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On the convergence of difference schemes for the Benjamin–Bona–Mahony (BBM) equation
Journal article   Peer reviewed

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

T. Achouri, N. Khiari and K. Omrani
Applied mathematics and computation, Vol.182(2), pp.999-1005
15/11/2006
DOI: https://doi.org/10.1016/j.amc.2006.04.069

Abstract

BBM equation Convergence Existence Finite difference scheme Linearization Stability Uniqueness
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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