Numerical Theory And Algorithm Research Of Difference Schemes For Two Classes SRLM Coupling Equations

The symmetric regularized long wave equations(SRLW)is a symmetrical description of the regularized long wave equations(RLW)proposed in the study of weak nonlinear ion acoustic waves and spatial acoustic wave propagation phenomena.In the practical applications,viscous damping and dissipation are inevitable,so it is very meaningful to study the numerical theory and algorithm of the dissipative symmetric regularized long wave equation with damping terms.In this paper,the difference method is used to study the initial boundary value problem of the dissipative symmetric regular long wave(SRLW)equations with damping term.Firstly,a high accuracy compact difference scheme is constructed for the initial boundary value problem of a class of two-dimensional dissipative symmetric regular long wave(SRLW)equations with a damping term in finite time.Combining with the energy analysis method,the existence and uniqueness of the difference solutions has been shown.We proved that the difference scheme is unconditionally stable and convergence,and its numerical convergence order is O(?~2+h~4).The reliability and validity of the numerical theory are proved by numerical experiments.Secondly,a new finite difference scheme is proposed for the long time behavior of a class of two-dimensional dissipative symmetric regular long wave(SRLW)equations with damping term.The existence and uniqueness of the difference solution and the priori estimation are proved.The long time stability and convergence of the finite difference scheme are obtained,and its numerical convergence order is O(?~2+h~2).