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Behzadi, Sh. Sadigh

Convergence of iterative methods applied to generalized Fisher equation. (English) Zbl 1213.35032

Int. J. Differ. Equ. 2010, Article ID 254675, 16 p. (2010).
Summary: A generalized Fisher’s equation is solved by using the modified Adomian decomposition method (MADM), variational iteration method (VIM), homotopy analysis method (HAM), and modified homotopy perturbation method (MHPM). The approximation solution of this equation is calculated in the form of series whose components are computed easily. The existence, uniqueness, and convergence of the proposed methods are proved. Numerical example is studied to demonstrate the accuracy of the present methods.

MSC:

35A35 Theoretical approximation in context of PDEs
35K57 Reaction-diffusion equations
35C10 Series solutions to PDEs

Keywords:

modified Adomian decomposition method; variational iteration method; homotopy analysis method; modified homotopy perturbation method
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References:

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