In this paper, the numerical solution of initial-boundary value problem for generalized Rosenau-KdV-RLW equation with non-homogeneous boundary is considered. A nonlinear two-level Grank-Nicolson difference scheme is designed. The difference schemes simulate two conservative quantities of the problem well. The existence and uniqueness of the difference solutions are also proved. It is proved by the discrete energy method that the difference scheme is second-order convergence and unconditionally stable. Numerical experiments verify the theoretical results.
