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Mathematical Problems in Engineering
Volume 2015, Article ID 274579, 9 pages
http://dx.doi.org/10.1155/2015/274579
Research Article

Runge-Kutta Integration of the Equal Width Wave Equation Using the Method of Lines

Department of Mathematics, Science Faculty for Girls, King Abdulaziz University, P.O. Box 80200, Jeddah 21589, Saudi Arabia

Received 31 August 2014; Revised 5 January 2015; Accepted 8 January 2015

Academic Editor: K. M. Liew

Copyright © 2015 M. A. Banaja and H. O. Bakodah. 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

The equal width (EW) equation governs nonlinear wave phenomena like waves in shallow water. Numerical solution of the (EW) equation is obtained by using the method of lines (MOL) based on Runge-Kutta integration. Using von Neumann stability analysis, the scheme is found to be unconditionally stable. Solitary wave motion and interaction of two solitary waves are studied using the proposed method. The three invariants of the motion are evaluated to determine the conservation properties of the generated scheme. Accuracy of the proposed method is discussed by computing the and error norms. The results are found in good agreement with exact solution.