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

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  • Shaheed N. Huseen
  • Said R. Grace

Abstract

A modified q‐homotopy analysis method (mq‐HAM) was proposed for solving nth‐order nonlinear differential equations. This method improves the convergence of the series solution in the nHAM which was proposed in (see Hassan and El‐Tawil 2011, 2012). The proposed method provides an approximate solution by rewriting the nth‐order nonlinear differential equation in the form of n first‐order differential equations. The solution of these n 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.

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  • Shaheed N. Huseen & Said R. Grace, 2013. "Approximate Solutions of Nonlinear Partial Differential Equations by Modified q‐Homotopy Analysis Method," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:569674
    DOI: 10.1155/2013/569674
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