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A review of some recent results for the approximate analytical solutions of nonlinear differential equations. (English) Zbl 1182.35011
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:
35A25Other special methods (PDE)
35A35Theoretical approximation to solutions of PDE