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Zbl 1182.35011
Pamuk, Serdal
A review of some recent results for the approximate analytical solutions of nonlinear differential equations. (English)
[J] Math. Probl. Eng. 2009, Article ID 202307, 34 p. (2009). ISSN 1024-123X; ISSN 1563-5147/e

Summary: 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.

MSC 2000:: *35A25 Other special methods (PDE)
35A35 Theoretical approximation to solutions of PDE

Keywords: Adomian's decomposition method; He's homotopy perturbation method; variational iteration method

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Zentralblatt MATH Berlin [Germany]