been investigated. The results of the present method are compared very well with analytical solution of the system. Differential transform method can easily be applied to linear or nonlinear problems and reduces the size of computational work. With this method, exact solutions may be obtained without any need of cumbersome work, and it is a useful tool for analytical and numerical solutions.
Eigenvalues of singular differential operators by finite difference methods. I.
Baxley, J. V.
1972-01-01
Approximation of the eigenvalues of certain self-adjoint operators defined by a formal differential operator in a Hilbert space. In general, two problems are studied. The first is the problem of defining a suitable Hilbert space operator that has eigenvalues. The second problem concerns the finite difference operators to be used.
Power decoupling method for single phase differential buck converter
DEFF Research Database (Denmark)
Yao, Wenli; Tang, Yi; Zhang, Xiaobin
2015-01-01
The well-known inherent second-order ripple power in single phase converters imposes harmonic stress on the dc link, resulting in low efficiency and overheating issues. In order to avoid installing bulky electrolytic capacitors or LC filters in the dc-link, this paper presents a differential buck...
A rapid differentiation method for enteroinvasive Escherichia coli.
Aribam, Swarmistha Devi; Hirota, Jiro; Kusumoto, Masahiro; Harada, Tomoyuki; Shiraiwa, Kazumasa; Ogawa, Yohsuke; Shimoji, Yoshihiro; Eguchi, Masahiro
2014-03-01
Enteroinvasive Escherichia coli (EIEC) comprise 21 major serotypes defined by the presence of O and H antigens, and diagnosis depends on determining its invasive potential. Using HEp-2 cells infected with an EIEC strain, we developed a simple growth-dependent assay that differentiated EIEC strain from non-invasive strains 6 h after infection.
Quadrature phase-shift error analysis using a homodyne laser interferometer.
Gregorcic, Peter; Pozar, Tomaz; Mozina, Janez
2009-08-31
The influence of quadrature phase shift on the measured displacement error was experimentally investigated using a two-detector polarizing homodyne laser interferometer with a quadrature detection system. Common nonlinearities, including the phase-shift error, were determined and effectively corrected by a robust data-processing algorithm. The measured phase-shift error perfectly agrees with the theoretically determined phase-shift error region. This error is systematic, periodic and severely asymmetrical around the nominal displacement value. The main results presented in this paper can also be used to assess and correct the detector errors of other interferometric and non-interferometric displacement-measuring devices based on phase-quadrature detection.
Uncontracted Rys Quadrature Implementation of up to G Functions on Graphical Processing Units.
Asadchev, Andrey; Allada, Veerendra; Felder, Jacob; Bode, Brett M; Gordon, Mark S; Windus, Theresa L
2010-03-09
An implementation is presented of an uncontracted Rys quadrature algorithm for electron repulsion integrals, including up to g functions on graphical processing units (GPUs). The general GPU programming model, the challenges associated with implementing the Rys quadrature on these highly parallel emerging architectures, and a new approach to implementing the quadrature are outlined. The performance of the implementation is evaluated for single and double precision on two different types of GPU devices. The performance obtained is on par with the matrix-vector routine from the CUDA basic linear algebra subroutines (CUBLAS) library.
Optimal displacement in apparent motion and quadrature models of motion sensing
Watson, Andrew B.
1990-01-01
A grating appears to move if it is displaced by some amount between two brief presentations, or between multiple successive presentations. A number of recent experiments have examined the influence of displacement size upon either the sensitivity to motion, or upon the induced motion aftereffect. Several recent motion models are based upon quadrature filters that respond in opposite quadrants in the spatiotemporal frequency plane. Predictions of the quadrature model are derived for both two-frame and multiframe displays. Quadrature models generally predict an optimal displacement of 1/4 cycle for two-frame displays, but in the multiframe case the prediction depends entirely on the frame rate.
B-Theory of Runge-Kutta methods for stiff Volterra functional differential equations
Institute of Scientific and Technical Information of China (English)
LI; Shoufu(李寿佛)
2003-01-01
B-stability and B-convergence theories of Runge-Kutta methods for nonlinear stiff Volterra func-tional differential equations (VFDEs) are established which provide unified theoretical foundation for the studyof Runge-Kutta methods when applied to nonlinear stiff initial value problems (IVPs) in ordinary differentialequations (ODEs), delay differential equations (DDEs), integro-differential equations (IDEs) and VFDEs ofother type which appear in practice.
Partial differential equations with variable exponents variational methods and qualitative analysis
Radulescu, Vicentiu D
2015-01-01
Partial Differential Equations with Variable Exponents: Variational Methods and Qualitative Analysis provides researchers and graduate students with a thorough introduction to the theory of nonlinear partial differential equations (PDEs) with a variable exponent, particularly those of elliptic type. The book presents the most important variational methods for elliptic PDEs described by nonhomogeneous differential operators and containing one or more power-type nonlinearities with a variable exponent. The authors give a systematic treatment of the basic mathematical theory and constructive meth
Simon, M. K.; Li, L.
2003-08-01
We show that MIL-STD shaped offset quadrature phase-shift keying (SOQPSK), a highly bandwidth-efficient constant-envelope modulation, can be represented in the form of a cross-correlated trellis-coded quadrature modulation, a generic structure containing both memory and cross-correlation between the in-phase and quadrature-phase channels. Such a representation allows identification of the optimum form of receiver for MIL-STD SOQPSK and at the same time, through modification of the equivalent I and Q encoders to recursive types, allows for it to be embedded as the inner code of a serial or parallel (turbo-like) concatenated coding structure together with iterative decoding.
Energy Technology Data Exchange (ETDEWEB)
Sanchez G, J., E-mail: julian.sanchez@inin.gob.mx [ININ, Carretera Mexico-Toluca s/n, 52750 Ocoyoacac, Estado de Mexico (Mexico)
2015-09-15
The solution of the so-called Canonical problems of neutron transport theory has been given by Case, who developed a method akin to the classical eigenfunction expansion procedure, extended to admit singular eigenfunctions. The solution is given as a set consisting of a Fredholm integral equation coupled with a transcendental equation, which has to be solved for the expansion coefficients by iteration. CASE's method make extensive use of the results of the theory of functions of a complex variable and many successful approaches to solve in an approximate form the above mentioned set have been reported in the literature. We present here an entirely different approach which deals with the canonical problems in a more direct and elementary manner. As far as we know, the original idea for the latter method is due to Carlvik who devised the escape probability approximation to the solution of the neutron transport equation in its integral form. In essence, the procedure consists in assuming a sectionally constant form of the neutron density that in turn yields a set of linear algebraic equations obeyed by the assumed constant values of the density. Very well established techniques of numerical analysis for the solution of integral equations consist in independent approaches that generalize the sectionally constant approach by assuming a sectionally low degree polynomial for the unknown function. This procedure also known as the arbitrary quadratures method is especially suited to deal with cases where the kernel of the integral equation is singular. The author wishes to present the results obtained with the arbitrary quadratures method for the numerical calculation of the monoenergetic neutron density in a critical, homogeneous sphere of finite radius with isotropic scattering. The singular integral equation obeyed by the neutron density in the critical sphere is introduced, an outline of the method's main features is given, and tables and graphs of the density
Numerical Solution of Fuzzy Differential Equations by Runge-Kutta Verner Method
Directory of Open Access Journals (Sweden)
T. Jayakumar
2015-01-01
Full Text Available In this paper we study the numerical methods for Fuzzy Differential equations by an application of the Runge-Kutta Verner method for fuzzy differential equations. We prove a convergence result and give numerical examples to illustrate the theory.
Energy Technology Data Exchange (ETDEWEB)
Zhang Huiqun [College of Mathematical Science, Qingdao University, Qingdao, Shandong 266071 (China)], E-mail: hellozhq@yahoo.com.cn
2009-02-15
By using some exact solutions of an auxiliary ordinary differential equation, a direct algebraic method is described to construct the exact complex solutions for nonlinear partial differential equations. The method is implemented for the NLS equation, a new Hamiltonian amplitude equation, the coupled Schrodinger-KdV equations and the Hirota-Maccari equations. New exact complex solutions are obtained.
Effect of Correlated Non-Gaussian Quadratures on the Performance of Binary Modulations
Directory of Open Access Journals (Sweden)
Valentine A. Aalo
2011-01-01
Full Text Available The received signal in many wireless communication systems comprises of the sum of waves with random amplitudes and random phases. In general, the composite signal consists of correlated nonidentical Gaussian quadrature components due to the central limit theorem (CLT. However, in the presence of a small number of random waves, the CLT may not always hold and the quadrature components may not be Gaussian distributed. In this paper, we assume that the fading environment is such that the quadrature components follow a correlated bivariate Student-t joint distribution. Then, we derive the envelope distribution of the received signal and obtain new expressions for the exact and high signal-to-noise (SNR approximate average BER for binary modulations. It also turns out that the derived envelope pdf approaches the Rayleigh and Hoyt distributions as limiting cases. Using the derived envelope pdf, we investigate the effect of correlated nonidentical quadratures on the error rate performance of digital communication systems.
Relation between the field quadratures and the characteristic function of a mirror
Energy Technology Data Exchange (ETDEWEB)
Rodriguez L, B.M.; Moya C, H. [INAOE, Coordinacion de Optica, A.P. 51 y 216, 72000 Puebla (Mexico)
2004-07-01
We analyse the possibility of measuring the state of a movable mirror by using its interaction with a quantum field. We show that measuring the field quadratures allows us to reconstruct the characteristic function corresponding to the mirror state. (Author)
Squeezed quadrature fluctuations in a gravitational wave detector using squeezed light.
Dwyer, S; Barsotti, L; Chua, S S Y; Evans, M; Factourovich, M; Gustafson, D; Isogai, T; Kawabe, K; Khalaidovski, A; Lam, P K; Landry, M; Mavalvala, N; McClelland, D E; Meadors, G D; Mow-Lowry, C M; Schnabel, R; Schofield, R M S; Smith-Lefebvre, N; Stefszky, M; Vorvick, C; Sigg, D
2013-08-12
Squeezed states of light are an important tool for optical measurements below the shot noise limit and for optical realizations of quantum information systems. Recently, squeezed vacuum states were deployed to enhance the shot noise limited performance of gravitational wave detectors. In most practical implementations of squeezing enhancement, relative fluctuations between the squeezed quadrature angle and the measured quadrature (sometimes called squeezing angle jitter or phase noise) are one limit to the noise reduction that can be achieved. We present calculations of several effects that lead to quadrature fluctuations, and use these estimates to account for the observed quadrature fluctuations in a LIGO gravitational wave detector. We discuss the implications of this work for quantum enhanced advanced detectors and even more sensitive third generation detectors.
Relation between the field quadratures and the characteristic function of a mirror
Rodríguez, B M
2002-01-01
We analyze the possibility of measuring the state of a movable mirror by using its interaction with a quantum field. We show that measuring the field quadratures allows to reconstruct the characteristic function corresponding to the mirror state.
Directly Solving Special Second Order Delay Differential Equations Using Runge-Kutta-Nyström Method
Directory of Open Access Journals (Sweden)
M. Mechee
2013-01-01
Full Text Available Runge-Kutta-Nyström (RKN method is adapted for solving the special second order delay differential equations (DDEs. The stability polynomial is obtained when this method is used for solving linear second order delay differential equation. A standard set of test problems is solved using the method together with a cubic interpolation for evaluating the delay terms. The same set of problems is reduced to a system of first order delay differential equations and then solved using the existing Runge-Kutta (RK method. Numerical results show that the RKN method is more efficient in terms of accuracy and computational time when compared to RK method. The methods are applied to a well-known problem involving delay differential equations, that is, the Mathieu problem. The numerical comparison shows that both methods are in a good agreement.
A novel approach to construct numerical methods for stochastic differential equations
Halidias, Nikolaos
2013-01-01
In this paper we propose a new numerical method for solving stochastic differential equations (SDEs). As an application of this method we propose an explicit numerical scheme for a super linear SDE for which the usual Euler scheme diverges.
DEFF Research Database (Denmark)
Mejlbro, Leif
1997-01-01
An alternative formula for the solution of linear differential equations of order n is suggested. When applicable, the suggested method requires fewer and simpler computations than the well-known method using Wronskians....
Velocity envelope of vector flow estimation with spatial quadrature
Kerr, Richard F.; Anderson, Martin E.
2003-05-01
We present the results of two studies investigating the optimal aperture configuration for maximized lateral blood flow velocity estimation using Heterodyned Spatial Quadrature. Our objective was to determine the maximum velocities that can be estimated at Doppler angles of 90 degrees and 60 degrees with a bias of less than 5% for both uniform scatterer motion in a tissue-mimicking phantom and blood-mimicking fluid circulated through a wall-less vessel flow phantom. Constant flow rates ranging from 3.0 to 18.0 ml/sec were applied in the flow phantom, producing expected peak velocities of 15.0 to 89.8 cm/sec under laminar flow conditions. Velocity estimates were obtained at each flow rate using 256 trials, with each trial consisting of an ensemble of 32 vectors. For an f/1 receive geometry with bi-lobed Hamming apodization, all peak flow velocities tested were estimated to within 5% of their expected values for both 90 degree and 60 degree Doppler angles. An f/2 receive geometry featuring bi-lobed Blackman apodization generally provided accurate lateral velocity estimates up to 71.9 cm/sec for a Doppler angle of 90 degrees, and accurate lateral component estimates up to 50.1 cm/sec for a 60 degree Doppler angle. The implications of these findings will be discussed.
Hollow vortices, capillary water waves and double quadrature domains
Energy Technology Data Exchange (ETDEWEB)
Crowdy, Darren G [Department of Mathematics, Imperial College London, 180 Queen' s Gate, London SW7 2AZ (United Kingdom); Roenby, Johan, E-mail: d.crowdy@imperial.ac.uk, E-mail: johan.roenby@gmail.com [DHI, Agern Allé 5, 2970 Hørsholm (Denmark)
2014-06-01
Two new classes of analytical solutions for hollow vortex equilibria are presented. One class involves a central hollow vortex, comprising a constant pressure region having non-zero circulation, surrounded by an n-polygonal array of point vortices with n⩾2. The solutions generalize the non-rotating polygonal point vortex configurations of Morikawa and Swenson (1971 Phys. Fluids 14 1058–73) to the case where the point vortex at the centre of the polygon is replaced by a hollow vortex. The results of Morikawa and Swenson would suggest that all equilibria for n≠3 will be linearly unstable to point vortex mode instabilities. However even the n = 3 case turns out to be unstable to a recently discovered displacement instability deriving from a resonance between the natural modes of an isolated circular hollow vortex. A second class of analytical solutions for periodic water waves co-travelling with a submerged point vortex row is also described. The analysis gives rise to new theoretical connections with free surface Euler flows with surface tension and, in particular, with Crapper's classical solutions for capillary water waves. It is pointed out that the equilibrium fluid regions found here have a mathematical interpretation as an abstract class of planar domains known as double quadrature domains. (ss 1)
Gökdoğan, Ahmet; Merdan, Mehmet; Yildirim, Ahmet
2012-01-01
The goal of this study is presented a reliable algorithm based on the standard differential transformation method (DTM), which is called the multi-stage differential transformation method (MsDTM) for solving Hantavirus infection model. The results obtanied by using MsDTM are compared to those obtained by using the Runge-Kutta method (R-K-method). The proposed technique is a hopeful tool to solving for a long time intervals in this kind of systems.
High-Order Quadratures for the Solution of Scattering Problems in Two Dimensions
2008-04-22
combination of high-order quadrature formulae, fast application of integral operators in Lippmann- Schwinger equations, and the stabilized biconjugate...functions in two and three dimensions; these are used to obtain rapidly convergent discretizations of Lippmann- Schwinger equations. The performance of the...Lippmann- Schwinger , High-Order, Quadratures, Singu- lar, Hankel 2 1 Introduction Forward scattering has been an active field of research in science
Numerical methods for the solution of ordinary differential equations
Azeem, M
1999-01-01
The ode 113 code solves non-stiff differential equations and is a fully variable step, variable order, PECE implementation in terms of modified divided differences of Adams-Bashforth-Moulton family of formulas of order 1-12. The main objectives of this project were to modify PECE mode of ode 113 into PEC mode, study the variable step size and variable order strategy of both the modes and finally, develop the switching strategy between both PECE and PEC modes to minimize the cost of solving the ordinary differential equations. Using some test problems (including stiff, mild stiff and non-stiff), it was found that the PEC mode was more efficient for non-stiff problems at crude and intermediate tolerances and the PECE mode for all problems at the stringent tolerance. An automatic switching strategy was developed using the results observed from the step size and order plots of all the test problems for both the modes and gave the optimum results.
Non-asymptotic fractional order differentiators via an algebraic parametric method
Liu, Dayan
2012-08-01
Recently, Mboup, Join and Fliess [27], [28] introduced non-asymptotic integer order differentiators by using an algebraic parametric estimation method [7], [8]. In this paper, in order to obtain non-asymptotic fractional order differentiators we apply this algebraic parametric method to truncated expansions of fractional Taylor series based on the Jumarie\\'s modified Riemann-Liouville derivative [14]. Exact and simple formulae for these differentiators are given where a sliding integration window of a noisy signal involving Jacobi polynomials is used without complex mathematical deduction. The efficiency and the stability with respect to corrupting noises of the proposed fractional order differentiators are shown in numerical simulations. © 2012 IEEE.
Energy Technology Data Exchange (ETDEWEB)
Odibat, Zaid [Prince Abdullah Bin Ghazi Faculty of Science and IT, Al-Balqa' Applied University, Salt 19117 (Jordan)], E-mail: odibat@bau.edu.jo; Momani, Shaher [Department of Mathematics, Mutah University, P.O. Box 7, Al-Karak (Jordan)], E-mail: shahermm@yahoo.com
2008-04-15
In this paper, a modification of He's homotopy perturbation method is presented. The new modification extends the application of the method to solve nonlinear differential equations of fractional order. In this method, which does not require a small parameter in an equation, a homotopy with an imbedding parameter p element of [0, 1] is constructed. The proposed algorithm is applied to the quadratic Riccati differential equation of fractional order. The results reveal that the method is very effective and convenient for solving nonlinear differential equations of fractional order.
Racism, differentialism and antiracism in everyday ideology. A mixed-methods study in Britain
Peter Martin
2013-01-01
Racism is ostracized in British public life, but continues to exist and exert influence in various forms. One such is the ideology of differentialism that enforces racialized distinctions by emphasizing culture and difference in place of biology and hierarchy. Although differentialism has been described by various authors, there has been no prior attempt to operationalize it in an attitude scale that could be used in national surveys. This mixed methods study of differentialism in a context o...
Numerical methods for partial differential equations an Overview and Applications
Jaun, A
This is the web edition of the 3-4 weeks course F2A5076 taught 1997-2001 at the Royal Institute of Technology in Stockholm (Sweden). The main target is to provide a robust introduction in computational methods to graduate- and lifelong learning students, using a distance learning method that can easily be tailored to professional schedules.
Directory of Open Access Journals (Sweden)
Shehu Maitama
2016-01-01
Full Text Available A hybrid analytical method for solving linear and nonlinear fractional partial differential equations is presented. The proposed analytical approach is an elegant combination of the Natural Transform Method (NTM and a well-known method, Homotopy Perturbation Method (HPM. In this analytical method, the fractional derivative is computed in Caputo sense and the nonlinear term is calculated using He’s polynomial. The proposed analytical method reduces the computational size and avoids round-off errors. Exact solution of linear and nonlinear fractional partial differential equations is successfully obtained using the analytical method.
An Algebraic Method for Constructing Exact Solutions to Difference-Differential Equations
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
In this paper, we present a method to solve difference differential equation(s). As an example, we apply this method to discrete KdV equation and Ablowitz-Ladik lattice equation. As a result, many exact solutions are obtained with the help of Maple including soliton solutions presented by hyperbolic functions sinh and cosh, periodic solutions presented by sin and cos and rational solutions. This method can also be used to other nonlinear difference-differential equation(s).
Convergence analysis for general linear methods applied to stiff delay differential equations
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
For Runge-Kutta methods applied to stiff delay differential equations (DDEs), the concept of D-convergence was proposed, which is an extension to that of B-convergence in ordinary differential equations (ODEs). In this paper, D-convergence of general linear methods is discussed and the previous related results are improved. Some order results to determine D-convergence of the methods are obtained.
Lagrange-Noether method for solving second-order differential equations
Institute of Scientific and Technical Information of China (English)
Wu Hui-Bin; Wu Run-Heng
2009-01-01
The purpose of this paper is to provide a new method called the Lagrange-Noether method for solving second-order differential equations. The method is,firstly,to write the second-order differential equations completely or partially in the form of Lagrange equations,and secondly,to obtain the integrals of the equations by using the Noether theory of the Lagrange system. An example is given to illustrate the application of the result.
Institute of Scientific and Technical Information of China (English)
LIMing-an; WANGZhong-min; GUOZhi-yong
2003-01-01
Based on a method of finite element model and combined with matrix theory,a method for solving differential equation with variable coefficients if proposed.With the method,it is easy to deal with the differential equations with variable coefficients.On most occasions and due to the nonuniformity nature,nonlinearity property can cause the equations of the kinds.Using the model,the satisfactory valuable results with only a few units can be obtained.
Institute of Scientific and Technical Information of China (English)
黎明安; 王忠民; 郭志勇
2003-01-01
Based on a method of finite element model and combined with matrix theory, a method for solving differential equation with variable coefficients is proposed. With the method, it is easy to deal with the differential equations with variable coefficients. On most occasions and due to the nonuniformity nature, nonlinearity property can cause the equations of the kinds. Using the model, the satisfactory valuable results with only a few units can be obtained.
Modeling Solution of Nonlinear Dispersive Partial Differential Equations using the Marker Method
Energy Technology Data Exchange (ETDEWEB)
Jerome L.V. Lewandowski
2005-01-25
A new method for the solution of nonlinear dispersive partial differential equations is described. The marker method relies on the definition of a convective field associated with the underlying partial differential equation; the information about the approximate solution is associated with the response of an ensemble of markers to this convective field. Some key aspects of the method, such as the selection of the shape function and the initial loading, are discussed in some details.
Application of Variational Iteration Method to Fractional Hyperbolic Partial Differential Equations
Directory of Open Access Journals (Sweden)
Fadime Dal
2009-01-01
Full Text Available The solution of the fractional hyperbolic partial differential equation is obtained by means of the variational iteration method. Our numerical results are compared with those obtained by the modified Gauss elimination method. Our results reveal that the technique introduced here is very effective, convenient, and quite accurate to one-dimensional fractional hyperbolic partial differential equations. Application of variational iteration technique to this problem has shown the rapid convergence of the sequence constructed by this method to the exact solution.
Methods for Differentiating Prion Types in Food-Producing Animals
Directory of Open Access Journals (Sweden)
Kevin C. Gough
2015-11-01
Full Text Available Prions are an enigma amongst infectious disease agents as they lack a genome yet confer specific pathologies thought to be dictated mainly, if not solely, by the conformation of the disease form of the prion protein (PrPSc. Prion diseases affect humans and animals, the latter including the food-producing ruminant species cattle, sheep, goats and deer. Importantly, it has been shown that the disease agent of bovine spongiform encephalopathy (BSE is zoonotic, causing variant Creutzfeldt Jakob disease (vCJD in humans. Current diagnostic tests can distinguish different prion types and in food-producing animals these focus on the differentiation of BSE from the non-zoonotic agents. Whilst BSE cases are now rare, atypical forms of both scrapie and BSE have been reported, as well as two types of chronic wasting disease (CWD in cervids. Typing of animal prion isolates remains an important aspect of prion diagnosis and is now becoming more focused on identifying the range of prion types that are present in food-producing animals and also developing tests that can screen for emerging, novel prion diseases. Here, we review prion typing methodologies in light of current and emerging prion types in food-producing animals.
Generalized Kudryashov Method for Time-Fractional Differential Equations
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Seyma Tuluce Demiray
2014-01-01
Full Text Available In this study, the generalized Kudryashov method (GKM is handled to find exact solutions of time-fractional Burgers equation, time-fractional Cahn-Hilliard equation, and time-fractional generalized third-order KdV equation. These time-fractional equations can be turned into another nonlinear ordinary differantial equation by travelling wave transformation. Then, GKM has been implemented to attain exact solutions of time-fractional Burgers equation, time-fractional Cahn-Hilliard equation, and time-fractional generalized third-order KdV equation. Also, some new hyperbolic function solutions have been obtained by using this method. It can be said that this method is a generalized form of the classical Kudryashov method.
Adaptive interpolation wavelet and homotopy perturbation method for partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Ma, Q; Mei, S [College of Information and Electrical Engineering, China Agricultural University, 17 Qinghua Donglu Road, Beijing 100083 (China)], E-mail: meishuli@163.com
2008-02-15
The homotopy perturbation method proposed by Ji-Huan He has been developed to solve nonlinear matrix differential equations. This paper constructs an adaptive multilevel quasi-wavelet operator according to the interpolation wavelet theory, with which the nonlinear partial differential equations can be discretized adaptively in physical spaces as a matrix differential equation, its numerical solution can be obtained by using the homotopy perturbation method. Numerical results show that the homotopy perturbation method is not sensitive to the time step, so the arithmetic error mainly arises in the space step. Burgers equation is taken as examples to illustrate its effectiveness and convenience.
Camporesi, Roberto
2011-01-01
We present an approach to the impulsive response method for solving linear constant-coefficient ordinary differential equations based on the factorization of the differential operator. The approach is elementary, we only assume a basic knowledge of calculus and linear algebra. In particular, we avoid the use of distribution theory, as well as of…
Camporesi, Roberto
2011-01-01
We present an approach to the impulsive response method for solving linear constant-coefficient ordinary differential equations based on the factorization of the differential operator. The approach is elementary, we only assume a basic knowledge of calculus and linear algebra. In particular, we avoid the use of distribution theory, as well as of…
Raju, Nambury S.; Fortmann-Johnson, Kristen A.; Kim, Wonsuk; Morris, Scott B.; Nering, Michael L.; Oshima, T. C.
2009-01-01
The recent study of Oshima, Raju, and Nanda proposes the item parameter replication (IPR) method for assessing statistical significance of the noncompensatory differential item functioning (NCDIF) index within the differential functioning of items and tests (DFIT) framework. Previous Monte Carlo simulations have found that the appropriate cutoff…
Solution to the one-dimensional Rayleigh-Plesset equation by the Differential Transform method
Narendranath, Aneet Dharmavaram
2016-01-01
The differential transform method (DTM) is a relatively new technique that may be used to find a series solution to differential equations (both linear and nonlinear) through an iterative process. This brief manuscript is an initial effort in applying the DTM to provide a series solution to the one-dimensional Rayleigh-Plesset equation (RPE).
Lie group analysis method for two classes of fractional partial differential equations
Chen, Cheng; Jiang, Yao-Lin
2015-09-01
In this paper we deal with two classes of fractional partial differential equation: n order linear fractional partial differential equation and nonlinear fractional reaction diffusion convection equation, by using the Lie group analysis method. The infinitesimal generators general formula of n order linear fractional partial differential equation is obtained. For nonlinear fractional reaction diffusion convection equation, the properties of their infinitesimal generators are considered. The four special cases are exhaustively investigated respectively. At the same time some examples of the corresponding case are also given. So it is very convenient to solve the infinitesimal generator of some fractional partial differential equation.
Avila, Gustavo; Carrington, Tucker
2011-08-01
In this paper we propose and test a method for computing numerically exact vibrational energy levels of a molecule with six atoms. We use a pruned product basis, a non-product quadrature, the Lanczos algorithm, and the exact normal-coordinate kinetic energy operator (KEO) with the πtμπ term. The Lanczos algorithm is applied to a Hamiltonian with a KEO for which μ is evaluated at equilibrium. Eigenvalues and eigenvectors obtained from this calculation are used as a basis to obtain the final energy levels. The quadrature scheme is designed, so that integrals for the most important terms in the potential will be exact. The procedure is tested on C2H4. All 12 coordinates are treated explicitly. We need only ˜1.52 × 108 quadrature points. A product Gauss grid with which one could calculate the same energy levels has at least 5.67 × 1013 points.
Final Report: Symposium on Adaptive Methods for Partial Differential Equations
Energy Technology Data Exchange (ETDEWEB)
Pernice, Michael; Johnson, Christopher R.; Smith, Philip J.; Fogelson, Aaron
1998-12-08
Complex physical phenomena often include features that span a wide range of spatial and temporal scales. Accurate simulation of such phenomena can be difficult to obtain, and computations that are under-resolved can even exhibit spurious features. While it is possible to resolve small scale features by increasing the number of grid points, global grid refinement can quickly lead to problems that are intractable, even on the largest available computing facilities. These constraints are particularly severe for three dimensional problems that involve complex physics. One way to achieve the needed resolution is to refine the computational mesh locally, in only those regions where enhanced resolution is required. Adaptive solution methods concentrate computational effort in regions where it is most needed. These methods have been successfully applied to a wide variety of problems in computational science and engineering. Adaptive methods can be difficult to implement, prompting the development of tools and environments to facilitate their use. To ensure that the results of their efforts are useful, algorithm and tool developers must maintain close communication with application specialists. Conversely it remains difficult for application specialists who are unfamiliar with the methods to evaluate the trade-offs between the benefits of enhanced local resolution and the effort needed to implement an adaptive solution method.
Directory of Open Access Journals (Sweden)
D. Vivek
2016-11-01
Full Text Available In this paper, the improved Euler method is used for solving hybrid fuzzy fractional differential equations (HFFDE of order $q \\in (0, 1 $ under Caputo-type fuzzy fractional derivatives. This method is based on the fractional Euler method and generalized Taylor's formula. The accuracy and efficiency of the proposed method is demonstrated by solving numerical examples.
Runge-Kutta collocation methods for differential-algebraic equations of indices 2 and 3
Skvortsov, L. M.
2012-10-01
Stiffly accurate Runge-Kutta collocation methods with explicit first stage are examined. The parameters of these methods are chosen so as to minimize the errors in the solutions to differential-algebraic equations of indices 2 and 3. This construction results in methods for solving such equations that are superior to the available Runge-Kutta methods.
Modified multistep method based on interpolation for solving ordinary differential problem
Ismail, Azman; Ahmad, Rokiah@Rozita; Din, Ummul Khair Salma; Hamid, Mohd Rosli A.
2014-06-01
This study is based on multistep method using interpolation formula. The coefficients of new formula are produced using modification on interpolation. This method is tested on ordinary differential equations. Comparisons are between the modified method and the classical Adams Bashforth and Adams-Moulton methods with equal step. Mathematica software is used to determine the new coefficients.
Tang, Chen; Zhang, Fang; Yan, Haiqing; Chen, Zhanqing
2006-04-01
Denoising in electronic speckle pattern interferometry fringes is the key problem in electronic speckle pattern interferometry. We present the new filtering method based on partial differential equations (called PDE filtering method) to electronic speckle pattern interferometry fringes. The PDE filtering method transforms the image processing to solving the partial differential equations. We test the proposed method on experimentally obtained electronic speckle pattern interferometry fringes, and compare with traditional mean filtering and low-pass Fourier filtering methods. The experimental results show that the technique is capable of effectively removing noise. The PDE filtering method is flexible and has fast computational speed and stable results.
Advanced Methods for the Solution of Differential Equations.
Goldstein, Marvin E.; Braun, Willis H.
This is a textbook, originally developed for scientists and engineers, which stresses the actual solutions of practical problems. Theorems are precisely stated, but the proofs are generally omitted. Sample contents include first-order equations, equations in the complex plane, irregular singular points, and numerical methods. A more recent idea,…
Analytic method for solitary solutions of some partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Ugurlu, Yavuz [Firat University, Department of Mathematics, 23119 Elazig (Turkey); Kaya, Dogan [Firat University, Department of Mathematics, 23119 Elazig (Turkey)], E-mail: dkaya@firat.edu.tr
2007-10-22
In this Letter by considering an improved tanh function method, we found some exact solutions of the clannish random walker's parabolic equation, the modified Korteweg-de Vries (KdV) equation, and the Sharma-Tasso-Olver (STO) equation with its fission and fusion, the Jaulent-Miodek equation.
Fast Numerical Methods for Stochastic Partial Differential Equations
2016-04-15
is fundamentally different and more powerful than existing methods. To the best of our knowledge , our proposed approach represents a first attempt to...alleviating the “ curse of dimensionality” problem for moderately high dimensional problems. To elaborate the basic idea of our proposed algorithm, we first
Modified Reduced Differential Transform Method for Partial Differential-Algebraic Equations
Directory of Open Access Journals (Sweden)
Brahim Benhammouda
2014-01-01
PDAEs in convergent series form. In addition, we present the posttreatment of the power series solutions with the Laplace-Padé resummation method as a useful technique to find exact solutions. The main advantage of the proposed technique is that it is based on a few straightforward steps and does not generate secular terms or depend on a perturbation parameter.
Link-based quantitative methods to identify differentially coexpressed genes and gene Pairs
Directory of Open Access Journals (Sweden)
Ye Zhi-Qiang
2011-08-01
Full Text Available Abstract Background Differential coexpression analysis (DCEA is increasingly used for investigating the global transcriptional mechanisms underlying phenotypic changes. Current DCEA methods mostly adopt a gene connectivity-based strategy to estimate differential coexpression, which is characterized by comparing the numbers of gene neighbors in different coexpression networks. Although it simplifies the calculation, this strategy mixes up the identities of different coexpression neighbors of a gene, and fails to differentiate significant differential coexpression changes from those trivial ones. Especially, the correlation-reversal is easily missed although it probably indicates remarkable biological significance. Results We developed two link-based quantitative methods, DCp and DCe, to identify differentially coexpressed genes and gene pairs (links. Bearing the uniqueness of exploiting the quantitative coexpression change of each gene pair in the coexpression networks, both methods proved to be superior to currently popular methods in simulation studies. Re-mining of a publicly available type 2 diabetes (T2D expression dataset from the perspective of differential coexpression analysis led to additional discoveries than those from differential expression analysis. Conclusions This work pointed out the critical weakness of current popular DCEA methods, and proposed two link-based DCEA algorithms that will make contribution to the development of DCEA and help extend it to a broader spectrum.
《伤寒论》辨证方法探讨%The method on syndrome differentiation in Shanghan Lun
Institute of Scientific and Technical Information of China (English)
杨运高
2012-01-01
Based on investigating the differentiating method of Shanghan Lun, the authors pointed out that the differentiating method of Shanghan Lun was programmatic syndrome differentiation of six channels, zang-fu viscera syndrome differentiation, major syndrome differentiation, pulse condition syndrome differentiation, induction syndrome differentiation and heuristics syndrome differentiation.%探讨《伤寒论》辨证的方法,认为其主要有六经为纲、脏腑定位、主症辨证、主脉辨证、类证辨证、试探性辨证等辨证方法.
National Aeronautics and Space Administration — The problem of estimating the aerodynamic models for flight control of damaged aircraft using an innovative differential vortex lattice method tightly coupled with...
Bounded index, entire solutions of ordinary differential equations and summability methods
Directory of Open Access Journals (Sweden)
G. H. Fricke
1981-01-01
Full Text Available A brief survey of recent results on functions of bounded index and bounded index summability methods is given. Theorems on entire solutions of ordinary differential equations with polynomial coefficients are included.
Method for solving the periodic problem for integro-differential equations
Directory of Open Access Journals (Sweden)
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.
Solution to the Linear Fractional Differential Equation Using Adomian Decomposition Method
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Jin-Fa Cheng
2011-01-01
Full Text Available We obtain the analytical general solution of the linear fractional differential equations with constant coefficients by Adomian decomposition method under nonhomogeneous initial value condition, which is in the sense of the Caputo fractional derivative.
National Aeronautics and Space Administration — Estimation of aerodynamic models for the control of damaged aircraft using an innovative differential vortex lattice method tightly coupled with an extended Kalman...
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.
The (G'/G)-expansion method for the nonlinear time fractional differential equations
Unsal, Omer; Guner, Ozkan; Bekir, Ahmet; Cevikel, Adem C.
2017-01-01
In this paper, we obtain exact solutions of two time fractional differential equations using Jumarie's modified Riemann-Liouville derivative which is encountered in mathematical physics and applied mathematics; namely (3 + 1)-dimensional time fractional KdV-ZK equation and time fractional ADR equation by using fractional complex transform and (G/'G )-expansion method. It is shown that the considered transform and method are very useful in solving nonlinear fractional differential equations.
Alam Khan, Najeeb; Razzaq, Oyoon Abdul
2016-03-01
In the present work a wavelets approximation method is employed to solve fuzzy boundary value differential equations (FBVDEs). Essentially, a truncated Legendre wavelets series together with the Legendre wavelets operational matrix of derivative are utilized to convert FB- VDE into a simple computational problem by reducing it into a system of fuzzy algebraic linear equations. The capability of scheme is investigated on second order FB- VDE considered under generalized H-differentiability. Solutions are represented graphically showing competency and accuracy of this method.
A Quantitative Comparison of Numerical Method for Solving Stiff Ordinary Differential Equations
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S. A. M. Yatim
2011-01-01
Full Text Available We derive a variable step of the implicit block methods based on the backward differentiation formulae (BDF for solving stiff initial value problems (IVPs. A simplified strategy in controlling the step size is proposed with the aim of optimizing the performance in terms of precision and computation time. The numerical results obtained support the enhancement of the method proposed as compared to MATLAB's suite of ordinary differential equations (ODEs solvers, namely, ode15s and ode23s.
SOLUTION OF SYSTEM OF FRACTIONAL DIFFERENTIAL EQUATIONS BY ADOMIAN DECOMPOSITION METHOD
Institute of Scientific and Technical Information of China (English)
Duan Junsheng; An Jianye; Xu Mingyu
2007-01-01
The aim of this paper is to apply the relatively new Adomian decomposition method to solving the system of linear fractional, in the sense of Riemann-Liouville and Caputo respectively, differential equations. The solutions are expressed in terms of Mittag-Leffier functions of matric argument. The Adomian decomposition method is straightforward, applicable for broader problems and avoids the difficulties in applying integral transforms. As the order is 1,the result here is simplified to that of first order differential equation.
Index-aware model order reduction methods applications to differential-algebraic equations
Banagaaya, N; Schilders, W H A
2016-01-01
The main aim of this book is to discuss model order reduction (MOR) methods for differential-algebraic equations (DAEs) with linear coefficients that make use of splitting techniques before applying model order reduction. The splitting produces a system of ordinary differential equations (ODE) and a system of algebraic equations, which are then reduced separately. For the reduction of the ODE system, conventional MOR methods can be used, whereas for the reduction of the algebraic systems new methods are discussed. The discussion focuses on the index-aware model order reduction method (IMOR) and its variations, methods for which the so-called index of the original model is automatically preserved after reduction.
Directory of Open Access Journals (Sweden)
Süleyman Öğrekçi
2015-01-01
Full Text Available We propose an efficient analytic method for solving nonlinear differential equations of fractional order. The fractional derivative is defined in the sense of modified Riemann-Liouville derivative. A new technique for calculating the generalized Taylor series coefficients (also known as “generalized differential transforms,” GDTs of nonlinear functions and a new approach of the generalized Taylor series method (GTSM are presented. This new method offers a simple algorithm for computing GDTs of nonlinear functions and avoids massive computational work that usually arises in the standard method. Several illustrative examples are demonstrated to show effectiveness of the proposed method.
Weak Second Order Explicit Stabilized Methods for Stiff Stochastic Differential Equations
Abdulle, Assyr
2013-01-01
We introduce a new family of explicit integrators for stiff Itô stochastic differential equations (SDEs) of weak order two. These numerical methods belong to the class of one-step stabilized methods with extended stability domains and do not suffer from the step size reduction faced by standard explicit methods. The family is based on the standard second order orthogonal Runge-Kutta-Chebyshev (ROCK2) methods for deterministic problems. The convergence, meansquare, and asymptotic stability properties of the methods are analyzed. Numerical experiments, including applications to nonlinear SDEs and parabolic stochastic partial differential equations are presented and confirm the theoretical results. © 2013 Society for Industrial and Applied Mathematics.
A New Numerical Method for Fast Solution of Partial Integro-Differential Equations
Dourbal, Pavel; Pekker, Mikhail
2016-01-01
A new method of numerical solution for partial differential equations is proposed. The method is based on a fast matrix multiplication algorithm. Two-dimensional Poison equation is used for comparison of the proposed method with conventional numerical methods. It was shown that the new method allows for linear growth in the number of elementary addition and multiplication operations with the growth of grid size, as contrasted with quadratic growth necessitated by the standard numerical method...
Institute of Scientific and Technical Information of China (English)
FENG Qing-Hua
2013-01-01
In this paper,an extended Riccati sub-ODE method is proposed to establish new exact solutions for fractional differential-difference equations in the sense of modified Riemann-Liouville derivative.By a fractional complex transformation,a given fractional differential-difference equation can be turned into another differential-difference equation of integer order.The validity of the method is illustrated by applying it to solve the fractional Hybrid lattice equation and the fractional relativistic Toda lattice system.As a result,some new exact solutions including hyperbolic function solutions,trigonometric function solutions and rational solutions are established.
Feng, Qing-Hua
2013-05-01
In this paper, an extended Riccati sub-ODE method is proposed to establish new exact solutions for fractional differential-difference equations in the sense of modified Riemann—Liouville derivative. By a fractional complex transformation, a given fractional differential-difference equation can be turned into another differential-difference equation of integer order. The validity of the method is illustrated by applying it to solve the fractional Hybrid lattice equation and the fractional relativistic Toda lattice system. As a result, some new exact solutions including hyperbolic function solutions, trigonometric function solutions and rational solutions are established.
Directory of Open Access Journals (Sweden)
Khaled A. Gepreel
2012-01-01
Full Text Available We modified the rational Jacobi elliptic functions method to construct some new exact solutions for nonlinear differential difference equations in mathematical physics via the lattice equation, the discrete nonlinear Schrodinger equation with a saturable nonlinearity, the discrete nonlinear Klein-Gordon equation, and the quintic discrete nonlinear Schrodinger equation. Some new types of the Jacobi elliptic solutions are obtained for some nonlinear differential difference equations in mathematical physics. The proposed method is more effective and powerful to obtain the exact solutions for nonlinear differential difference equations.
Camporesi, Roberto
2011-06-01
We present an approach to the impulsive response method for solving linear constant-coefficient ordinary differential equations based on the factorization of the differential operator. The approach is elementary, we only assume a basic knowledge of calculus and linear algebra. In particular, we avoid the use of distribution theory, as well as of the other more advanced approaches: Laplace transform, linear systems, the general theory of linear equations with variable coefficients and the variation of constants method. The approach presented here can be used in a first course on differential equations for science and engineering majors.
Validation of MIMGO: a method to identify differentially expressed GO terms in a microarray dataset
2012-01-01
Background We previously proposed an algorithm for the identification of GO terms that commonly annotate genes whose expression is upregulated or downregulated in some microarray data compared with in other microarray data. We call these “differentially expressed GO terms” and have named the algorithm “matrix-assisted identification method of differentially expressed GO terms” (MIMGO). MIMGO can also identify microarray data in which genes annotated with a differentially expressed GO term are upregulated or downregulated. However, MIMGO has not yet been validated on a real microarray dataset using all available GO terms. Findings We combined Gene Set Enrichment Analysis (GSEA) with MIMGO to identify differentially expressed GO terms in a yeast cell cycle microarray dataset. GSEA followed by MIMGO (GSEA + MIMGO) correctly identified (p GO terms are upregulated. We found that GSEA + MIMGO was slightly less effective than, or comparable to, GSEA (Pearson), a method that uses Pearson’s correlation as a metric, at detecting true differentially expressed GO terms. However, unlike other methods including GSEA (Pearson), GSEA + MIMGO can comprehensively identify the microarray data in which genes annotated with a differentially expressed GO term are upregulated or downregulated. Conclusions MIMGO is a reliable method to identify differentially expressed GO terms comprehensively. PMID:23232071
JACOBI PSEUDOSPECTRAL METHOD FOR FOURTH ORDER PROBLEMS
Institute of Scientific and Technical Information of China (English)
Zheng-su Wan; Ben-yu Guo; Zhong-qing Wang
2006-01-01
In this paper, we investigate Jacobi pseudospectral method for fourth order problems.We establish some basic results on the Jacobi-Gauss-type interpolations in non-uniformly weighted Sobolev spaces, which serve as important tools in analysis of numerical quadratures, and numerical methods of differential and integral equations. Then we propose Jacobi pseudospectral schemes for several singular problems and multiple-dimensional problems of fourth order. Numerical results demonstrate the spectral accuracy of these schemes,and coincide well with theoretical analysis.
Schuyler, Adam D; Maciejewski, Mark W; Stern, Alan S; Hoch, Jeffrey C
2015-01-01
Nonuniform sampling (NUS) in multidimensional NMR permits the exploration of higher dimensional experiments and longer evolution times than the Nyquist Theorem practically allows for uniformly sampled experiments. However, the spectra of NUS data include sampling-induced artifacts and may be subject to distortions imposed by sparse data reconstruction techniques, issues not encountered with the discrete Fourier transform (DFT) applied to uniformly sampled data. The characterization of these NUS-induced artifacts allows for more informed sample schedule design and improved spectral quality. The DFT–Convolution Theorem, via the point-spread function (PSF) for a given sampling scheme, provides a useful framework for exploring the nature of NUS sampling artifacts. In this work, we analyze the PSFs for a set of specially constructed NUS schemes to quantify the interplay between randomization and dimensionality for reducing artifacts relative to uniformly undersampled controls. In particular, we find a synergistic relationship between the indirect time dimensions and the “quadrature phase dimension” (i.e. the hypercomplex components collected for quadrature detection). The quadrature phase dimension provides additional degrees of freedom that enable partial-component NUS (collecting a subset of quadrature components) to further reduce sampling-induced aliases relative to traditional full-component NUS (collecting all quadrature components). The efficacy of artifact reduction is exponentially related to the dimensionality of the sample space. Our results quantify the utility of partial-component NUS as an additional means for introducing decoherence into sampling schemes and reducing sampling artifacts in high dimensional experiments. PMID:25899289
Song, Junqiang; Leng, Hongze; Lu, Fengshun
2014-01-01
We present a new numerical method to get the approximate solutions of fractional differential equations. A new operational matrix of integration for fractional-order Legendre functions (FLFs) is first derived. Then a modified variational iteration formula which can avoid “noise terms” is constructed. Finally a numerical method based on variational iteration method (VIM) and FLFs is developed for fractional differential equations (FDEs). Block-pulse functions (BPFs) are used to calculate the FLFs coefficient matrices of the nonlinear terms. Five examples are discussed to demonstrate the validity and applicability of the technique. PMID:24511303
Directory of Open Access Journals (Sweden)
Khaled A. Gepreel
2016-07-01
Full Text Available In this paper, we improve the extended trial equation method to construct the exact solutions for nonlinear coupled system of partial differential equations in mathematical physics. We use the extended trial equation method to find some different types of exact solutions such as the Jacobi elliptic function solutions, soliton solutions, trigonometric function solutions and rational, exact solutions to the nonlinear coupled Schrodinger Boussinesq equations when the balance number is a positive integer. The performance of this method is reliable, effective and powerful for solving more complicated nonlinear partial differential equations in mathematical physics. The balance number of this method is not constant as we have in other methods. This method allows us to construct many new types of exact solutions. By using the Maple software package we show that all obtained solutions satisfy the original partial differential equations.
Directory of Open Access Journals (Sweden)
Li Yuanlu
2015-06-01
Full Text Available Non–integer order differentiation is changing application of traditional differentiation because it can achieve a continuous interpolation of the integer order differentiation. However, implementation of the non–integer order differentiation is much more complex than that of integer order differentiation. For this purpose, a Haar wavelet-based implementation method of non–integer order differentiation is proposed. The basic idea of the proposed method is to use the operational matrix to compute the non–integer order differentiation of a signal through expanding the signal by the Haar wavelets and constructing Haar wavelet operational matrix of the non–integer order differentiation. The effectiveness of the proposed method was verified by comparison of theoretical results and those obtained by another non–integer order differential filtering method. Finally, non–integer order differentiation was applied to enhance signal.
DEFF Research Database (Denmark)
Ganji, S. S.; Barari, Amin; Ibsen, Lars Bo
2010-01-01
. In current research the authors utilized the Differential Transformation Method (DTM) for solving the nonlinear problem and compared the analytical results with those ones obtained by the 4th order Runge-Kutta Method (RK4) as a numerical method. Further illustration embedded in this paper shows the ability...
DEFF Research Database (Denmark)
Ganji, S.; Barari, Amin; Ibsen, Lars Bo
2012-01-01
. In current research the authors utilized the Differential Transformation Method (DTM) for solving the nonlinear problem and compared the analytical results with those ones obtained by the 4th order Runge-Kutta Method (RK4) as a numerical method. Further illustration embedded in this paper shows the ability...
Bota, C.; Cǎruntu, B.; Bundǎu, O.
2013-10-01
In this paper we applied the Squared Remainder Minimization Method (SRMM) to find analytic approximate polynomial solutions for Riccati differential equations. Two examples are included to demonstrated the validity and applicability of the method. The results are compared to those obtained by other methods.
1986-05-19
eary and identify by block number) We developed and applied numerical methods for singularly perturbed two-point boundary value problems and time...Numerical Methods for Singularly Perturbed Differential Equations During the period of this contract. we developed and applied numerical methods for
Low Voltage Low Power Quadrature LC Oscillator Based on Back-gate Superharmonic Capacitive Coupling
Ma, Minglin; Li, Zhijun
2013-09-01
This work introduces a new low voltage low power superharmonic capacitive coupling quadrature LC oscillator (QLCO) made by coupling two identical cross-connected LC oscillators without tail transistor. In each of the core oscillators, the back-gate nodes of the cross-coupled NMOS pair and PMOS pair, acting as common mode nodes, have been connected directly. Then the core oscillators are coupled together via capacitive coupling of the PMOS common mode node in one of the core oscillators to the NMOS common mode node in the other core oscillator, and vice versa. Only capacitors are used for coupling of the two core oscillators and therefore no extra noise sources are imposed on the circuit. Operation of the proposed QLCO was investigated with simulation using a commercial 0.18 µm RF CMOS technology: it shows a power dissipation of 5.2 mW from a 0.6 V supply voltage. Since the proposed core oscillator has Complementary NMOS and PMOS cross coupled pairs, and capacitive coupling method will not introduce extra phase noise, so this circuit can operate with a low phase noise as low as -126.8 dBc/Hz at 1 MHz offset from center oscillation frequency of 2.4 GHz, as confirmed with simulation.
Niebauer, T M; Constantino, A; Billson, R; Hankla, A; Nelson, P G
2015-06-20
A corner-cube retroreflector has the property that the optical path length for a reflected laser beam is insensitive to rotations about a mathematical point called its optical center (OC). This property is exploited in ballistic absolute gravity meters in which a proof mass containing a corner-cube retroreflector is dropped in a vacuum, and its position is accurately determined with a laser interferometer. In order to avoid vertical position errors when the proof mass rotates during free fall, it is important to collocate its center of mass (COM) with the OC of the retroreflector. This is commonly done using a mechanical scale-based balancing procedure, which has limited accuracy due to the difficulty in finding the exact position of the COM and the OC. This paper describes a novel way to achieve the collocation by incorporating the proof mass into a pendulum and using a quadrature interferometer to interrogate its apparent translation in its twist mode. The mismatch between the COM and OC generates a signal in a quiet part of the spectrum where no mechanical resonance exists. This allows us to tune the position of the COM relative to the OC to an accuracy of about 1 μm in all three axes. This provides a way to directly demonstrate that a rotation of the proof mass by several degrees causes an apparent translation in the direction of the laser beam of less than 1 nm. This technique allows an order of magnitude improvement over traditional methods of balancing.
Inoshita, Kensuke; Hama, Yoshimitsu; Kishikawa, Hiroki; Goto, Nobuo
2016-12-01
In photonic label routers, various optical signal processing functions are required; these include optical label extraction, recognition of the label, optical switching and buffering controlled by signals based on the label information and network routing tables, and label rewriting. Among these functions, we focus on photonic label recognition. We have proposed two kinds of optical waveguide circuits to recognize 16 quadrature amplitude modulation codes, i.e., recognition from the minimum output port and from the maximum output port. The recognition function was theoretically analyzed and numerically simulated by finite-difference beam-propagation method. We discuss noise tolerance in the circuit and show numerically simulated results to evaluate bit-error-rate (BER) characteristics against optical signal-to-noise ratio (OSNR). The OSNR required to obtain a BER less than 1.0×10-3 for the symbol rate of 2.5 GBaud was 14.5 and 27.0 dB for recognition from the minimum and maximum output, respectively.
Directory of Open Access Journals (Sweden)
HASHEM SABERI NAJAFI
2016-07-01
Full Text Available Generalized differential transform method (GDTM is a powerful method to solve the fractional differential equations. In this paper, a new fractional model for systems with single degree of freedom (SDOF is presented, by using the GDTM. The advantage of this method compared with some other numerical methods has been shown. The analysis of new approximations, damping and acceleration of systems are also described. Finally, by reducing damping and analysis of the errors, in one of the fractional cases, we have shown that in addition to having a suitable solution for the displacement close to the exact one, the system enjoys acceleration once crossing the equilibrium point.
Series: Utilization of Differential Equations and Methods for Solving Them in Medical Physics (4).
Murase, Kenya
Partial differential equations are often used in the field of medical physics. In this (final) issue, the methods for solving the partial differential equations were introduced, which include separation of variables, integral transform (Fourier and Fourier-sine transforms), Green's function, and series expansion methods. Some examples were also introduced, in which the integral transform and Green's function methods were applied to solving Pennes' bioheat transfer equation and the Fourier series expansion method was applied to Navier-Stokes equation for analyzing the wall shear stress in blood vessels.Finally, the author hopes that this series will be helpful for people who engage in medical physics.
The Telegraph Equation and Its Solution by Reduced Differential Transform Method
Directory of Open Access Journals (Sweden)
Vineet K. Srivastava
2013-01-01
Full Text Available One-dimensional second-order hyperbolic telegraph equation was formulated using Ohm’s law and solved by a recent and reliable semianalytic method, namely, the reduced differential transform method (RDTM. Using this method, it is possible to find the exact solution or a closed approximate solution of a differential equation. Three numerical examples have been carried out in order to check the effectiveness, the accuracy, and convergence of the method. The RDTM is a powerful mathematical technique for solving wide range of problems arising in science and engineering fields.
Directory of Open Access Journals (Sweden)
C. Ünlü
2013-01-01
Full Text Available A modification of the variational iteration method (VIM for solving systems of nonlinear fractional-order differential equations is proposed. The fractional derivatives are described in the Caputo sense. The solutions of fractional differential equations (FDE obtained using the traditional variational iteration method give good approximations in the neighborhood of the initial position. The main advantage of the present method is that it can accelerate the convergence of the iterative approximate solutions relative to the approximate solutions obtained using the traditional variational iteration method. Illustrative examples are presented to show the validity of this modification.
A novel approach for solving fractional Fisher equation using differential transform method
Indian Academy of Sciences (India)
MIRZAZADEH M
2016-05-01
In the present paper, an analytic solution of nonlinear fractional Fisher equation is deduced with the help of the powerful differential transform method (DTM). To illustrate the method, two examples have been prepared. The method for this equation has led to an exact solution. The reliability, simplicity and cost-effectiveness of the method are confirmed by applying this method on different forms of functional equations.
Block Hybrid Collocation Method with Application to Fourth Order Differential Equations
Directory of Open Access Journals (Sweden)
Lee Ken Yap
2015-01-01
Full Text Available The block hybrid collocation method with three off-step points is proposed for the direct solution of fourth order ordinary differential equations. The interpolation and collocation techniques are applied on basic polynomial to generate the main and additional methods. These methods are implemented in block form to obtain the approximation at seven points simultaneously. Numerical experiments are conducted to illustrate the efficiency of the method. The method is also applied to solve the fourth order problem from ship dynamics.
A Consistent Direct Method for Estimating Parameters in Ordinary Differential Equations Models
Holte, Sarah E.
2016-01-01
Ordinary differential equations provide an attractive framework for modeling temporal dynamics in a variety of scientific settings. We show how consistent estimation for parameters in ODE models can be obtained by modifying a direct (non-iterative) least squares method similar to the direct methods originally developed by Himmelbau, Jones and Bischoff. Our method is called the bias-corrected least squares (BCLS) method since it is a modification of least squares methods known to be biased. Co...
Vinayaka : A Semi-Supervised Projected Clustering Method Using Differential Evolution
Satish Gajawada; Durga Toshniwal
2012-01-01
Differential Evolution (DE) is an algorithm for evolutionary optimization. Clustering problems have beensolved by using DE based clustering methods but these methods may fail to find clusters hidden insubspaces of high dimensional datasets. Subspace and projected clustering methods have been proposed inliterature to find subspace clusters that are present in subspaces of dataset. In this paper we proposeVINAYAKA, a semi-supervised projected clustering method based on DE. In this method DE opt...
Design of a quadrature surface coil for hyperpolarized 13C MRS cardiac metabolism studies in pigs
DEFF Research Database (Denmark)
Giovannetti, G.; Frijia, F.; Hartwig, V.;
2013-01-01
This work describes the design of a quadrature surface coil constituted by a circular loop and a butterfly coil, employed in transmit/receive (TX/RX) mode for hyperpolarized 13C studies of pig heart with a clinical 3T scanner. The coil characterization is performed by developing an SNR model...... for coil performance evaluation in terms of coil resistance, sample-induced resistance and magnetic field pattern. Experimental SNR-vs.-depth profiles, extracted from the [1-13C]acetate phantom chemical shift image (CSI), showed good agreement with the theoretical SNR-vs.-depth profiles. Moreover......, the performance of the quadrature coil was compared with the single TX/RX circular and TX/RX butterfly coil, in order to verify the advantage of the proposed configuration over the single coils throughout the volume of interest for cardiac imaging in pig. Finally, the quadrature surface coil was tested...
Semi-implicit spectral deferred correction methods for ordinary differential equations
Energy Technology Data Exchange (ETDEWEB)
Minion, Michael L.
2002-10-06
A semi-implicit formulation of the method of spectral deferred corrections (SISDC) for ordinary differential equations with both stiff and non-stiff terms is presented. Several modifications and variations to the original spectral deferred corrections method by Dutt, Greengard, and Rokhlin concerning the choice of integration points and the form of the correction iteration are presented. The stability and accuracy of the resulting ODE methods are explored analytically and numerically. The SISDC methods are intended to be combined with the method of lines approach to yield a flexible framework for creating higher-order semi-implicit methods for partial differential equations. A discussion and numerical examples of the SISDC method applied to advection-diffusion type equations are included. The results suggest that higher-order SISDC methods are more efficient than semi-implicit Runge-Kutta methods for moderately stiff problems in terms of accuracy per function evaluation.
Piret, Cécile
2012-05-01
Much work has been done on reconstructing arbitrary surfaces using the radial basis function (RBF) method, but one can hardly find any work done on the use of RBFs to solve partial differential equations (PDEs) on arbitrary surfaces. In this paper, we investigate methods to solve PDEs on arbitrary stationary surfaces embedded in . R3 using the RBF method. We present three RBF-based methods that easily discretize surface differential operators. We take advantage of the meshfree character of RBFs, which give us a high accuracy and the flexibility to represent the most complex geometries in any dimension. Two out of the three methods, which we call the orthogonal gradients (OGr) methods are the result of our work and are hereby presented for the first time. © 2012 Elsevier Inc.
Parrish, Robert M; Hohenstein, Edward G; Martínez, Todd J; Sherrill, C David
2013-05-21
We investigate the application of molecular quadratures obtained from either standard Becke-type grids or discrete variable representation (DVR) techniques to the recently developed least-squares tensor hypercontraction (LS-THC) representation of the electron repulsion integral (ERI) tensor. LS-THC uses least-squares fitting to renormalize a two-sided pseudospectral decomposition of the ERI, over a physical-space quadrature grid. While this procedure is technically applicable with any choice of grid, the best efficiency is obtained when the quadrature is tuned to accurately reproduce the overlap metric for quadratic products of the primary orbital basis. Properly selected Becke DFT grids can roughly attain this property. Additionally, we provide algorithms for adopting the DVR techniques of the dynamics community to produce two different classes of grids which approximately attain this property. The simplest algorithm is radial discrete variable representation (R-DVR), which diagonalizes the finite auxiliary-basis representation of the radial coordinate for each atom, and then combines Lebedev-Laikov spherical quadratures and Becke atomic partitioning to produce the full molecular quadrature grid. The other algorithm is full discrete variable representation (F-DVR), which uses approximate simultaneous diagonalization of the finite auxiliary-basis representation of the full position operator to produce non-direct-product quadrature grids. The qualitative features of all three grid classes are discussed, and then the relative efficiencies of these grids are compared in the context of LS-THC-DF-MP2. Coarse Becke grids are found to give essentially the same accuracy and efficiency as R-DVR grids; however, the latter are built from explicit knowledge of the basis set and may guide future development of atom-centered grids. F-DVR is found to provide reasonable accuracy with markedly fewer points than either Becke or R-DVR schemes.
Solving evolutionary-type differential equations and physical problems using the operator method
Zhukovsky, K. V.
2017-01-01
We present a general operator method based on the advanced technique of the inverse derivative operator for solving a wide range of problems described by some classes of differential equations. We construct and use inverse differential operators to solve several differential equations. We obtain operator identities involving an inverse derivative operator, integral transformations, and generalized forms of orthogonal polynomials and special functions. We present examples of using the operator method to construct solutions of equations containing linear and quadratic forms of a pair of operators satisfying Heisenberg-type relations and solutions of various modifications of partial differential equations of the Fourier heat conduction type, Fokker-Planck type, Black-Scholes type, etc. We demonstrate using the operator technique to solve several physical problems related to the charge motion in quantum mechanics, heat propagation, and the dynamics of the beams in accelerators.
Suzuki, Meisaku; Kanno, Atsushi; Yamamoto, Naokatsu; Sotobayashi, Hideyuki
2016-02-01
The effects of in-phase/quadrature-phase (IQ) imbalances are evaluated with a direct IQ down-converter in the W-band (75-110 GHz). The IQ imbalance of the converter is measured within a range of +/-10 degrees in an intermediate frequency of DC-26.5 GHz. 1-8-G-baud quadrature phase-shift keying (QPSK) signals are transmitted successfully with observed bit error rates within a forward error correction limit of 2×10-3 using radio over fiber (RoF) techniques. The direct down-conversion technique is applicable to next-generation high-speed wireless access communication systems in the millimeter-wave band.
On quadrature formulas for singular integral equations of the first and the second kind
DEFF Research Database (Denmark)
Krenk, Steen
1975-01-01
It is shown that by proper choice of the collocation points singular integral equations of the first and the second kind can be integrated by use of the usual Gauss-Jacobi quadrature formula. Detailed formulas are given for various values of the index.......It is shown that by proper choice of the collocation points singular integral equations of the first and the second kind can be integrated by use of the usual Gauss-Jacobi quadrature formula. Detailed formulas are given for various values of the index....
Lobatto and Radau positive quadrature formulas for linear combinations of Jacobi polynomials
Bustamante, Jorge; Martíez-Cruz, Reinaldo
2012-01-01
For a given $\\theta\\in (-1,1)$, we find out all parameters $\\alpha,\\beta\\in \\{0,1\\}$ such that, there exists a linear combination of Jacobi polynomials $J_{n+1}^{(\\alpha,\\beta)}(x)-C J_{n}^{(\\alpha,\\beta)}(x)$ which generates a Lobatto (Radau) positive quadrature formula of degree of exactness \\textcolor{red}{$2n+2$ ($2n+1$)} and contains the point $\\theta$ as a node. These positive quadratures are very useful in studying problems in one-sided polynomial $L_1$ approximation.
A method for solving systems of non-linear differential equations with moving singularities
Gousheh, S S; Ghafoori-Tabrizi, K
2003-01-01
We present a method for solving a class of initial valued, coupled, non-linear differential equations with `moving singularities' subject to some subsidiary conditions. We show that this type of singularities can be adequately treated by establishing certain `moving' jump conditions across them. We show how a first integral of the differential equations, if available, can also be used for checking the accuracy of the numerical solution.
Symmetries of the Gas Dynamics Equations Using the Differential Form Method
Schmidt, Joe; Ramsey, Scott; Baty, Roy
2016-11-01
A brief review of the theory of exterior differential systems and isovector symmetry analysis methods is presented in the context of the one-dimensional inviscid compressible flow equations. These equations are formulated as an exterior differential system with equation of state (EOS) closure provided in terms of an adiabatic bulk modulus. The scaling symmetry generators - and corresponding EOS constraints - otherwise appearing in the existing literature are recovered through the application of and invariance under Lie derivative dragging operations.
A note on the auxiliary equation method for solving nonlinear partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Liu, Chunping [Institute of Mathematics, Yangzhou University, Yangzhou 225002 (China)]. E-mail: yzslcp@pub.yz.jsinfo.net; Liu, Xiaoping [Gaoyou Branch, Yangzhou Education College, Gaoyou 225600 (China)
2006-01-02
First, we pick up some solutions of an auxiliary ordinary differential equation, which were neglected by Sirendaoreji and Sun Jiong in the auxiliary equation method. Then, we give the classification of the solutions for the auxiliary ordinary differential equation depending on its three parameters. Finally, we consider the (2+1)-dimensional dispersive long wave equations and get its more exact solitary wave solutions and reveal the relation of the exact solitary wave solutions obtained by Sirendaoreji and Sun Jiong in their paper.
Semi-implicit Runge.Kutta Method for Solving Stiff Ordinary Differential Equations
Institute of Scientific and Technical Information of China (English)
LONGYongxing; MOUZongze; DONGJiaqi; ZHAOHuaiguo
2003-01-01
Runge-Kutta method is widely applied to solve the initial value problem of ordinary differential equations. The implicitRunge-Kutta with better numerical stability for the numerical integration of stiff differential systems,but the formulate has traditionally been on solving the nonlinear equations resulting from a modified Newton iteration in every time.Semi-implicit formulate have the major computationally advantage that it is necessary to solve only linear systems of algebraic equations to find the Ka.
Directory of Open Access Journals (Sweden)
Ammar Ali Neamah
2014-01-01
Full Text Available The paper uses the Local fractional variational Iteration Method for solving the second kind Volterra integro-differential equations within the local fractional integral operators. The analytical solutions within the non-differential terms are discussed. Some illustrative examples will be discussed. The obtained results show the simplicity and efficiency of the present technique with application to the problems for the integral equations.
Fractal-Based Methods and Inverse Problems for Differential Equations: Current State of the Art
Kunze, Herb E.; Davide La Torre; Franklin Mendivil; Manuel Ruiz Galán; Rachad Zaki
2014-01-01
We illustrate, in this short survey, the current state of the art of fractal-based techniques and their application to the solution of inverse problems for ordinary and partial differential equations. We review several methods based on the Collage Theorem and its extensions. We also discuss two innovative applications: the first one is related to a vibrating string model while the second one considers a collage-based approach for solving inverse problems for partial differential equations on ...
Differentiation method for localization of Compton edge in organic scintillation detectors
Safari, M J; Afarideh, H
2016-01-01
This paper, presents a simple method for accurate calibration of organic scintillation detectors. The method is based on the fact that differentiating the response function leads to accurate estimation of the Compton edge. The differentiation method in addition to the location of the Compton edge, gives insights into the parameters of the folded Gaussian function which is useful for determination of the energy resolution. Moreover, it is observed that the uncorrelated noise in the measurement of the response function does not impose significant uncertainties in the evaluations. By simulation of the bounded electrons and considering the Doppler effects, we are able to calculate a first estimation for the intrinsic Doppler resolution of a plastic scintillator, benefiting from the capability of the differentiation method.
A simple method of measuring differentially-excited on-wafer spiral inductor-like components
Jie, Pan; Haigang, Yang; Liwu, Yang
2009-07-01
This paper proposes a simple method of measuring differentially-excited on-wafer RF CMOS spiral inductor-like components. This method requires only two common 'G-S-G' probes and an ordinary two-port VNA. Using a network instead of a detailed equivalent circuit, this method completes the de-embedding with only one 'Through' dummy, and thus the measurements are greatly simplified. By designing the ports 'Open' or 'Short-circuited' deliberately, a multi-port transformer can be transformed into three two-port networks with different terminators. Then, couplings between the two coils can be solved, and the differentially-excited scattering parameters (S-parameters) can be constructed. Also, a group of differential inductors and transformers were designed and measured, and then comparisons between simulated and measured electromagnetic results are performed to verify this method.
DEFF Research Database (Denmark)
Ganji, S. S.; Barari, Amin; Ibsen, Lars Bo
2010-01-01
In this paper we aim to find an analytical solution for jamming transition in traffic flow. Generally the Jamming Transition Problem (JTP) can be modeled via Lorentz system. So, in this way, the governing differential equation achieved is modeled in the form of a nonlinear damped oscillator....... In current research the authors utilized the Differential Transformation Method (DTM) for solving the nonlinear problem and compared the analytical results with those ones obtained by the 4th order Runge-Kutta Method (RK4) as a numerical method. Further illustration embedded in this paper shows the ability...... of DTM in solving nonlinear problems when a so accurate solution is required....
Hesameddini, Esmail; Rahimi, Azam
2015-05-01
In this article, we propose a new approach for solving fractional partial differential equations with variable coefficients, which is very effective and can also be applied to other types of differential equations. The main advantage of the method lies in its flexibility for obtaining the approximate solutions of time fractional and space fractional equations. The fractional derivatives are described based on the Caputo sense. Our method contains an iterative formula that can provide rapidly convergent successive approximations of the exact solution if such a closed form solution exists. Several examples are given, and the numerical results are shown to demonstrate the efficiency of the newly proposed method.
A PCR-RFLP method for the simultaneous differentiation of three Entamoeba species.
Fontecha, Gustavo A; García, Kimberly; Rueda, María Mercedes; Sosa-Ochoa, Wilfredo; Sánchez, Ana Lourdes; Leiva, Byron
2015-01-01
Amoebiasis caused by Entamoeba histolytica continues to be one of the most common parasitic diseases in the developing world. Despite its relevance, due to the lack of accurate diagnostic methods, the true clinical and public health importance of this parasite remains uncertain. The aim of this study was to develop a new diagnostic tool to differentiate E.histolytica from the morphologically undistinguishable E.dispar and E.moshkovskii. We developed a specific, fast and simple PCR-RFLP method that was able to accurately differentiate experimentally-obtained restriction patterns from the three Entamoeba species. This new method could prove useful for clinical and epidemiological purposes.
A block Krylov subspace time-exact solution method for linear ordinary differential equation systems
Botchev, M.A.
2013-01-01
We propose a time-exact Krylov-subspace-based method for solving linear ordinary differential equation systems of the form $y'=-Ay+g(t)$ and $y"=-Ay+g(t)$, where $y(t)$ is the unknown function. The method consists of two stages. The first stage is an accurate piecewise polynomial approximation of th
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
In this paper, we extend the mapping transformation method through introducing variable coefficients.By means of the extended mapping transformation method, many explicit and exact general solutions with arbitrary functions for some nonlinear partial differential equations, which contain solitary wave solutions, trigonometric function solutions, and rational solutions, are obtained.
On Exact Solutions to Partial Differential Equations by the Modified Homotopy Perturbation Method
Institute of Scientific and Technical Information of China (English)
Gang YANG; Ru-yun CHEN; Luo-gen YAO
2012-01-01
Based on the modified homotopy perturbation method (MHPM),exact solutions of certain partial differential equations are constructed by separation of variables and choosing the finite terms of a series in p as exact solutions.Under suitable initial conditions,the PDE is transformed into an ODE.Some illustrative examples reveal the efficiency of the proposed method.
Institute of Scientific and Technical Information of China (English)
Long Shuyao; Zhang Qin
2000-01-01
In this paper the dual reciprocity boundary element method is employed to solve nonlinear differential equation 2 u + u + εu3 = b. Results obtained in an example have a good agreement with those by FEM and show the applicability and simplicity of dual reciprocity method(DRM) in solving nonlinear dif ferential equations.
D-CONVERGENCE OF RUNGE-KUTTA METHODS FOR STIFF DELAY DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
Cheng-ming Huang; Hong-yuan Fu; Shou-fu Li; Guang-nan Chen
2001-01-01
This paper is concerned with the numerical solution of delay differential equations(DDEs).We focus on the error behaviour of Runge-Kutta methods for stiff DDEs. We investigate D-convergence properties of algebraically stable Runge-Kutta methods with three kinds of interpolation procedures.
Indian Academy of Sciences (India)
Wenjun Liu; Kewang Chen
2013-09-01
In this paper, we implemented the functional variable method and the modified Riemann–Liouville derivative for the exact solitary wave solutions and periodic wave solutions of the time-fractional Klein–Gordon equation, and the time-fractional Hirota–Satsuma coupled KdV system. This method is extremely simple but effective for handling nonlinear time-fractional differential equations.
Comparison of the Monte Carlo adjoint-weighted and differential operator perturbation methods
Energy Technology Data Exchange (ETDEWEB)
Kiedrowski, Brian C [Los Alamos National Laboratory; Brown, Forrest B [Los Alamos National Laboratory
2010-01-01
Two perturbation theory methodologies are implemented for k-eigenvalue calculations in the continuous-energy Monte Carlo code, MCNP6. A comparison of the accuracy of these techniques, the differential operator and adjoint-weighted methods, is performed numerically and analytically. Typically, the adjoint-weighted method shows better performance over a larger range; however, there are exceptions.
Variational iteration method for solving partial differential equations with variable coefficients
Energy Technology Data Exchange (ETDEWEB)
Ali, A.H.A. [Mathematics Department, Faculty of Science, Menoufia University, Shebein El-Koom (Egypt)], E-mail: ahaali_49@yahoo.com; Raslan, K.R. [Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr-City, Cairo (Egypt)], E-mail: kamal_raslan@yahoo.com
2009-05-15
An extremely simple and elementary but rigorous derivation of exact solutions of partial differential equations in different dimensions with variable coefficients is given using the variational iteration method. The efficiency of the considered method is illustrated by some examples. The results show that the proposed iteration technique, without linearization or small perturbation, is very effective and convenient.
Directory of Open Access Journals (Sweden)
Abaker. A. Hassaballa.
2015-10-01
Full Text Available - In recent years, many more of the numerical methods were used to solve a wide range of mathematical, physical, and engineering problems linear and nonlinear. This paper applies the homotopy perturbation method (HPM to find exact solution of partial differential equation with the Dirichlet and Neumann boundary conditions.
D-CONVERGENCE OF ONE-LEG METHODS FOR STIFF DELAY DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
Cheng-ming Huang; Shou-fu Li; Hong-yuan Fu; Guang-nan Chen
2001-01-01
This paper is concerned with the numerical solution of delay differential equations(DDEs).We focus on the error analysis of one-leg methods applied nonlinear stiff DDEs. It is proved that an A-stable one-leg method with a simple linear interpolation is D-convergent of order p, if it is consistent of order p in the classical sense.
A block Krylov subspace time-exact solution method for linear ordinary differential equation systems
Bochev, Mikhail A.
2013-01-01
We propose a time-exact Krylov-subspace-based method for solving linear ordinary differential equation systems of the form $y'=-Ay+g(t)$ and $y"=-Ay+g(t)$, where $y(t)$ is the unknown function. The method consists of two stages. The first stage is an accurate piecewise polynomial approximation of
An Effective Method for Seeking Conservation Laws of Partial Differential Equations
Institute of Scientific and Technical Information of China (English)
QIN Mao-Chang; MEI Feng-Xiang; FAN Gui-Hong
2006-01-01
This paper introduces an effective method for seeking localconservation laws of general partial differential equations (PDEs). The well-known variational principle does not involve in this method. Alternatively, the conservation laws can be derived from symmetries, which include the symmetries of the associated linearized equation of the PDEs,and the adjoint symmetries of the adjoint equation of the PDEs.
Three-stage Stiffly Accurate Runge-Kutta Methods for Stiff Stochastic Differential Equations
Institute of Scientific and Technical Information of China (English)
WANG PENG
2011-01-01
In this paper we discuss diagonally implicit and semi-implicit methods based on the three-stage stiffly accurate Runge-Kutta methods for solving Stratonovich stochastic differential equations (SDEs). Two methods, a three-stage stiffly accurate semi-implicit (SASI3) method and a three-stage stiffly accurate diagonally implicit (SADI3) method, are constructed in this paper. In particular, the truncated random variable is used in the implicit method. The stability properties and numerical results show the effectiveness of these methods in the pathwise approximation of stiff SDEs.
Chatterjee, Ishita; Li, Fei; Kohler, Erin E.; Rehman, Jalees; Malik, Asrar B.; Wary, Kishore K.
2015-01-01
Summary The studies of stem cell behavior and differentiation in a developmental context is complex, time-consuming and expensive, and for this reason, cell culture remains a method of choice for developmental and regenerative biology and mechanistic studies. Similar to ES cells, iPS cells have the ability to differentiate into endothelial cells (ECs), and the route for differentiation appears to mimic the developmental process that occurs during the formation of an embryo. Traditional EC induction methods from embryonic stem (ES) cells rely mostly on the formation the embryoid body (EB), which employs feeder or feeder-free conditions in the presence or absence of supporting cells. Similar to ES cells, iPS cells can be cultured in feeder-layer or feeder-free conditions. Here, we describe the iPS cell culture methods and induction differentiation of these cells into ECs. We use anti-mouse Flk1 and anti-mouse VE-cadherin to isolate and characterize mouse ECs, because these antibodies are commercially available and their use has been described in the literature, including by our group. The ECs produced by this method have been used by our laboratory, and we have demonstrated their in vivo potential. We also discuss how iPS cells differ in their ability to differentiate into endothelial cells in culture. PMID:25687301
Chatterjee, Ishita; Li, Fei; Kohler, Erin E; Rehman, Jalees; Malik, Asrar B; Wary, Kishore K
2016-01-01
The study of stem cell behavior and differentiation in a developmental context is complex, time-consuming, and expensive, and for this reason, cell culture remains a method of choice for developmental and regenerative biology and mechanistic studies. Similar to ES cells, iPS cells have the ability to differentiate into endothelial cells (ECs), and the route for differentiation appears to mimic the developmental process that occurs during the formation of an embryo. Traditional EC induction methods from embryonic stem (ES) cells rely mostly on the formation of embryoid body (EB), which employs feeder or feeder-free conditions in the presence or absence of supporting cells. Similar to ES cells, iPS cells can be cultured in feeder layer or feeder-free conditions. Here, we describe the iPS cell culture methods and induction differentiation of these cells into ECs. We use anti-mouse Flk1 and anti-mouse VE-cadherin to isolate and characterize mouse ECs, because these antibodies are commercially available and their use has been described in the literature, including by our group. The ECs produced by this method have been used by our laboratory, and we have demonstrated their in vivo potential. We also discuss how iPS cells differ in their ability to differentiate into endothelial cells in culture.
An analysis of the wide area differential method of geostationary orbit satellites
Institute of Scientific and Technical Information of China (English)
CAI ChengLin; LI XiaoHui; WU HaiTao
2009-01-01
This work aims to obtain a wide area differential method for geostationary orbit (GEO) constellation. A comparison between the dilution of precision (DOP) of four-dimensional (4D) calculation including satellite clock errors and ephemeris errors and that of three-dimensional (3D) calculation only including ephemeris errors with the inverse positioning theory of GPS shows the conclusion that all the 3D PDOPs are greatly reduced. Based on this, a basic idea of correcting satellite clock errors and ephem-eris errors apart is put forward, and moreover, a specific method of separation is proposed. Satellite clock errors are separated in a master station with time synchronization, and all the remaining pseudo-range errors after the satellite clock errors have been deducted are used to work out ephemeris corrections of all GEO satellites. By a comparative analysis of user positioning accuracy before and after differential, the wide area differential method is verified to be quite valid for GEO constellation.
Meleshko, Sergey V
2005-01-01
Differential equations, especially nonlinear, present the most effective way for describing complex physical processes. Methods for constructing exact solutions of differential equations play an important role in applied mathematics and mechanics. This book aims to provide scientists, engineers and students with an easy-to-follow, but comprehensive, description of the methods for constructing exact solutions of differential equations.
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
In order to solve the problems that the novel wide area differential method on the satellite clock and ephemeris relative correction (CERC) in the non-geostationary orbit satellite constellation, a virtual reference satellite (VRS) differential principle using relative correction of satellite ephemeris errors is proposed. It is referred to be as the VRS differential principle, and the elaboration is focused on the construction of pseudo-range errors of VRS. Through qualitative analysis, it can be found that the impact of the satellite’s clock and ephemeris errors on positioning can basically be removed and the users’ positioning errors are near zero. Through simulation analysis of the differential performance, it is verified that the differential method is universal in all kinds of satellite navigation systems with geostationary orbit (GEO) constellation, Medium orbit (MEO) constellation or hybrid orbit constellation, and it has insensitivity to abnormal aspects of a satellite ephemeris and clock. Moreover, the real time positioning accuracy of differential users can be maintained within several decimeters after the pseudo-range measurement noise is effectively weakened or eliminated.
Cai, Chenglin; Li, Xiaohui; Wu, Haitao
2010-12-01
In order to solve the problems that the novel wide area differential method on the satellite clock and ephemeris relative correction (CERC) in the non-geostationary orbit satellite constellation, a virtual reference satellite (VRS) differential principle using relative correction of satellite ephemeris errors is proposed. It is referred to be as the VRS differential principle, and the elaboration is focused on the construction of pseudo-range errors of VRS. Through qualitative analysis, it can be found that the impact of the satellite's clock and ephemeris errors on positioning can basically be removed and the users' positioning errors are near zero. Through simulation analysis of the differential performance, it is verified that the differential method is universal in all kinds of satellite navigation systems with geostationary orbit (GEO) constellation, Medium orbit (MEO) constellation or hybrid orbit constellation, and it has insensitivity to abnormal aspects of a satellite ephemeris and clock. Moreover, the real time positioning accuracy of differential users can be maintained within several decimeters after the pseudo-range measurement noise is effectively weakened or eliminated.
Directory of Open Access Journals (Sweden)
Phuc Van Pham
2015-06-01
Full Text Available Breast cancer stem cells were considered as origins of breast cancer. Previously published studies showed that breast cancer stem cells exhibited high multi-drug resistance. This study aimed to evaluate the spontaneous differentiation of human breast cancer stem cells and investigate some in vitro conditions to control this process. Human breast cancer stem cells (BCSCs were sorted from primary culture of breast malignant tumors based on expression of CD44 and CD24. The in vitro spontaneous differentiation of BCSCs was evaluated in the popular culture medium DMEM/F12 supplemented with 10% fetal bovine serum (FBS, 1% antibiotic-antimycotic. There were some different methods to control the spontaneous differentiation of BCSCs included free serum culture, mammosphere culture, basic fibroblast growth factor and epidermal growth factor supplement to serum medium, and hypoxia culture. The results showed that BCSCs always were spontaneously differentiated in vitro in the popular culture medium DMEM/F12 plus 10% FBS. The percentage of BCSCs gradually decreased according to sub-culture times and became stable after 20 sub-culture times. All investigated methods could not completely inhibit the spontaneous differentiation of BCSCs. Serum-free culture combined with hypoxia condition had strongest inhibition of this process. These results demonstrated that the spontaneous differentiation is nature process of BCSCs; therefore this process should be determined and suitably controlled depending on different experiments. [Biomed Res Ther 2015; 2(6.000: 290-296
NUMERICAL METHOD BASED ON HAMILTON SYSTEM AND SYMPLECTIC ALGORITHM TO DIFFERENTIAL GAMES
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
The resolution of differential games often concerns the difficult problem of two points border value (TPBV), then ascribe linear quadratic differential game to Hamilton system. To Hamilton system, the algorithm of symplectic geometry has the merits of being able to copy the dynamic structure of Hamilton system and keep the measure of phase plane. From the viewpoint of Hamilton system, the symplectic characters of linear quadratic differential game were probed; as a try, Symplectic-Runge-Kutta algorithm was presented for the resolution of infinite horizon linear quadratic differential game. An example of numerical calculation was given, and the result can illuminate the feasibility of this method. At the same time, it embodies the fine conservation characteristics of symplectic algorithm to system energy.
Directory of Open Access Journals (Sweden)
Emad A.-B. Abdel-Salam
2013-01-01
Full Text Available The fractional Riccati expansion method is proposed to solve fractional differential equations. To illustrate the effectiveness of the method, space-time fractional Korteweg-de Vries equation, regularized long-wave equation, Boussinesq equation, and Klein-Gordon equation are considered. As a result, abundant types of exact analytical solutions are obtained. These solutions include generalized trigonometric and hyperbolic functions solutions which may be useful for further understanding of the mechanisms of the complicated nonlinear physical phenomena and fractional differential equations. Among these solutions, some are found for the first time. The periodic and kink solutions are founded as special case.
Abdel-Salam, Emad A-B; Hassan, Gmal F
2015-01-01
In this paper, the fractional projective Riccati expansion method is proposed to solve fractional differential equations. To illustrate the effectiveness of the method, we discuss the space-time fractional Burgers equation, the space-time fractional mKdV equation and time fractional biological population model. The solutions are expressed in terms of fractional hyperbolic functions. These solutions are useful to understand the mechanisms of the complicated nonlinear physical phenomena and fractional differential equations. Among these solutions, some are found for the first time. The fractal index for the obtained results is equal to one. Counter examples to compute the fractal index are introduced in appendix.
Energy Technology Data Exchange (ETDEWEB)
Yang, Xiao-Jun, E-mail: dyangxiaojun@hotmail.com [Department of Mathematics and Mechanics, China University of Mining and Technology, Xuzhou, Jiangsu, 221008 (China); Institute of Applied Mathematics, Qujing Normal University, Qujing 655011 (China); Srivastava, H.M., E-mail: harimsri@math.uvic.ca [Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4 (Canada); He, Ji-Huan, E-mail: hejihuan@suda.edu.cn [National Engineering Laboratory for Modern Silk, College of Textile and Clothing Engineering, Soochow University, 199 Ren-ai Road, Suzhou 215123 (China); Baleanu, Dumitru, E-mail: dumitru@cankaya.edu.tr [Department of Mathematics and Computer Sciences, Faculty of Arts and Sciences, Cankaya University, Ankara, 06530 (Turkey); Department of Chemical and Materials Engineering, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah, 21589 (Saudi Arabia); Institute of Space Sciences, Magurele-Bucharest (Romania)
2013-10-15
In this Letter, we propose to use the Cantor-type cylindrical-coordinate method in order to investigate a family of local fractional differential operators on Cantor sets. Some testing examples are given to illustrate the capability of the proposed method for the heat-conduction equation on a Cantor set and the damped wave equation in fractal strings. It is seen to be a powerful tool to convert differential equations on Cantor sets from Cantorian-coordinate systems to Cantor-type cylindrical-coordinate systems.
Exponential rational function method for space-time fractional differential equations
Aksoy, Esin; Kaplan, Melike; Bekir, Ahmet
2016-04-01
In this paper, exponential rational function method is applied to obtain analytical solutions of the space-time fractional Fokas equation, the space-time fractional Zakharov Kuznetsov Benjamin Bona Mahony, and the space-time fractional coupled Burgers' equations. As a result, some exact solutions for them are successfully established. These solutions are constructed in fractional complex transform to convert fractional differential equations into ordinary differential equations. The fractional derivatives are described in Jumarie's modified Riemann-Liouville sense. The exact solutions obtained by the proposed method indicate that the approach is easy to implement and effective.
A survey of differentiation methods for national greenhouse gas reduction targets
Energy Technology Data Exchange (ETDEWEB)
Torvanger, Asbjoern; Godal, Odd
1999-11-01
The aim of the report is to contribute to exploring the potential differentiation methods for national greenhouse gas reduction targets. The Kyoto Protocol to the United Nations Framework Convention on Climate Change (UNFCCC) from 1997 established differentiation of targets among countries. A more systematic approach to differentiation would facilitate future negotiations. Three sources of methods or proposals are employed. The first are proposals from the Ad Hoc Group on the Berlin Mandate (AGBM) process from 1995 until the Kyoto Protocol was adopted in December 1997, in all 17 proposals were selected. The second source is the EU`s Triptique approach for differentiation of targets among its member states. The third source is recent academic literature where 8 contributions from the period 1992 to 1998 were included. The proposals are presented in a catalogue style. Based on 4 criteria on the usefulness of proposals or methods for future negotiations we have chosen 5 proposals, a Japanese, French, Norwegian, Brazilian in addition to the EU`s Triptique approach. Some numerical illustrations for the Baltic Sea region are presented. Given the joint Kyoto Protocol reduction target for the region we compare the burden sharing consequences for the proposals. For illustrations we employ the following fairness principles as differentiation methods: 1) The Sovereignty principle. 2) The Egalitarian principle. 3) The Ability to Pay principle. With the aim to evaluate the political feasibility of the various differentiation methods we compare the results across the countries in the Baltic Sea region and divide them into OECD and EIT countries. The outcome of the Kyoto Protocol is interpreted as an example of a politically feasible differentiation scheme. On the basis of the observations we find principles 1) and 2) less interesting. A ranking of the differentiation methods according to political feasibility is made and discussed. Among the countries in the Baltic Sea region
Functional differential equations—a reciprocity principle
Directory of Open Access Journals (Sweden)
Lloyd K. Williams
1986-01-01
Full Text Available The functional differential equations proposed for solution here are mainly ordinary differential equations with fairly general argument deviations. Included among them are equations with involutions and some with reflections of the argument. Solutions will be obtained by quadratures in terms of implicitly defined functions. They have a wide range of applicability from the stability theory of differential-difference equations to electrodynamics and biological models.
Directory of Open Access Journals (Sweden)
Mishra Vinod
2016-01-01
Full Text Available Numerical Laplace transform method is applied to approximate the solution of nonlinear (quadratic Riccati differential equations mingled with Adomian decomposition method. A new technique is proposed in this work by reintroducing the unknown function in Adomian polynomial with that of well known Newton-Raphson formula. The solutions obtained by the iterative algorithm are exhibited in an infinite series. The simplicity and efficacy of method is manifested with some examples in which comparisons are made among the exact solutions, ADM (Adomian decomposition method, HPM (Homotopy perturbation method, Taylor series method and the proposed scheme.
An Accurate Block Hybrid Collocation Method for Third Order Ordinary Differential Equations
Directory of Open Access Journals (Sweden)
Lee Ken Yap
2014-01-01
Full Text Available The block hybrid collocation method with two off-step points is proposed for the direct solution of general third order ordinary differential equations. Both the main and additional methods are derived via interpolation and collocation of the basic polynomial. These methods are applied in block form to provide the approximation at five points concurrently. The stability properties of the block method are investigated. Some numerical examples are tested to illustrate the efficiency of the method. The block hybrid collocation method is also implemented to solve the nonlinear Genesio equation and the problem in thin film flow.
Variational iteration method for solving non-linear partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Hemeda, A.A. [Department of Mathematics, Faculty of Science, University of Tanta, Tanta (Egypt)], E-mail: aahemeda@yahoo.com
2009-02-15
In this paper, we shall use the variational iteration method to solve some problems of non-linear partial differential equations (PDEs) such as the combined KdV-MKdV equation and Camassa-Holm equation. The variational iteration method is superior than the other non-linear methods, such as the perturbation methods where this method does not depend on small parameters, such that it can fined wide application in non-linear problems without linearization or small perturbation. In this method, the problems are initially approximated with possible unknowns, then a correction functional is constructed by a general Lagrange multiplier, which can be identified optimally via the variational theory.
CONVERGENCE OF PARALLEL DIAGONAL ITERATION OF RUNGE-KUTTA METHODS FOR DELAY DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
Xiao-hua Ding; Mingzhu Liu
2004-01-01
Implicit Runge-Kutta method is highly accurate and stable for stiff initial value prob-lem. But the iteration technique used to solve implicit Runge-Kutta method requires lots of computational efforts. In this paper, we extend the Parallel Diagonal Iterated Runge-Kutta(PDIRK) methods to delay differential equations(DDEs). We give the convergence region of PDIRK methods, and analyze the speed of convergence in three parts for the P-stability region of the Runge-Kutta corrector method. Finally, we analysis the speed-up factor through a numerical experiment. The results show that the PDIRK methods to DDEs are efficient.
Institute of Scientific and Technical Information of China (English)
丛玉豪
2001-01-01
The stability analysis of linear multistep methods for the numerical solutions of the systems of generalized neutral delay differential equations is discussed. The stability behaviour of linear multistep methods was analysed for the solution of the generalized system of linear neutral test equations. After the establishment of a sufficient condition for asymptotic stability of the solutions of the generalized system, it is shown that a linear multistep method is NGPG-stable if and only if it is A-stable.
Institute of Scientific and Technical Information of China (English)
Rui QI; Cheng-jian ZHANG; Yu-jie ZHANG
2012-01-01
This paper is concerned with the numerical dissipativity of multistep Runge-Kutta methods for nonlinear Volterra delay-integro-differential equations. We investigate the dissipativity properties of (k,l)-algebraically stable multistep Runge-Kutta methods with constrained grid and an uniform grid.The finitedimensional and infinite-dimensional dissipativity results of (k,l)-algebraically stable Runge-Kutta methods are obtained.
NONLINEAR STABILITY OF NATURAL RUNGE-KUTTA METHODS FOR NEUTRAL DELAY DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
Cheng-jian Zhang
2002-01-01
This paper first presents the stability analysis of theoretical solutions for a class of nonlinear neutral delay-differential equations (NDDEs). Then the numerical analogous results, of the natural Runge-Kutta (NRK) methods for the same class of nonlinear NDDEs,are given. In particular, it is shown that the (k, l)-algebraic stability of a RK method for ODEs implies the generalized asymptotic stability and the global stability of the induced NRK method.
Stability Analysis of Runge-Kutta Methods for Delay Integro-Differential Equations
Institute of Scientific and Technical Information of China (English)
甘四清; 郑纬民
2004-01-01
Considering a linear system of delay integro-differential equations with a constant delay whose zero solution is asympototically stable, this paper discusses the stability of numerical methods for the system. The adaptation of Runge-Kutta methods with a Lagrange interpolation procedure was focused on inheriting the asymptotic stability of underlying linear systems. The results show that an A-stable Runge-Kutta method preserves the asympototic stability of underlying linear systems whenever an unconstrained grid is used.
Directory of Open Access Journals (Sweden)
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.
Quadrature Rotating-Frame Gradient Fields for Ultra-Low FieldNuclear Magnetic Resonance and Imaging
Energy Technology Data Exchange (ETDEWEB)
Bouchard, Louis-Serge
2005-12-30
Magnetic resonance imaging (MRI) in very low fields isfundamentally limited by untruncated concomitant gradients which causesevere distortions in image acquisition and volume selection if thegradient fields are strong compared to the static field. In this paper,it is shown that gradient fields oscillating in quadrature can be usedfor spatial encoding in low fields and provide substantial improvementsover conventional encoding methods using static gradients. In particular,cases where the gradient field is comparable to or higher than theexternal field, Gmax/B0>1, are examined. It is shown thatundistorted slice selection and image encoding is possible because ofsmaller geometric phase errors introduced during cyclic motions of theHamiltonian. In the low field limit (Gmax/B_0 ->infinity) sliceselection is achieved with a combination of soft pulse segments and acoherent train of hard pulses to average out concomitant fields over thefast scale of the rf Hamiltonian.
Statistical shape and texture model of quadrature phase information for prostate segmentation.
Ghose, Soumya; Oliver, Arnau; Martí, Robert; Lladó, Xavier; Freixenet, Jordi; Mitra, Jhimli; Vilanova, Joan C; Comet-Batlle, Josep; Meriaudeau, Fabrice
2012-01-01
Prostate volume estimation from segmentation of transrectal ultrasound (TRUS) images aids in diagnosis and treatment of prostate hypertrophy and cancer. Computer-aided accurate and computationally efficient prostate segmentation in TRUS images is a challenging task, owing to low signal-to-noise ratio, speckle noise, calcifications, and heterogeneous intensity distribution in the prostate region. A multi-resolution framework using texture features in a parametric deformable statistical model of shape and appearance was developed to segment the prostate. Local phase information of log-Gabor quadrature filter extracted texture of the prostate region in TRUS images. Large bandwidth of log-Gabor filter ensures easy estimation of local orientations, and zero response for a constant signal provides invariance to gray level shift. This aids in enhanced representation of the underlying texture information of the prostate unaffected by speckle noise and imaging artifacts. The parametric model of the propagating contour is derived from principal component analysis of prior shape and texture information of the prostate from the training data. The parameters were modified using prior knowledge of the optimization space to achieve segmentation. The proposed method achieves a mean Dice similarity coefficient value of 0.95 ± 0.02 and mean absolute distance of 1.26 ± 0.51 millimeter when validated with 24 TRUS images of 6 data sets in a leave-one-patient-out validation framework. The proposed method for prostate TRUS image segmentation is computationally efficient and provides accurate prostate segmentations in the presence of intensity heterogeneities and imaging artifacts.
On the amplitude and phase errors of quadrature LC-tank CMOS oscillators
DEFF Research Database (Denmark)
Mazzanti, Andrea; Svelto, Francesco; Andreani, Pietro
2006-01-01
An analytic approach for the estimation of the phase and amplitude imbalances caused by component mismatches and parasitic magnetic fields in two popular quadrature LC oscillators is presented. Very simple and closed-form equations are derived, proving that, although the two topologies share...
A Quantized Analog Delay for an ir-UWB Quadrature Downconversion Autocorrelation Receiver
Bagga, S.; Zhang, L.; Serdijn, W.A.; Long, J.R.; Busking, E.B.
2005-01-01
A quantized analog delay is designed as a requirement for the autocorrelation function in the quadrature downconversion autocorrelation receiver (QDAR). The quantized analog delay is comprised of a quantizer, multiple binary delay lines and an adder circuit. Being the foremost element, the quantizer
Directory of Open Access Journals (Sweden)
V. M. Stechenko
1982-12-01
Full Text Available The results of the study of quadrature bridge device to a range of 10 to 100 MHz and 30-300 MHz. The apparatus consists of two adders for magnetically lines and a constant phase shift of the phase shifter.
Analysis and Design of a 1.8-GHz CMOS LC Quadrature VCO
DEFF Research Database (Denmark)
Andreani, Pietro; Bonfanti, A.; Romanò, L.
2002-01-01
This paper presents a quadrature voltage-controlled oscillator (QVCO) based on the coupling of two LC-tank VCOs. A simplified theoretical analysis for the oscillation frequency and phase noise displayed by the QVCO in the 1/f3 region is developed, and good agreement is found between theory...
Single-Stage Low-Power Quadrature RF Receiver Front-End: The LMV Cell
DEFF Research Database (Denmark)
Liscidini, Antonio; Mazzanti, Andrea; Tonietto, Riccardo;
2006-01-01
This paper presents the first quadrature RF receiver front-end where, in a single stage, low-noise amplifier (LNA), mixer and voltage-controlled oscillator (VCO) share the same bias current. The new structure exploits the intrinsic mixing functionality of a classical LC-tank oscillator providing...
47.8 GHz InPHBT quadrature VCO with 22% tuning range
DEFF Research Database (Denmark)
Hadziabdic, Dzenan; Johansen, Tom Keinicke; Krozer, Viktor;
2007-01-01
A 38-47.8 GHz quadrature voltage controlled oscillator (QVCO) in InP HBT technology is presented. The measured output power is - 15 dBm. The simulated phase noise ranges from -84 to -86 dBc/Hz at 1 MHz offset. It is believed that this is the first millimetre-wavc QVCO implemented in InP HBT techn...
Håvie, T.
1970-01-01
Some quadrature formulae using the derivatives of the integrand are discussed. As special cases are obtained generalizations of both the ordinary and the modified Romberg algorithms. In all cases the error terms are expressed in terms of Bernoulli polynomials and functions.
AM to PM noise conversion in a cross-coupled quadrature harmonic oscillator
DEFF Research Database (Denmark)
Djurhuus, Torsten; Krozer, Viktor; Vidkjær, Jens
2006-01-01
We derive the dynamic equations governing the cross-coupled quadrature oscillator, perturbed by noise, leading to an expression for the close-in phase noise. The theory shows that a nonlinear coupling transconductance results in AM-PM noise conversion close to the carrier, which increases...
Quadrature phase shift keying coherent state discrimination via a hybrid receiver
DEFF Research Database (Denmark)
Müller, C. R.; Castaneda, Mario A. Usuga; Wittmann, C.;
2012-01-01
We propose and experimentally demonstrate a near-optimal discrimination scheme for the quadrature phase shift keying (QPSK) protocol. We show in theory that the performance of our hybrid scheme is superior to the standard scheme—heterodyne detection—for all signal amplitudes and underpin the pred...
A modified method by differential adhesion for enrichment of bladder cancer stem cells
Directory of Open Access Journals (Sweden)
Yong-tong Zhu
Full Text Available ABSTRACT Purpose: In a previous study the vaccine was effective against bladder cancer in a mouse model. However, a small portion of tumors regrew because the vaccine could not eliminate bladder cancer stem cells (CSCs. In this study, we showed a modified method for the isolation of bladder CSCs using a combination of differential adhesion method and serum-free culture medium (SFM method. Materials and Methods: Trypsin-resistant cells and trypsin-sensitive cells were isolated from MB49, EJ and 5637 cells by a combination of differential adhesion method and SFM method. The CSCs characterizations of trypsin-resistant cells were verified by the flow cytometry, the western blotting, the quantitative polymerase chain reaction, the resistance to chemotherapy assay, the transwell assay, and the tumor xenograft formation assay. Results: Trypsin-resistant cells were isolated and identified in CSCs characters, with high expression of CSCs markers, higher resistance to chemotherapy, greater migration in vitro, and stronger tumorigenicity in vivo. Conclusion: Trypsin-resistant cells displayed specific CSCs properties. Our study showed trypsin-resistant cells were isolated successfully with a modified method using a combination of differential adhesion method and SFM method.
A low-phase-noise wide-band CMOS quadrature VCO for multi-standard RF front-ends
DEFF Research Database (Denmark)
Fard, Ali; Andreani, Pietro
2005-01-01
A low phase noise CMOS LC quadrature VCO (QVCO) with a wide frequency range of 3.6-5.6 GHz, designed in a standard 0.18 μm process for multi-standard front-ends, is presented. A significant advantage of the topology is the larger oscillation amplitude when compared to other conventional QVCO...... structures. The QVCO is compared to a double cross-coupled LC-tank differential oscillator, both in theory and experiments, for evaluation of its phase noise, providing a good insight into its performance. The measured data displays up to 2 dBc/Hz lower phase noise in the 1/f2 region for the QVCO, when...... consuming twice the current of the differential VCO, based on an identical LC-tank. Experimental results on the QVCO show a phase noise level of -127.5 dBc/Hz at 3 MHz offset from a 5.6 GHz carrier while dissipating 8 mA of current, resulting in a figure of merit of 181.3 dBc/Hz....
THE COLLOCATION METHODS FOR SINGULAR INTEGRAL EQUATIONS WITH CAUCHY KERNELS
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
This paper applies the singular integral operators,singular quadrature operators and discretization matrices associated withsingular integral equations with Cauchy kernels, which are established in [1],to give a unified framework for various collocation methods of numericalsolutions of singular integral equations with Cauchy kernels. Under theframework, the coincidence of the direct quadrature method and the indirectquadrature method is very simple and obvious.
Chen, Shuo; Kang, Jian; Xing, Yishi; Wang, Guoqing
2015-12-01
Group-level functional connectivity analyses often aim to detect the altered connectivity patterns between subgroups with different clinical or psychological experimental conditions, for example, comparing cases and healthy controls. We present a new statistical method to detect differentially expressed connectivity networks with significantly improved power and lower false-positive rates. The goal of our method was to capture most differentially expressed connections within networks of constrained numbers of brain regions (by the rule of parsimony). By virtue of parsimony, the false-positive individual connectivity edges within a network are effectively reduced, whereas the informative (differentially expressed) edges are allowed to borrow strength from each other to increase the overall power of the network. We develop a test statistic for each network in light of combinatorics graph theory, and provide p-values for the networks (in the weak sense) by using permutation test with multiple-testing adjustment. We validate and compare this new approach with existing methods, including false discovery rate and network-based statistic, via simulation studies and a resting-state functional magnetic resonance imaging case-control study. The results indicate that our method can identify differentially expressed connectivity networks, whereas existing methods are limited.
THE NUMERICAL STABILITY OF THE BLOCK θ-METHODS FOR DELAY DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
This paper focuses on the numerical stability of the block θ-methods adapted to differential equations with a dday argument. For the block θ-methods, an interpolation procedure is introduced which leads to the mumerical processes that satisfy an important asymptotic stability condition related to the class of test problems y＇ (t)=ay(t)+by(t-r) with a,b∈C, Re(a)＜- ｜b｜ and τ>0. We prove that the block θ-method is GP-stable if and only if the method is A-stable for ordinary differential equations. Furthermore, it is proved that the P-and GP-stability are equivalent for the block θ-method.
Directory of Open Access Journals (Sweden)
J. Prakash
2016-03-01
Full Text Available In this paper, a numerical algorithm based on a modified He-Laplace method (MHLM is proposed to solve space and time nonlinear fractional differential-difference equations (NFDDEs arising in physical phenomena such as wave phenomena in fluids, coupled nonlinear optical waveguides and nanotechnology fields. The modified He-Laplace method is a combined form of the fractional homotopy perturbation method and Laplace transforms method. The nonlinear terms can be easily decomposed by the use of He’s polynomials. This algorithm has been tested against time-fractional differential-difference equations such as the modified Lotka Volterra and discrete (modified KdV equations. The proposed scheme grants the solution in the form of a rapidly convergent series. Three examples have been employed to illustrate the preciseness and effectiveness of the proposed method. The achieved results expose that the MHLM is very accurate, efficient, simple and can be applied to other nonlinear FDDEs.
Sharma, Dinkar; Singh, Prince; Chauhan, Shubha
2016-01-01
In this paper, a combined form of the Laplace transform method with the homotopy perturbation method (HPTM) is applied to solve nonlinear systems of partial differential equations viz. the system of third order KdV Equations and the systems of coupled Burgers' equations in one- and two- dimensions. The nonlinear terms can be easily handled by the use of He's polynomials. The results shows that the HPTM is very efficient, simple and avoids the round-off errors. Four test examples are considered to illustrate the present scheme. Further the results are compared with Homotopy perturbation method (HPM) which shows that this method is a suitable method for solving systems of partial differential equations.
High order aberrations calculation of a hexapole corrector using a differential algebra method
Kang, Yongfeng; Liu, Xing; Zhao, Jingyi; Tang, Tiantong
2017-02-01
A differential algebraic (DA) method is proved as an unusual and effective tool in numerical analysis. It implements conveniently differentiation up to arbitrary high order, based on the nonstandard analysis. In this paper, the differential algebra (DA) method has been employed to compute the high order aberrations up to the fifth order of a practical hexapole corrector including round lenses and hexapole lenses. The program has been developed and tested as well. The electro-magnetic fields of arbitrary point are obtained by local analytic expressions, then field potentials are transformed into new forms which can be operated in the DA calculation. In this paper, the geometric and chromatic aberrations up to fifth order of a practical hexapole corrector system are calculated by the developed program.
Approximation of weak adjoints by reverse automatic differentiation of BDF methods
Beigel, Dörte; Wirsching, Leonard; Bock, Hans Georg
2011-01-01
With this contribution, we shed light on the relation between the discrete adjoints of multistep backward differentiation formula (BDF) methods and the solution of the adjoint differential equation. To this end, we develop a functional-analytic framework based on a constrained variational problem and introduce the notion of weak adjoint solutions. We devise a finite element Petrov-Galerkin interpretation of the BDF method together with its discrete adjoint scheme obtained by reverse internal numerical differentiation. We show how the finite element approximation of the weak adjoint is computed by the discrete adjoint scheme and prove its asymptotic convergence in the space of normalized functions of bounded variation. We also obtain asymptotic convergence of the discrete adjoints to the classical adjoints on the inner time interval. Finally, we give numerical results for non-adaptive and fully adaptive BDF schemes. The presented framework opens the way to carry over the existing theory on global error estimat...
Subich, Christopher J.
2015-08-01
This work extends the machinery of the moving mesh partial differential equation (MMPDE) method to the spectral collocation discretization of time-dependent partial differential equations. Unlike previous approaches which bootstrap the moving grid from a lower-order, finite-difference discretization, this work uses a consistent spectral collocation discretization for both the grid movement problem and the underlying, physical partial differential equation. Additionally, this work develops an error monitor function based on filtering in the spectral domain, which concentrates grid points in areas of locally poor resolution without relying on an assumption of locally steep gradients. This makes the MMPDE method more robust in the presence of rarefaction waves which feature rapid change in higher-order derivatives.
Nkouawa, Agathe; Sako, Yasuhito; Nakao, Minoru; Nakaya, Kazuhiro; Ito, Akira
2009-01-01
Rapid detection and differentiation of Taenia species are required for the control and prevention of taeniasis and cysticercosis in areas where these diseases are endemic. Because of the lower sensitivity and specificity of the conventional diagnosis based on microscopical examination, molecular tools are more reliable for differential diagnosis of these diseases. In this study, we developed and evaluated a loop-mediated isothermal amplification (LAMP) assay for differential diagnosis of infections with Taenia species with cathepsin L-like cysteine peptidase (clp) and cytochrome c oxidase subunit 1 (cox1) genes. LAMP with primer sets to the cox1 gene could differentiate between three species, and LAMP with primer sets to the clp gene could differentiate Taenia solium from Taenia saginata/Taenia asiatica. Restriction enzyme digestion of the LAMP products from primer set Tsag-clp allowed the differentiation of Taenia saginata from Taenia asiatica. We demonstrated the high specificity of LAMP by testing known parasite DNA samples extracted from proglottids (n = 100) and cysticerci (n = 68). LAMP could detect one copy of the target gene or five eggs of T. asiatica and T. saginata per gram of feces, showing sensitivity similar to that of PCR methods. Furthermore, LAMP could detect parasite DNA in all taeniid egg-positive fecal samples (n = 6). Due to the rapid, simple, specific, and sensitive detection of Taenia species, the LAMP assays are valuable tools which might be easily applicable for the control and prevention of taeniasis and cysticercosis in countries where these diseases are endemic.
Directory of Open Access Journals (Sweden)
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.
Exact solutions of some nonlinear partial differential equations using functional variable method
Indian Academy of Sciences (India)
A Nazarzadeh; M Eslami; M Mirzazadeh
2013-08-01
The functional variable method is a powerful solution method for obtaining exact solutions of some nonlinear partial differential equations. In this paper, the functional variable method is used to establish exact solutions of the generalized forms of Klein–Gordon equation, the (2 + 1)-dimensional Camassa–Holm Kadomtsev–Petviashvili equation and the higher-order nonlinear Schrödinger equation. By using this useful method, we found some exact solutions of the above-mentioned equations. The obtained solutions include solitary wave solutions, periodic wave solutions and combined formal solutions. It is shown that the proposed method is effective and general.
Feng, Qing-Hua
2014-08-01
In this paper, a new fractional projective Riccati equation method is proposed to establish exact solutions for fractional partial differential equations in the sense of modified Riemann—Liouville derivative. This method can be seen as the fractional version of the known projective Riccati equation method. For illustrating the validity of this method, we apply this method to solve the space-time fractional Whitham—Broer—Kaup (WBK) equations and the nonlinear fractional Sharma—Tasso—Olever (STO) equation, and as a result, some new exact solutions for them are obtained.
Racism, Differentialism, and Antiracism in Everyday Ideology: A Mixed-Methods Study in Britain
Directory of Open Access Journals (Sweden)
Peter Martin
2013-06-01
Full Text Available Racism is ostracized in British public life, but continues to exist and exert influence in various forms. One such is the ideology of differentialism that enforces racialized distinctions by emphasizing culture and difference in place of biology and hierarchy. Although differentialism has been described by various authors, there has been no prior attempt to operationalize it in an attitude scale that could be used in national surveys. This mixed methods study of differentialism in a context of official antiracism presents an attitude scale of Everyday Differentialism and applies it in a postal survey in two areas of London. Scale quality was tested using psychometric methods and qualitative interviews with a sub-sample of survey respondents. The analysis suggests that quantitative and qualitative data converge toward the same classification of individuals: differentialists, antiracists, and those of ambiguous opinion. A detailed qualitative analysis reveals how respondents deal with ambiguity and contradictory attitudes within the ideological field of differentialism and anti-racism. Although the denial of racism is now part of racist ideology itself, we also find evidence of genuine ambiguity in respondents’ thinking about issues of racism.
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
Using direct algebraic method,exact solitary wave solutions are performed for a class of third order nonlinear dispersive disipative partial differential equations. These solutions are obtained under certain conditions for the relationship between the coefficients of the equation. The exact solitary waves of this class are rational functions of real exponentials of kink-type solutions.