共查询到20条相似文献,搜索用时 12 毫秒
1.
Byungsoo Moon 《Journal of Difference Equations and Applications》2019,25(5):630-646
We present a general and effective method, known as the Fokas method, to solve an arbitrary discrete linear evolution equation posed in a finite lattice. The method is based on the simultaneous analysis of both parts of Lax pair, as well as the global relation that involves initial and boundary values. We show that, as in the continuum problems, the method can be applied effectively to solve general linear differential-difference equations in a finite lattice. In particular, we demonstrate the method by addressing a number of significant examples and we discuss the continuum limits of the solution and the boundary values. 相似文献
2.
何学中 《应用数学学报(英文版)》1995,11(2):184-191
GLOBALATTRACTIVITYOFLINEARNON-AUTONOMOUSNEUTRALDIFFERENTIAL-DIFFERENCEEQUATIONSHEXUEZHONG(何学中)(DepartmentofMathematics,Ningxi... 相似文献
3.
Hong Zhao 《Applied mathematics and computation》2010,216(4):1219-479
This paper presents a new algebraic procedure to construct exact solutions of selected nonlinear differential-difference equations. The discrete sine-Gordon equation and differential-difference asymmetric Nizhnik-Novikov-Veselov equations are chosen as examples to illustrate the efficiency and effectiveness of the new procedure, where various types of exact travelling wave solutions for these nonlinear differential-difference equations have been constructed. It is anticipated that the new procedure can also be used to produce solutions for other nonlinear differential-difference equations. 相似文献
4.
Lipschitz quasistability of impulsive differential-difference equations with variable impulsive perturbations 总被引:1,自引:0,他引:1
D.D. Bainov A.B. Dishliev I.M. Stamova 《Journal of Computational and Applied Mathematics》1996,70(2):267-277
In the present paper, by means of a suitable comparison lemma sufficient conditions for uniform Lipschitz stability of an arbitrary solution of an impulsive system of differential-difference equations with variable impulsive perturbations are obtained. 相似文献
5.
It is well known that a system of power polynomial equations can be reduced to a single-variable polynomial equation by exploiting the so-called Newton's identities. In this work, by further exploring Newton's identities, we discover a binomial decomposition rule for composite elementary symmetric polynomials. Utilizing this decomposition rule, we solve three types of systems of composite power polynomial equations by converting each type to single-variable polynomial equations that can be solved easily. For each type of system, we discuss potential applications and characterize the number of nontrivial solutions (up to permutations) and the complexity of our proposed algorithmic solution.
6.
The Tau Method produces polynomial approximations of solutions of differential equations. The purpose of this paper is (i) to extend the recursive formulation of this method to general linear operator equations defined in a separable Hilbert space, and (ii) to develop an iterative refinement procedure which improves on the accuracy of Tau approximations. Applications to Fredholm integral equations demonstrate the effectiveness of this technique.
7.
A. V. Schmidt 《Computational Mathematics and Mathematical Physics》2007,47(2):249-261
Exact solutions to two-component systems of reaction-diffusion equations are sought by the method of linear determining equations (LDEs) generalizing the methods of the classical group analysis of differential equations. LDEs are constructed for a system of two second-order evolutionary equations. The results of solving the LDEs are presented for two-component systems of reaction-diffusion equations with polynomial nonlinearities in the diffusion coefficients. Examples of constructing noninvariant solutions are presented for the reaction-diffusion systems that possess invariant manifolds. 相似文献
8.
构造非线性差分方程精确解的一种方法 总被引:1,自引:0,他引:1
套格图案 《高校应用数学学报(A辑)》2008,23(3)
在齐次平衡法、试探函数法的基础上,给出指数函数所组成的两种试探函数法,并借助符号计算系统Mathematica构造了Hybrid-Lattice系统、mKdV差分微分方程、Ablowitz-Ladik.Lattice6系统等非线性离散系统的新的精确孤波解. 相似文献
9.
L. F. Yukhno 《Computational Mathematics and Mathematical Physics》2007,47(11):1737-1744
A modification of certain well-known methods of the conjugate direction type is proposed and examined. The modified methods are more stable with respect to the accumulation of round-off errors. Moreover, these methods are applicable for solving ill-conditioned systems of linear algebraic equations that, in particular, arise as approximations of ill-posed problems. Numerical results illustrating the advantages of the proposed modification are presented. 相似文献
10.
L. F. Yukhno 《Computational Mathematics and Mathematical Physics》2007,47(12):1893-1901
The use of modifications of certain well-known methods of the conjugate direction type for solving systems of linear algebraic equations with rectangular matrices is examined. The modified methods are shown to be superior to the original versions with respect to the round-off accumulation; the advantage is especially large for ill-conditioned matrices. Examples are given of the efficient use of the modified methods for solving certain fairly large ill-conditioned problems. 相似文献
11.
W. Forster 《Journal of Global Optimization》1992,2(4):317-356
This paper gives a brief survey and assessment of computational methods for finding solutions to systems of nonlinear equations and systems of polynomial equations. Starting from methods which converge locally and which find one solution, we progress to methods which are globally convergent and find an a priori determinable number of solutions. We will concentrate on simplicial algorithms and homotopy methods. Enhancements of published methods are included and further developments are discussed. 相似文献
12.
A. A. Panov 《Mathematical Notes》1998,64(5):622-628
We estimate the number of periodic solutions for special classes ofnth-order ordinary differential equations with variable coefficients.
Translated fromMatematicheskie Zametki, Vol. 64, No. 5, pp. 720–727, November, 1998.
The author thanks Yu. S. Il'yashenko for setting the problems, permanent advice, and overall support. The author is also thankful
to D. A. Panov for numerous discussions.
This research was supported by the CRDF Foundation under grant MR1-220, by the INTAS Foundation under grant No. 93-05-07,
and by the Russian Foundation for Basic Research under grant No. 95-01-01258. 相似文献
13.
Kübra Erdem Salih Yalçinbaş Mehmet Sezer 《Journal of Difference Equations and Applications》2013,19(10):1619-1631
In this study, an approximate method based on Bernoulli polynomials and collocation points has been presented to obtain the solution of higher order linear Fredholm integro-differential-difference equations with the mixed conditions. The method we have used consists of reducing the problem to a matrix equation which corresponds to a system of linear algebraic equations. The obtained matrix equation is based on the matrix forms of Bernoulli polynomials and their derivatives by means of collocations. The solutions are obtained as the truncated Bernoulli series which are defined in the interval [a,b]. To illustrate the method, it is applied to the initial and boundary values. Also error analysis and numerical examples are included to demonstrate the validity and applicability of the technique. 相似文献
14.
Lingyun GAO 《数学物理学报(B辑英文版)》2017,37(1):187-194
In this paper, we will mainly investigate entire solutions with finite order of two types of systems of differential-difference equations, and obtain some interesting results. It extends some results concerning complex differential (difference) equations to the systems of differential-difference equations. 相似文献
15.
Antonio Rivera-Figueroa José Manuel Rivera-Rebolledo 《International Journal of Mathematical Education in Science & Technology》2016,47(4):636-649
In this paper, we give a new and straightforward method to solve the non-homogeneous second-order linear difference equations with constant coefficients. It is new because it does not require the uniqueness theorem of the solution of the problem of initial values. Neither does it require a fundamental system of solutions, nor the method of variation of parameters. Moreover, we get a unique formula that expresses the general solution independently of the multiplicities of the roots of the characteristic equation. 相似文献
16.
A numerical study is made for solving a class of time-dependent singularly perturbed convection–diffusion problems with retarded terms which often arise in computational neuroscience. To approximate the retarded terms, a Taylor’s series expansion has been used and the resulting time-dependent singularly perturbed differential equation is approximated using parameter-uniform numerical methods comprised of a standard implicit finite difference scheme to discretize in the temporal direction on a uniform mesh by means of Rothe’s method and a B-spline collocation method in the spatial direction on a piecewise-uniform mesh of Shishkin type. The method is shown to be accurate of order O(M−1 + N−2 ln3N), where M and N are the number of mesh points used in the temporal direction and in the spatial direction respectively. An extensive amount of analysis has been carried out to prove the uniform convergence with respect to the singular perturbation parameter. Numerical results are given to illustrate the parameter-uniform convergence of the numerical approximations. Comparisons of the numerical solutions are performed with an upwind and midpoint upwind finite difference scheme on a piecewise-uniform mesh to demonstrate the efficiency of the method. 相似文献
17.
Osman Raşit Işik Zekeriya Güney 《Journal of Difference Equations and Applications》2013,19(3):357-374
In this study, a new collocation method based on the Bernstein polynomials is introduced for the approximate solution of the pantograph-type differential equations with retarded case or advanced case. In addition, the method is presented with error and stability analysis. 相似文献
18.
H. Azad A. Laradji M. T. Mustafa 《Mathematical Methods in the Applied Sciences》2013,36(12):1615-1624
Conditions for the existence of polynomial solutions of certain second‐order differential equations have recently been investigated by several authors. In this paper, a new algorithmic procedure is given to determine necessary and sufficient conditions for a differential equation with polynomial coefficients containing parameters to admit polynomial solutions and to compute these solutions. The effectiveness of this approach is illustrated by applying it to determine new solutions of several differential equations of current interest. A comparative analysis is given to demonstrate the advantage of this algorithmic procedure over existing software. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
19.
Mustafa Gülsu Burcu GürbüzYalç?n Öztürk Mehmet Sezer 《Applied mathematics and computation》2011,217(15):6765-6776
This paper presents a numerical method for the approximate solution of mth-order linear delay difference equations with variable coefficients under the mixed conditions in terms of Laguerre polynomials. The aim of this article is to present an efficient numerical procedure for solving mth-order linear delay difference equations with variable coefficients. Our method depends mainly on a Laguerre series expansion approach. This method transforms linear delay difference equations and the given conditions into matrix equation which corresponds to a system of linear algebraic equation. The reliability and efficiency of the proposed scheme are demonstrated by some numerical experiments and performed on the computer algebraic system Maple. 相似文献
20.
M. Morh 《Mathematical and Computer Modelling》1994,19(12):85-93
The paper presents an error-free algorithm to solve a system of linear equations with polynomial coefficients. Modular arithmetic in residual polynomial class and in residual numeric class is employed. The algorithm is iterative and well suited for implementation for computers with vector operations and fast and error-free convolutors. 相似文献