Numerical solution of the nonlinear Klein-Gordon equation using radial basis functions

被引：274

作者：

Dehghan, Mehdi ^{[1
]}

Shokri, Ali ^{[1
]}

机构：

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

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2009年 / 230卷 / 02期

关键词：

Nonlinear Klein-Gordon equation; Collocation; Radial basis functions (RBF); Thin plate splines (TPS); PARTIAL-DIFFERENTIAL-EQUATIONS; COMPUTATIONAL FLUID-DYNAMICS; DATA APPROXIMATION SCHEME; DECOMPOSITION METHOD; PARABOLIC EQUATION; WAVE SOLUTIONS; COLLOCATION; INTERPOLATION; MULTIQUADRICS; CONVERGENCE;

D O I：

10.1016/j.cam.2008.12.011

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The nonlinear Klein-Gordon equation is used to model many nonlinear phenomena. In this paper, we propose a numerical scheme to solve the one-dimensional nonlinear Klein-Gordon equation with quadratic and cubic nonlinearity. Our scheme uses the collocation points and approximates the solution using Thin Plate Splines (TPS) radial basis functions (RBF). The implementation of the method is simple 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) 2008 Elsevier B.V. All rights reserved.

引用

页码：400 / 410

页数：11

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