unconditionally stable difference scheme for the numerical solution of nonlinear rosenau-kdv equation

In this paper we investigate a nonlinear evolution model described by the rosenau-kdv equation. we propose a threelevel average implicit finite difference scheme for its numerical solutions and prove that this scheme is stable and convergent in the order of o(τ2 + h2). furthermore we show the existence and uniqueness of numerical solutions. comparing the numerical results with other methods in the literature show the efficiency and high accuracy of the proposed method.