Analysis of new conservative difference scheme for two-dimensional Rosenau-RLW equation

In this article, numerical solution for the Rosenau-RLW equation in 2D is considered and a conservative Crank–Nicolson finite difference scheme is proposed. Existence of the numerical solutions for the difference scheme has been shown by Browder fixed point theorem. A priori bound and uniqueness as well as conservation of discrete mass and discrete energy for the finite difference solutions are discussed. Unconditional stability and a second-order accuracy on both space and time of the difference scheme are proved. Numerical experiments are given to support our theoretical results.