Research On The Linear Difference Method Of Rosenau-KDV-RLW Equation

The iteration is not to be avoided in the process of numerical calculation of the nonlinear difference scheme,which takes a lot of time,so it is pretty meaningful work to construct the linearized difference scheme in the field of numerical research.As the further consideration for nonlinear long wave,it is necessary to add a viscous term+u_xxx to the Rosenau-RLW equation to obtain the Rosenau-KdV-RLW equation.However,there are few analytical solutions for these nonlinear long wave equations.Studies of numerical methods for wave equations undoubtedly are of important theoretical and practical significance.Firstly,a two-level linearized difference scheme with second-order theoretical accuracy is proposed for the initial-boundary value problem of the Rosenau-KdV-RLW equation.The difference scheme simulates the conservation property of the problem quite well.The existence and uniqueness of the difference solutions are also proved.Furthermore,it is proved that the difference scheme is convergent and stable by the discrete function analysis.And the results are demonstrated by the numerical examples.In addition,two three-level linearized difference schemes with second-order theoretical accuracy are proposed for the initial-boundary value problem of the Rosenau-KdV-RLW equation.The existence and uniqueness of difference solutions are proved for these two schemes.And it is proved that the difference schemes are convergent and stable by the discrete function analysis.The numerical examples are given.