Abstract and Applied Analysis
Volume 2011 (2011), Article ID 823273, 14 pages
http://dx.doi.org/10.1155/2011/823273
Research Article

Spectral Shifted Jacobi Tau and Collocation Methods for Solving Fifth-Order Boundary Value Problems

A. H. Bhrawy,1,2 A. S. Alofi,2 and S. I. El-Soubhy3

1Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef 62511, Egypt
2Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
3Department of Mathematics, Faculty of Science, Taibah University, Al Madinah, Saudi Arabia

Received 29 March 2011; Revised 29 April 2011; Accepted 9 May 2011

Academic Editor: Simeon Reich

Copyright © 2011 A. H. Bhrawy 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 have presented an efficient spectral algorithm based on shifted Jacobi tau method of linear fifth-order two-point boundary value problems (BVPs). An approach that is implementing the shifted Jacobi tau method in combination with the shifted Jacobi collocation technique is introduced for the numerical solution of fifth-order differential equations with variable coefficients. The main characteristic behind this approach is that it reduces such problems to those of solving a system of algebraic equations which greatly simplify the problem. Shifted Jacobi collocation method is developed for solving nonlinear fifth-order BVPs. Numerical examples are performed to show the validity and applicability of the techniques. A comparison has been made with the existing results. The method is easy to implement and gives very accurate results.