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

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:230

Article

Dehghan, Mehdi¹  Shokri, Ali¹ 

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

关键词: Nonlinear Klein-Gordon equation;    Collocation;    Radial basis functions (RBF);    Thin plate splines (TPS);   

DOI  :  10.1016/j.cam.2008.12.011

来源: Elsevier

【 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.

【 授权许可】

Free