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Advances in Mathematical Physics
Volume 2014 (2014), Article ID 734067, 11 pages
http://dx.doi.org/10.1155/2014/734067
Research Article

A Modified Three-Level Average Linear-Implicit Finite Difference Method for the Rosenau-Burgers Equation

Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand

Received 23 January 2014; Accepted 16 March 2014; Published 17 April 2014

Academic Editor: Pavel Kurasov

Copyright © 2014 Jiraporn Janwised et al. 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 introduce a new technique, a three-level average linear-implicit finite difference method, for solving the Rosenau-Burgers equation. A second-order accuracy on both space and time numerical solution of the Rosenau-Burgers equation is obtained using a five-point stencil. We prove the existence and uniqueness of the numerical solution. Moreover, the convergence and stability of the numerical solution are also shown. The numerical results show that our method improves the accuracy of the solution significantly.