On the convergence of difference schemes for the Benjamin–Bona–Mahony (BBM) equation

In this paper, we analyze a Crank–Nicolson-type finite difference scheme for the BBM equation. We prove the second-order convergence in discrete H1-norm of the difference approximate solutions. The existence, stability and uniqueness are also discussed in detail. At last a linearized difference scheme is given and its convergence is also proved.