Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 603463, 16 pages
http://dx.doi.org/10.1155/2012/603463
Research Article

Numerical Solution of Nonlinear Volterra Integral Equations System Using Simpson’s 3/8 Rule

Adem Kılıçman,1 L. Kargaran Dehkordi,2 and M. Tavassoli Kajani2

1Department of Mathematics and Institute for Mathematical Research, University Putra Malaysia, 43400 Serdang, Malaysia
2Department of Mathematics, Islamic Azad University, Khorasgan Branch, Isfahan 81595-158, Iran

Received 30 April 2012; Accepted 31 July 2012

Academic Editor: Sheng-yong Chen

Copyright © 2012 Adem Kılıçman 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

The Simpson’s 3/8 rule is used to solve the nonlinear Volterra integral equations system. Using this rule the system is converted to a nonlinear block system and then by solving this nonlinear system we find approximate solution of nonlinear Volterra integral equations system. One of the advantages of the proposed method is its simplicity in application. Further, we investigate the convergence of the proposed method and it is shown that its convergence is of order . Numerical examples are given to show abilities of the proposed method for solving linear as well as nonlinear systems. Our results show that the proposed method is simple and effective.