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On the homotopy analysis method for the exact solutions of Helmholtz equation

Author

Listed:
  • Alomari, A.K.
  • Noorani, M.S.M.
  • Nazar, R.

Abstract

In this paper, the exact solutions of Helmholtz equation are obtained by means of the homotopy analysis method (HAM). This analytical method is employed to give approximate analytical solutions of Helmholtz equation. The auxiliary parameter ℏ in the HAM solutions has provided a convenient way of controlling the convergence region of series solutions. It is also shown that the solutions which are obtained by the Adomian decomposition method (ADM) and variational iteration method (VIM) are special cases of the solution obtained by HAM.

Suggested Citation

  • Alomari, A.K. & Noorani, M.S.M. & Nazar, R., 2009. "On the homotopy analysis method for the exact solutions of Helmholtz equation," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1873-1879.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:4:p:1873-1879
    DOI: 10.1016/j.chaos.2008.07.038
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    References listed on IDEAS

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    1. Wu, Yongyan & Wang, Chun & Liao, Shi-Jun, 2005. "Solving the one-loop soliton solution of the Vakhnenko equation by means of the Homotopy analysis method," Chaos, Solitons & Fractals, Elsevier, vol. 23(5), pages 1733-1740.
    2. Wu, Wan & Liao, Shi-Jun, 2005. "Solving solitary waves with discontinuity by means of the homotopy analysis method," Chaos, Solitons & Fractals, Elsevier, vol. 26(1), pages 177-185.
    3. Sajid, M. & Hayat, T., 2008. "The application of homotopy analysis method to thin film flows of a third order fluid," Chaos, Solitons & Fractals, Elsevier, vol. 38(2), pages 506-515.
    4. Allan, Fathi M., 2009. "Construction of analytic solution to chaotic dynamical systems using the Homotopy analysis method," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1744-1752.
    5. Abbasbandy, S., 2009. "Solitary wave solutions to the modified form of Camassa–Holm equation by means of the homotopy analysis method," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 428-435.
    6. 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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