About this Journal Submit a Manuscript Table of Contents
Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 365792, 18 pages
http://dx.doi.org/10.1155/2012/365792
Research Article

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

1Department of Mathematics, Faculty of Science, Al Balqa Applied University, Salt 19117, Jordan
2Department of Mathematics, Faculty of Science, University of Jordan, Amman 11942, Jordan

Received 1 April 2012; Accepted 19 June 2012

Academic Editor: Gabriele Bonanno

Copyright © 2012 Ahmad El-Ajou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.