Mathematical Problems in Engineering
Volume 2009 (2009), Article ID 202307, 34 pages
Review Article

A Review of Some Recent Results for the Approximate Analytical Solutions of Nonlinear Differential Equations

Department of Mathematics, University of Kocaeli, Umuttepe, 41800 Kocaeli, Turkey

Received 15 January 2009; Revised 21 April 2009; Accepted 29 April 2009

Academic Editor: Ji Huan He

Copyright © 2009 Serdal Pamuk. 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 features a survey of some recent developments in techniques for obtaining approximate analytical solutions of some nonlinear differential equations arising in various fields of science and engineering. Adomian's decomposition method is applied to some nonlinear problems, and some mathematical tools such as He's homotopy perturbation method and variational iteration method are introduced to overcome the shortcomings of Adomian's method. The results of some comparisons of these three methods appearing in the research literature are given.