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A Reliable Treatment of Homotopy Perturbation Method for Solving the Nonlinear Klein‐Gordon Equation of Arbitrary (Fractional) Orders

Author

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  • A. M. A. El-Sayed
  • A. Elsaid
  • D. Hammad

Abstract

The reliable treatment of homotopy perturbation method (HPM) is applied to solve the Klein‐Gordon partial differential equation of arbitrary (fractional) orders. This algorithm overcomes the difficulty that arises in calculating complicated integrals when solving nonlinear equations. Some numerical examples are presented to illustrate the efficiency of this technique.

Suggested Citation

  • A. M. A. El-Sayed & A. Elsaid & D. Hammad, 2012. "A Reliable Treatment of Homotopy Perturbation Method for Solving the Nonlinear Klein‐Gordon Equation of Arbitrary (Fractional) Orders," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:581481
    DOI: 10.1155/2012/581481
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    References listed on IDEAS

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    1. Wang, Qi, 2008. "Homotopy perturbation method for fractional KdV-Burgers equation," Chaos, Solitons & Fractals, Elsevier, vol. 35(5), pages 843-850.
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    Cited by:

    1. Cuicui Liao & Xiaohua Ding, 2012. "Nonstandard Finite Difference Variational Integrators for Multisymplectic PDEs," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    2. Mohammed Ali & Marwan Alquran & Mahmoud Mohammad, 2012. "Solitonic Solutions for Homogeneous KdV Systems by Homotopy Analysis Method," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    3. Asma Ali Elbeleze & Adem Kılıçman & Bachok M. Taib, 2014. "Note on the Convergence Analysis of Homotopy Perturbation Method for Fractional Partial Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    4. Fukang Yin & Junqiang Song & Yongwen Wu & Lilun Zhang, 2013. "Numerical Solution of the Fractional Partial Differential Equations by the Two‐Dimensional Fractional‐Order Legendre Functions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    5. Abdon Atangana & Adem Kılıçman, 2013. "Analytical Solutions of Boundary Values Problem of 2D and 3D Poisson and Biharmonic Equations by Homotopy Decomposition Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).

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