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