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Approximate Solutions of the Generalized Abel’s Integral Equations Using the Extension Khan’s Homotopy Analysis Transformation Method

Author

Listed:
  • Mohamed S. Mohamed
  • Khaled A. Gepreel
  • Faisal A. Al-Malki
  • Maha Al-Humyani

Abstract

User friendly algorithm based on the optimal homotopy analysis transform method (OHATM) is proposed to find the approximate solutions to generalized Abel’s integral equations. The classical theory of elasticity of material is modeled by the system of Abel integral equations. It is observed that the approximate solutions converge rapidly to the exact solutions. Illustrative numerical examples are given to demonstrate the efficiency and simplicity of the proposed method. Finally, several numerical examples are given to illustrate the accuracy and stability of this method. Comparison of the approximate solution with the exact solutions shows that the proposed method is very efficient and computationally attractive. We can use this method for solving more complicated integral equations in mathematical physical.

Suggested Citation

  • Mohamed S. Mohamed & Khaled A. Gepreel & Faisal A. Al-Malki & Maha Al-Humyani, 2015. "Approximate Solutions of the Generalized Abel’s Integral Equations Using the Extension Khan’s Homotopy Analysis Transformation Method," Journal of Applied Mathematics, John Wiley & Sons, vol. 2015(1).
    • Handle: RePEc:wly:jnljam:v:2015:y:2015:i:1:n:357861
    DOI: 10.1155/2015/357861
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    References listed on IDEAS

    as
    1. S. M. Abo-Dahab & Mohamed S. Mohamed & T. A. Nofal, 2013. "A One Step Optimal Homotopy Analysis Method for Propagation of Harmonic Waves in Nonlinear Generalized Magnetothermoelasticity with Two Relaxation Times under Influence of Rotation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. Abdul-Majid Wazwaz, 2011. "Linear and Nonlinear Integral Equations," Springer Books, Springer, number 978-3-642-21449-3, March.
    3. S. M. Abo-Dahab & Mohamed S. Mohamed & T. A. Nofal, 2013. "A One Step Optimal Homotopy Analysis Method for Propagation of Harmonic Waves in Nonlinear Generalized Magnetothermoelasticity with Two Relaxation Times under Influence of Rotation," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-14, September.
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