Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 837218, 14 pages
http://dx.doi.org/10.1155/2011/837218
Research Article

New Algorithm for the Numerical Solutions of Nonlinear Third-Order Differential Equations Using Jacobi-Gauss Collocation Method

A. H. Bhrawy1,2 and W. M. Abd-Elhameed3

1Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia
2Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt
3Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt

Received 14 November 2010; Revised 25 January 2011; Accepted 27 January 2011

Academic Editor: Carlo Cattani

Copyright © 2011 A. H. Bhrawy and W. M. Abd-Elhameed. 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 algorithm for solving the general nonlinear third-order differential equation is developed by means of a shifted Jacobi-Gauss collocation spectral method. The shifted Jacobi-Gauss points are used as collocation nodes. Numerical examples are included to demonstrate the validity and applicability of the proposed algorithm, and some comparisons are made with the existing results. The method is easy to implement and yields very accurate results.