Numerical Solution of Coupled-BBM Systems of Boussinesq type by Implicit Finite Difference Method

In this paper we study a numerical solution of coupled BBM systems of Boussinesq type, which describes approximately the two ways propagation of surface wave in a uniform horizontal channel of length l filled in its undisturbed depth h. This paper is devoted to drive the matrix algebraic equation for the one-dimensional nonlinear BBM system which is obtaining from using the implicit finite difference method. The convergence analysis of the solution is proved. Numerical experiments are presented with a variety of initial conditions describing the generation and evolution of such waves, and their interactions.