Journal of Applied Mathematics
Volume 2012 (2012), Article ID 351764, 10 pages
http://dx.doi.org/10.1155/2012/351764
Research Article

Finite Difference Method for Solving a System of Third-Order Boundary Value Problems

Muhammad Aslam Noor,1 Eisa Al-Said,2 and Khalida Inayat Noor1

1Department of Mathematics, COMSATS Institute of Information Technology, Park Road, Chak Shahzad, Islamabad, Pakistan
2Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Received 2 November 2011; Revised 7 February 2012; Accepted 8 February 2012

Academic Editor: Zhenyu Huang

Copyright © 2012 Muhammad Aslam Noor 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 develop a new-two-stage finite difference method for computing approximate solutions of a system of third-order boundary value problems associated with odd-order obstacle problems. Such problems arise in physical oceanography (Dunbar (1993) and Noor (1994), draining and coating flow problems (E. O. Tuck (1990) and L. W. Schwartz (1990)), and can be studied in the framework of variational inequalities. We show that the present method is of order three and give numerical results that are better than the other available results. Numerical example is presented to illustrate the applicability and efficiency of the new method.