Homotopy Analysis Method for Second-Order Boundary Value Problems of Integrodifferential Equations. (19th September 2012)

• Record Type: Journal Article
• Authors: El-Ajou, Ahmad; Abu Arqub, Omar; Momani, Shaher
• Other Names: Bonanno Gabriele Academic Editor.
• Is Part Of: Discrete dynamics in nature and society. Volume 2012(2012)
• Publication Date: 2012-09-19
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2012/365792
• Languages: English
• ISSNs: 1026-0226

Abstract

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.