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Abstract and Applied Analysis
Volume 2013, Article ID 760542, 12 pages
Research Article

A Jacobi Collocation Method for Solving Nonlinear Burgers-Type Equations

1Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt
2Department of Chemical and Materials Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia
3Department of Mathematics and Computer Sciences, Faculty of Arts and Sciences, Cankaya University, Eskiehir Yolu 29 Km, 06810 Ankara, Turkey
4Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
5Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef 62511, Egypt

Received 24 July 2013; Accepted 15 August 2013

Academic Editor: Soheil Salahshour

Copyright © 2013 E. H. Doha 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.


We solve three versions of nonlinear time-dependent Burgers-type equations. The Jacobi-Gauss-Lobatto points are used as collocation nodes for spatial derivatives. This approach has the advantage of obtaining the solution in terms of the Jacobi parameters α and β. In addition, the problem is reduced to the solution of the system of ordinary differential equations (SODEs) in time. This system may be solved by any standard numerical techniques. Numerical solutions obtained by this method when compared with the exact solutions reveal that the obtained solutions produce high-accurate results. Numerical results show that the proposed method is of high accuracy and is efficient to solve the Burgers-type equation. Also the results demonstrate that the proposed method is a powerful algorithm to solve the nonlinear partial differential equations.