Mathematical Problems in Engineering
Volume 2009 (2009), Article ID 234849, 25 pages
Review Article

Some Relatively New Techniques for Nonlinear Problems

1Department of Basic Sciences, Heavy Industries Taxila Education City (HITEC) University, Taxila Cantt 44000, Pakistan
2Department of Mathematics, COMSATS Institute of Information Technology, Islamabad 44000, Pakistan

Received 11 January 2009; Revised 14 February 2009; Accepted 25 March 2009

Academic Editor: Ji Huan He

Copyright © 2009 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.


This paper outlines a detailed study of some relatively new techniques which are originated by He for solving diversified nonlinear problems of physical nature. In particular, we will focus on the variational iteration method (VIM) and its modifications, the homotopy perturbation method (HPM), the parameter expansion method, and exp-function method. These relatively new but very reliable techniques proved useful for solving a wide class of nonlinear problems and are capable to cope with the versatility of the physical problems. Several examples are given to reconfirm the efficiency of these algorithms. Some open problems are also suggested for future research work.