Table of Contents
Chinese Journal of Mathematics
Volume 2014 (2014), Article ID 146013, 6 pages
http://dx.doi.org/10.1155/2014/146013
Research Article

New Operational Matrix of Integrations and Coupled System of Fredholm Integral Equations

Department of Mathematics, University of Malakand, Chakdara, Dir(L), Khyber Pakhtunkhwa, Dir Lower 23050, Pakistan

Received 7 December 2013; Accepted 31 December 2013; Published 13 February 2014

Academic Editors: Y. Feng and X.-l. Luo

Copyright © 2014 Hammad Khalil and Rahmat Ali Khan. 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

We study Legendre polynomials and develop new operational matrix of integration. Based on the operational matrix, we develop a new method to solve a coupled system of Fredholm integral equations of the form , , where , , , and are real constants and . The method reduces the coupled system to a system of easily solvable algebraic equations without discretizing the original system. As an application, we provide examples and numerical simulations demonstrating that the results obtained using the new technique match very well with the exact solutions of the problems. To show the efficiency of the method, we compare our results with some of the results already studied with other available methods in the literature.