Journal of Applied Mathematics
Volume 2012 (2012), Article ID 254123, 17 pages
http://dx.doi.org/10.1155/2012/254123
Research Article
A Boundary Integral Equation with the Generalized Neumann Kernel for a Certain Class of Mixed Boundary Value Problem
1Department of Mathematics, Faculty of Science, King Khalid University, P.O. Box 9004, Abha, Saudi Arabia
2Department of Mathematics, Faculty of Science, Ibb University, P.O. Box 70270, Ibb, Yemen
3Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia
4Ibnu Sina Institute for Fundamental Science Studies, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia
Received 21 May 2012; Revised 29 August 2012; Accepted 12 September 2012
Academic Editor: Yuantong Gu
Copyright © 2012 Mohamed M. S. Nasser 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
We present a uniquely solvable boundary integral equation with the generalized Neumann kernel for solving two-dimensional Laplace’s equation on multiply connected regions with mixed boundary condition. Two numerical examples are presented to verify the accuracy of the proposed method.