Approximate Solutions of Nonlinear Partial Differential Equations by Modified -Homotopy Analysis Method

Shaheed N. Huseen and Said R. Grace

Journal of Applied Mathematics, 2013, vol. 2013, 1-9

Abstract:

A modified -homotopy analysis method (m -HAM) was proposed for solving th-order nonlinear differential equations. This method improves the convergence of the series solution in the HAM which was proposed in (see Hassan and El-Tawil 2011, 2012). The proposed method provides an approximate solution by rewriting the th-order nonlinear differential equation in the form of first-order differential equations. The solution of these differential equations is obtained as a power series solution. This scheme is tested on two nonlinear exactly solvable differential equations. The results demonstrate the reliability and efficiency of the algorithm developed.

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:569674

DOI: 10.1155/2013/569674

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