Abstract and Applied Analysis
Volume 2012 (2012), Article ID 839836, 16 pages
http://dx.doi.org/10.1155/2012/839836
Research Article

Application of Reproducing Kernel Method for Solving Nonlinear Fredholm-Volterra Integrodifferential Equations

Omar Abu Arqub,1 Mohammed Al-Smadi,2 and Shaher Momani3

1Department of Mathematics, Al-Balqa Applied University, Salt 19117, Jordan
2Department of Mathematics and Information Technology, Tafila Technical University, Tafila 66110, Jordan
3Department of Mathematics, University of Jordan, Amman 11942, Jordan

Received 24 June 2012; Revised 24 July 2012; Accepted 24 July 2012

Academic Editor: Irena Lasiecka

Copyright © 2012 Omar Abu Arqub 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

This paper investigates the numerical solution of nonlinear Fredholm-Volterra integro-differential equations using reproducing kernel Hilbert space method. The solution 𝑢 ( 𝑥 ) is represented in the form of series in the reproducing kernel space. In the mean time, the n-term approximate solution 𝑢 𝑛 ( 𝑥 ) is obtained and it is proved to converge to the exact solution 𝑢 ( 𝑥 ) . Furthermore, the proposed method has an advantage that it is possible to pick any point in the interval of integration and as well the approximate solution and its derivative will be applicable. Numerical examples are included to demonstrate the accuracy and applicability of the presented technique. The results reveal that the method is very effective and simple.