Finite difference discretization of the Benjamin‐Bona‐Mahony‐Burgers equation

Abstract Numerical solutions of the Benjamin‐Bona‐Mahony‐Burgers equation in one space dimension are considered using Crank‐Nicolson‐type finite difference method. Existence of solutions is shown by using the Brower's fixed point theorem. The stability and uniqueness of the corresponding methods are proved by the means of the discrete energy method. The convergence in L ∞ ‐norm of the difference solution is obtained. A conservative difference scheme is presented for the Benjamin‐Bona‐Mahony equation. Some numerical experiments have been conducted in order to validate the theoretical results.© 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007