Abstract: Based on the study of the dynamic systems， the numerical method of the initialboundary value problem of generalized RosenauBurgers equation was discussed and the dissipation problems of nonlinear wave were revealed. A new implicit finite difference scheme of twolevel was proposed and the prior estimate of the finite difference solution was obtained. Existence and uniqueness of numerical solutions were derived. It was proved that the finite difference scheme is convergent and stable. Numerical experiments indicated the scheme is efficient and good stability， the proposed scheme has theoretical significance and availability.

Key words: generalized RosenauBurgers equation, finite difference scheme, solvability, convergence, stability