International Journal of Differential Equations
Volume 2010 (2010), Article ID 426213, 28 pages
doi:10.1155/2010/426213
Review Article

Variational Iteration Method for Initial and Boundary Value Problems Using He's Polynomials

Syed Tauseef Mohyud-Din,1 Ahmet Yildirim,2 and M. M. Hosseini3

1HITEC University, Taxila Cantonment, Pakistan
2Department of Mathematics, Ege University, Bornova 35100, İzmir, Turkey
3Faculty of Mathematics, Yazd University, P.O. Box 89195-74, Yazd, Iran

Received 7 October 2009; Revised 4 December 2009; Accepted 11 February 2010

Academic Editor: Ganji Dormiti Ganji

Copyright © 2010 Syed Tauseef Mohyud-Din 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 outlines a detailed study of the coupling of He's polynomials with correction functional of variational iteration method (VIM) for solving various initial and boundary value problems. The elegant coupling gives rise to the modified versions of VIM which is very efficient in solving nonlinear problems of diversified nature. It is observed that the variational iteration method using He's polynomials (VIMHP) is very efficient, easier to implements, and more user friendly. Several examples are given to reconfirm the efficiency of the proposed VIMHP.