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Biazar, Jafar; Aminikhah, Hossein

Study of convergence of homotopy perturbation method for systems of partial differential equations. (English) Zbl 1189.65246

Comput. Math. Appl. 58, No. 11-12, 2221-2230 (2009).
Summary: The aim of this paper is convergence study of homotopy perturbation method for systems of nonlinear partial differential equations. The sufficient condition for convergence of the method is addressed. Since mathematical modeling of numerous scientific and engineering experiments lead to Brusselator and Burgers’ system of equations, it is worth trying new methods to solve these systems. We construct a new efficient recurrent relation to solve nonlinear Burgers’ and Brusselator systems of equations. Comparison of the results obtained by homotopy perturbation method with those of Adomian’s decomposition method and dual-reciprocity boundary element method leads to significant consequences. Two standard problems are used to validate the method.

Cited in 27 Documents

MSC:

65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
35Q53 KdV equations (Korteweg-de Vries equations)

Keywords:

Brusselator equations; Burgers’ equations; homotopy perturbation method; convergence sequence
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\textit{J. Biazar} and \textit{H. Aminikhah}, Comput. Math. Appl. 58, No. 11--12, 2221--2230 (2009; Zbl 1189.65246)
Full Text: DOI

References:

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