A new high accuracy linearized difference algorithm for the BBM equation

Abstract:

In this paper, an initial boundary value problem of Benjamin-Bona-Mahony equation is studied numerically. Firstly, the problem is discretized and linearized by extrapolating in time layer, and then extrapolated at the space level with Richardson's extrapolation idea, thus a three-layer linear difference scheme is proposed. Secondly, the existence and uniqueness of the decomposition of difference of the discrete solution are proved. Finally, the convergence and stability of the scheme are proved by combining mathematical induction and discrete functional analysis. Numerical experiments show that the accuracy of the scheme is obviously better than that of the known linear layer difference scheme.