A high-accuracy conservative difference approximation for Rosenau-KdV equation

In this paper, we study the initial-boundary value problem of Rosenau-KdV equation. A conservative two level nonlinear Crank-Nicolson difference scheme, which has the theoretical accuracy O(τ² + h^4), is proposed. The scheme simulates two conservative properties of the initial boundary value problem. Existence, uniqueness, and priori estimates of difference solution are obtained. Furthermore, we analyze the convergence and unconditional stability of the scheme by the energy method. Numerical experiments demonstrate the theoretical results.