A numerical method for one-dimensional nonlinear Sine-Gordon equation using collocation and radial basis functions

被引：77

作者：

Dehghan, M. ^{[1
]}

Shokri, Ali ^{[1
]}

机构：

[1] Amirkabir Univ Technol, Fac Math & Comp Sci, Dept Appl Math, Tehran, Iran

来源：

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS | 2008年 / 24卷 / 02期

关键词：

collocation; one-dimensional undamped Sine-Gordon equation; radial basis function (RBF); thin plate splines (TPS);

D O I：

10.1002/num.20289

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we propose a numerical scheme to solve the one-dimensional undamped Sine-Gordon equation using collocation points and approximating the solution using Thin Plate Splines (TPS) radial basis function (RBF). The scheme works in a similar fashion as finite difference methods. The results of numerical experiments are presented and are compared with analytical solutions to confirm the good accuracy of the presented scheme. (c) 2007 Wiley Periodicals, Inc.

引用

页码：687 / 698

页数：12

共 42 条

[1] On the numerical solution of the sine-Gordon equation .1. Integrable discretizations and homoclinic manifolds [J].