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Extension of Khan’s Homotopy Transformation Method via Optimal Parameter for Differential Difference Equations

Author

Listed:
  • Mohamed S. Mohamed
  • Khaled A. Gepreel
  • Faisal A. Al-Malki
  • Nouf Altalhi

Abstract

A new scheme, deduced from Khan’s homotopy perturbation transform method (HPTM) (Khan, 2014; Khan and Wu, 2011) via optimal parameter, is presented for solving nonlinear differential difference equations. Simple but typical examples are given to illustrate the validity and great potential of Khan’s homotopy perturbation transform method (HPTM) via optimal parameter in solving nonlinear differential difference equation. The numerical solutions show that the proposed method is very efficient and computationally attractive. It provides more realistic series solutions that converge very rapidly for nonlinear real physical problems. The results reveal that the method is very effective and simple. This method gives more reliable results as compared to other existing methods available in the literature. The numerical results demonstrate the validity and applicability of the method.

Suggested Citation

  • Mohamed S. Mohamed & Khaled A. Gepreel & Faisal A. Al-Malki & Nouf Altalhi, 2014. "Extension of Khan’s Homotopy Transformation Method via Optimal Parameter for Differential Difference Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:813474
    DOI: 10.1155/2014/813474
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    References listed on IDEAS

    as
    1. Khaled A. Gepreel & Taher A. Nofal & Ali A. Al-Thobaiti, 2012. "The Modified Rational Jacobi Elliptic Functions Method for Nonlinear Differential Difference Equations," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-30, October.
    2. Khaled A. Gepreel & Taher A. Nofal & Fawziah M. Alotaibi, 2013. "Exact Solutions for Nonlinear Differential Difference Equations in Mathematical Physics," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    3. Khaled A. Gepreel & Taher A. Nofal & Ali A. Al-Thobaiti, 2012. "The Modified Rational Jacobi Elliptic Functions Method for Nonlinear Differential Difference Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    4. Khaled A. Gepreel & Taher A. Nofal & Fawziah M. Alotaibi, 2013. "Exact Solutions for Nonlinear Differential Difference Equations in Mathematical Physics," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-10, February.
    5. He, Ji-Huan, 2005. "Application of homotopy perturbation method to nonlinear wave equations," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 695-700.
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