High precise nonlinear CN difference scheme for BBM Equation

Abstract:

In this paper, numerical solution for the initial-boundary value problem of BBM equation with homogeneous boundary is considered. A two-level nonlinear difference scheme with second order in time and fourth order in space is proposed. The difference scheme simulates the conservation property of the problem. The existence and uniqueness of the difference solutions are proved. Using the discrete energy method, the stability and convergence are proved. Numerical experiments confirm the theortical results.