Journal of Applied Mathematics
Volume 2012 (2012), Article ID 370843, 19 pages
http://dx.doi.org/10.1155/2012/370843
Research Article

Approximate Solutions for Nonlinear Initial Value Problems Using the Modified Variational Iteration Method

Taher A. Nofal1,2

1Mathematics Department, Faculty of Science, El-Minia University, El-Minia 61519, Egypt
2Mathematics Department, Faculty of Science, Taif University, Taif 21974, Saudi Arabia

Received 19 February 2012; Revised 27 March 2012; Accepted 28 March 2012

Academic Editor: Pablo González-Vera

Copyright © 2012 Taher A. Nofal. 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

We have used the modified variational iteration method (MVIM) to find the approximate solutions for some nonlinear initial value problems in the mathematical physics, via the Burgers-Fisher equation, the Kuramoto-Sivashinsky equation, the coupled Schrodinger-KdV equations, and the long-short wave resonance equations together with initial conditions. The results of these problems reveal that the modified variational iteration method is very powerful, effective, convenient, and quite accurate to systems of nonlinear equations. It is predicted that this method can be found widely applicable in engineering and physics.