Journal of Applied Mathematics
Volume 2013 (2013), Article ID 157956, 11 pages
http://dx.doi.org/10.1155/2013/157956
Research Article

Couple of the Variational Iteration Method and Legendre Wavelets for Nonlinear Partial Differential Equations

Fukang Yin,1 Junqiang Song,1 Xiaoqun Cao,1 and Fengshun Lu2

1College of Computer, National University of Defense Technology, Changsha 410073, China
2China Aerodynamics Research and Development Center, Mianyang, Sichuan 621000, China

Received 17 October 2012; Revised 27 December 2012; Accepted 27 December 2012

Academic Editor: Francisco Chiclana

Copyright © 2013 Fukang Yin et al. 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

This paper develops a modified variational iteration method coupled with the Legendre wavelets, which can be used for the efficient numerical solution of nonlinear partial differential equations (PDEs). The approximate solutions of PDEs are calculated in the form of a series whose components are computed by applying a recursive relation. Block pulse functions are used to calculate the Legendre wavelets coefficient matrices of the nonlinear terms. The main advantage of the new method is that it can avoid solving the nonlinear algebraic system and symbolic computation. Furthermore, the developed vector-matrix form makes it computationally efficient. The results show that the proposed method is very effective and easy to implement.