Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 537909, 8 pages
doi:10.1155/2010/537909
Research Article

Block-by-Block Method for Solving Nonlinear Volterra-Fredholm Integral Equation

Abdallah A. Badr

Department of Mathematics, Faculty of Science, Alexandria University, Alexandria, Egypt

Received 21 April 2010; Accepted 27 December 2010

Academic Editor: Christos H. Skiadas

Copyright © 2010 Abdallah A. Badr. 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 consider a nonlinear Volterra-Fredholm integral equation (NVFIE) of the second kind. The Volterra kernel is time dependent, and the Fredholm kernel is position dependent. Existence and uniqueness of the solution to this equation, under certain conditions, are discussed. The block-by-block method is introduced to solve such equations numerically. Some numerical examples are given to illustrate our results.