Boundary Value Problems
Volume 2010 (2010), Article ID 516260, 13 pages
doi:10.1155/2010/516260
Research Article

A New Conservative Difference Scheme for the General Rosenau-RLW Equation

Jin-Ming Zuo,1 Yao-Ming Zhang,1 Tian-De Zhang,2 and Feng Chang2

1School of Science, Shandong University of Technology, Zibo 255049, China
2School of Mathematics, Shandong University, Jinan 250100, China

Received 28 May 2010; Accepted 14 October 2010

Academic Editor: Colin Rogers

Copyright © 2010 Jin-Ming Zuo 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

A new conservative finite difference scheme is presented for an initial-boundary value problem of the general Rosenau-RLW equation. Existence of its difference solutions are proved by Brouwer fixed point theorem. It is proved by the discrete energy method that the scheme is uniquely solvable, unconditionally stable, and second-order convergent. Numerical examples show the efficiency of the scheme.