Journal of Applied Mathematics
Volume 2012 (2012), Article ID 308410, 14 pages
http://dx.doi.org/10.1155/2012/308410
Research Article

Numerical Analysis of a Linear-Implicit Average Scheme for Generalized Benjamin-Bona-Mahony-Burgers Equation

Hai-tao Che,1,2 Xin-tian Pan,2 Lu-ming Zhang,3 and Yi-ju Wang1

1School of Management Science, Qufu Normal University, Rizhao 276800, China
2School of Mathematics and Information Science, Weifang University, Weifang 261061, China
3Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

Received 14 October 2011; Accepted 21 December 2011

Academic Editor: Yuantong Gu

Copyright © 2012 Hai-tao Che 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 linear-implicit finite difference scheme is given for the initial-boundary problem of GBBM-Burgers equation, which is convergent and unconditionally stable. The unique solvability of numerical solutions is shown. A priori estimate and second-order convergence of the finite difference approximate solution are discussed using energy method. Numerical results demonstrate that the scheme is efficient and accurate.