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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 323260, 10 pages
http://dx.doi.org/10.1155/2014/323260
Research Article

A Fourth Order Finite Difference Method for the Good Boussinesq Equation

Department of Mathematics, College of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

Received 24 October 2013; Accepted 16 January 2014; Published 26 February 2014

Academic Editor: Youyu Wang

Copyright © 2014 M. S. Ismail and Farida Mosally. 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 “good” Boussinesq equation is transformed into a first order differential system. A fourth order finite difference scheme is derived for this system. The resulting scheme is analyzed for accuracy and stability. Newton’s method and linearization techniques are used to solve the resulting nonlinear system. The exact solution and the conserved quantity are used to assess the accuracy and the efficiency of the derived method. Head-on and overtaking interactions of two solitons are also considered. The numerical results reveal the good performance of the derived method.