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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 527467, 15 pages
http://dx.doi.org/10.1155/2012/527467
Research Article

A Galerkin Solution for Burgers' Equation Using Cubic B-Spline Finite Elements

Department of Mathematics, Faculty of Education, Suez Canal University, Al-Arish 45111, Egypt

Received 13 May 2012; Accepted 24 July 2012

Academic Editor: Benchawan Wiwatanapataphee

Copyright © 2012 A. A. Soliman. 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

Numerical solutions for Burgers’ equation based on the Galerkins’ method using cubic B-splines as both weight and interpolation functions are set up. It is shown that this method is capable of solving Burgers’ equation accurately for values of viscosity ranging from very small to large. Three standard problems are used to validate the proposed algorithm. A linear stability analysis shows that a numerical scheme based on a Cranck-Nicolson approximation in time is unconditionally stable.