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Analytical Solutions of Boundary Values Problem of 2D and 3D Poisson and Biharmonic Equations by Homotopy Decomposition Method

Author

Listed:
  • Abdon Atangana
  • Adem Kılıçman

Abstract

The homotopy decomposition method, a relatively new analytical method, is used to solve the 2D and 3D Poisson equations and biharmonic equations. The method is chosen because it does not require the linearization or assumptions of weak nonlinearity, the solutions are generated in the form of general solution, and it is more realistic compared to the method of simplifying the physical problems. The method does not require any corrected function or any Lagrange multiplier and it avoids repeated terms in the series solutions compared to the existing decomposition method including the variational iteration method, the Adomian decomposition method, and Homotopy perturbation method. The approximated solutions obtained converge to the exact solution as N tends to infinity.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:380484
    DOI: 10.1155/2013/380484
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    References listed on IDEAS

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    1. 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, Hindawi, vol. 2012, pages 1-13, February.
    2. Asma Ali Elbeleze & Adem Kiliçman & Bachok M. Taib, 2012. "Application of Homotopy Perturbation and Variational Iteration Methods for Fredholm Integrodifferential Equation of Fractional Order," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-14, October.
    3. Syed Tauseef Mohyud-Din & Ahmet Yildirim & M. M. Hosseini, 2010. "Variational Iteration Method for Initial and Boundary Value Problems Using He's Polynomials," International Journal of Differential Equations, Hindawi, vol. 2010, pages 1-28, April.
    4. 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).
    5. Asma Ali Elbeleze & Adem Kiliçman & Bachok M. Taib, 2012. "Application of Homotopy Perturbation and Variational Iteration Methods for Fredholm Integrodifferential Equation of Fractional Order," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
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    Cited by:

    1. Chun-Guang Zhao & Ai-Min Yang & Hossein Jafari & Ahmad Haghbin, 2014. "The Yang‐Laplace Transform for Solving the IVPs with Local Fractional Derivative," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    2. Abdon Atangana & Aden Ahmed & Suares Clovis Oukouomi Noutchie, 2014. "On the Hamilton‐Jacobi‐Bellman Equation by the Homotopy Perturbation Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    3. Shun-Qin Wang & Yong-Ju Yang & Hassan Kamil Jassim, 2014. "Local Fractional Function Decomposition Method for Solving Inhomogeneous Wave Equations with Local Fractional Derivative," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

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