A three-level linear implicit conservative scheme for the Rosenau-KdV-RLW equation

A three-level linear conservative implicit finite difference scheme for solving the Rosenau-KdV-RLW equation is proposed. The existence, uniqueness, and conservation for energy of the difference solution are proved by the discrete energy method. The new scheme is 2nd-order convergent and unconditionally stable. Several numerical experiments verify that the theoretical results are accurate and the scheme is efficient and reliable.