Taylor collocation method and convergence analysis for the Volterra-Fredholm integral equations

被引：43

作者：

Wang, Keyan ^{[1
]}

Wang, Qisheng ^{[1
]}

机构：

[1] Wuyi Univ, Sch Math & Computat Sci, Jiangmen 529020, Guangdong, Peoples R China

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2014年 / 260卷

基金：

中国国家自然科学基金;

关键词：

Taylor collocation method; Volterra Fredholm integral equations; Convergence analysis; NUMERICAL-SOLUTION; 2ND KIND;

D O I：

10.1016/j.cam.2013.09.050

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, the Taylor collocation method is presented for numerically solving the Volterra-Fredholm integral equations in terms of Taylor polynomials. This method transforms the integral equation to a matrix equation via the collocation points. The convergence analysis of the collocation solution on the integral equation is given. The method is computationally attractive, and applications are demonstrated through illustrative examples. (C) 2013 Elsevier B.V. All rights reserved.

引用

页码：294 / 300

页数：7

共 16 条

[1] Fredholm-Volterra integral equation of the first kind and contact problem [J].

Abdou, MA .

APPLIED MATHEMATICS AND COMPUTATION, 2002, 125 (2-3) :177-193

[2] Taylor collocation method for the numerical solution of the nonlinear Schrodinger equation using quintic B-spline basis [J].

Aksoy, A. M. ;

Irk, D. ;

Dag, I. .

PHYSICS OF WAVE PHENOMENA, 2012, 20 (01) :67-79

[3] Existence and uniqueness of nontrivial collocation solutions of implicitly linear homogeneous Volterra integral equations [J].

Benitez, R. ;

Bolos, V. J. .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2011, 235 (12) :3661-3672

[4] ASYMPTOTIC BOUNDS FOR SOLUTIONS TO A SYSTEM OF DAMPED INTEGRODIFFERENTIAL EQUATIONS OF ELECTROMAGNETIC THEORY [J].

BLOOM, F .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1980, 73 (02) :524-542

[5] The solution of the Bagley-Torvik equation with the generalized Taylor collocation method [J].

Cenesiz, Yuecel ;

Keskin, Yildiray ;

Kurnaz, Aydin .

JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, 2010, 347 (02) :452-466

[6] Spectral methods for weakly singular Volterra integral equations with smooth solutions [J].

Chen, Yanping ;

Tang, Tao .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2009, 233 (04) :938-950

[7]

Frankel J., 1995, Q APPL MATH, V24, P145

[8] A Taylor Collocation Method for Solving High-Order Linear Pantograph Equations with Linear Functional Argument [J].

Gulsu, Mustafa ;

Sezer, Mehmet .

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2011, 27 (06) :1628-1638

[9] Numerical solution of linear Volterra integral equations of the second kind with sharp gradients [J].

Isaacson, Samuel A. ;

Kirby, Robert M. .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2011, 235 (14) :4283-4301

[10] A Taylor collocation method for the solution of linear integro-differential equations [J].

Karamete, A ;

Sezer, M .

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2002, 79 (09) :987-1000

← 1 2 →