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

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  • Shaheed N. Huseen
  • Said R. Grace

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.

Suggested Citation

  • Shaheed N. Huseen & Said R. Grace, 2013. "Approximate Solutions of Nonlinear Partial Differential Equations by Modified -Homotopy Analysis Method," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-9, November.
    • Handle: RePEc:hin:jnljam:569674
    DOI: 10.1155/2013/569674
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    Cited by:

    1. Akinyemi, Lanre & Huseen, Shaheed N., 2020. "A powerful approach to study the new modified coupled Korteweg–de Vries system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 177(C), pages 556-567.

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