Journal of Applied Mathematics
Volume 2012 (2012), Article ID 714973, 10 pages
http://dx.doi.org/10.1155/2012/714973
Research Article

A New Direct Method for Solving Nonlinear Volterra-Fredholm-Hammerstein Integral Equations via Optimal Control Problem

M. A. El-Ameen1 and M. El-Kady2

1Faculty of Engineering, Umm Al-Qura University, P.O. Box 5555, Mecca, Saudi Arabia
2Faculty of Science, Helwan University, Helwan, Egypt

Received 28 December 2011; Accepted 28 January 2012

Academic Editor: Shuyu Sun

Copyright © 2012 M. A. El-Ameen and M. El-Kady. 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

A new method for solving nonlinear Volterra-Fredholm-Hammerstein (VFH) integral equations is presented. This method is based on reformulation of VFH to the simple form of Fredholm integral equations and hence converts it to optimal control problem. The existence and uniqueness of proposed method are achieved. Numerical results are given at the end of this paper.