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Homotopy Analysis Method for Second-Order Boundary Value Problems of Integrodifferential Equations

Author

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  • Ahmad El-Ajou
  • Omar Abu Arqub
  • Shaher Momani

Abstract

In this paper, series solution of second-order integrodifferential equations with boundary conditions of the Fredholm and Volterra types by means of the homotopy analysis method is considered. The new approach provides the solution in the form of a rapidly convergent series with easily computable components using symbolic computation software. The homotopy analysis method provides us with a simple way to adjust and control the convergence region of the infinite series solution by introducing an auxiliary parameter. The proposed technique is applied to a few test examples to illustrate the accuracy, efficiency, and applicability of the method. The results reveal that the method is very effective, straightforward, and simple.

Suggested Citation

  • Ahmad El-Ajou & Omar Abu Arqub & Shaher Momani, 2012. "Homotopy Analysis Method for Second-Order Boundary Value Problems of Integrodifferential Equations," Discrete Dynamics in Nature and Society, Hindawi, vol. 2012, pages 1-18, September.
    • Handle: RePEc:hin:jnddns:365792
    DOI: 10.1155/2012/365792
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    Cited by:

    1. Kenzu Abdella & Glen Ross, 2020. "Solving Integro-Differential Boundary Value Problems Using Sinc-Derivative Collocation," Mathematics, MDPI, vol. 8(9), pages 1-13, September.

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