Numerical analysis of a linear-implicit average scheme for generalized Benjamin-Bona-Mahony-Burgers equation

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. Copyright © 2012 Hai-tao Che et al.