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

Abstract In this paper, we analyze a Crank–Nicolson-type finite difference scheme for the BBM equation. We prove the second-order convergence in discrete H 1 -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.

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