Table of Contents
ISRN Applied Mathematics
Volume 2012 (2012), Article ID 254086, 15 pages
http://dx.doi.org/10.5402/2012/254086
Research Article

Taylor's Meshless Petrov-Galerkin Method for the Numerical Solution of Burger's Equation by Radial Basis Functions

Department of Mathematics, K. N. Toosi University of Technology, P.O. Box 16315-1618, Tehran, Iran

Received 19 September 2011; Accepted 26 October 2011

Academic Editor: E. A. Navarro

Copyright © 2012 Maryam Sarboland and Azim Aminataei. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

During the last two decades, there has been a considerable interest in developing efficient radial basis functions (RBFs) algorithms for solving partial differential equations (PDEs). In this paper, we introduce the Petrov-Galerkin method for the numerical solution of the one-dimensional nonlinear Burger equation. In this method, the trial space is generated by the multiquadric (MQ) RBF and the test space is generated by the compactly supported RBF. In the time discretization of the equation, the Taylor series expansion is used. This method is applied on some test experiments, and the numerical results have been compared with the exact solutions. The ๐ฟ 2 , ๐ฟ โˆž , and root-mean-square (RMS) errors in the solutions show the efficiency and the accuracy of the method.