In this paper, numerical solution of the initial-boundary value problem for the Rosenau-KdV-RLW equation under homogeneous boundary is considered. A three-level linear difference scheme with second order accuracy is proposed and the existence and uniqueness of the difference solution are proved. Despite the absence of the maximum mold estimation of the difference solutions, we still prove that the difference scheme is convergent and stable by using the mathematical induction and discrete function analysis. The analytical results are demonstrated by the numerical examples.
