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International Journal of Differential Equations
Volume 2012 (2012), Article ID 587208, 15 pages
http://dx.doi.org/10.1155/2012/587208
Research Article

Numerical Solution of the Modified Equal Width Wave Equation

Department of Mathematics, Faculty of Education, İnönü University, 44280 Malatya, Turkey

Received 18 May 2011; Accepted 30 September 2011

Academic Editor: Sabri Arik

Copyright © 2012 Seydi Battal Gazi Karakoç and Turabi Geyikli. 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 solution of the modified equal width wave equation is obtained by using lumped Galerkin method based on cubic B-spline finite element method. Solitary wave motion and interaction of two solitary waves are studied using the proposed method. Accuracy of the proposed method is discussed by computing the numerical conserved laws 𝐿 2 and 𝐿 error norms. The numerical results are found in good agreement with exact solution. A linear stability analysis of the scheme is also investigated.