Table of Contents
International Journal of Computational Mathematics
Volume 2014 (2014), Article ID 178024, 12 pages
http://dx.doi.org/10.1155/2014/178024
Research Article

Solving the Generalized Regularized Long Wave Equation Using a Distributed Approximating Functional Method

Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 002, South Africa

Received 23 March 2014; Revised 5 July 2014; Accepted 21 July 2014; Published 12 August 2014

Academic Editor: Tobias Preusser

Copyright © 2014 Edson Pindza and Eben Maré. 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 generalized regularized long wave (GRLW) equation is solved numerically by using a distributed approximating functional (DAF) method realized by the regularized Hermite local spectral kernel. Test problems including propagation of single solitons, interaction of two and three solitons, and conservation properties of mass, energy, and momentum of the GRLW equation are discussed to test the efficiency and accuracy of the method. Furthermore, using the Maxwellian initial condition, we show that the number of solitons which are generated can be approximately determined. Comparisons are made between the results of the proposed method, analytical solutions, and numerical methods. It is found that the method under consideration is a viable alternative to existing numerical methods.