Table of Contents
International Journal of Partial Differential Equations
Volume 2014, Article ID 407387, 8 pages
http://dx.doi.org/10.1155/2014/407387
Research Article

Numerical Solutions of Two-Way Propagation of Nonlinear Dispersive Waves Using Radial Basis Functions

1Department of Mathematical Sciences, Delaware State University, Dover, DE 19901, USA
2Departamento de Matemáticas, UAM Iztapalapa, Apartado Postal 55-534, 09340 Iztapalapa, DF, Mexico

Received 28 May 2014; Accepted 15 July 2014; Published 3 August 2014

Academic Editor: Nikolai A. Kudryashov

Copyright © 2014 Pablo U. Suárez and J. Héctor Morales. 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

We obtain the numerical solution of a Boussinesq system for two-way propagation of nonlinear dispersive waves by using the meshless method, based on collocation with radial basis functions. The system of nonlinear partial differential equation is discretized in space by approximating the solution using radial basis functions. The discretization leads to a system of coupled nonlinear ordinary differential equations. The equations are then solved by using the fourth-order Runge-Kutta method. A stability analysis is provided and then the accuracy of method is tested by comparing it with the exact solitary solutions of the Boussinesq system. In addition, the conserved quantities are calculated numerically and compared to an exact solution. The numerical results show excellent agreement with the analytical solution and the calculated conserved quantities.