A Fourth-Order Compact and Conservative Difference Scheme for the Generalized Rosenau-Korteweg de Vries Equation in Two Dimensions (Journal of Computational Mathematics, 2019)
In this paper, a conservative difference scheme for the Rosenau-Korteweg de Vries(RKdV) equation in 2D is proposed. The system satisfies the conservative laws in energyand mass. Existence and uniqueness of its difference solution have been shown. The orderof $O(τ^2 +h^4)$ in the discrete $L^∞$-norm with time step $τ$ and mesh size $h$ is obtained. Someimportant lemmas are proposed to prove the high order convergence. We prove that thepresent scheme is unconditionally stable. Numerical results are also given in order to checkthe properties of analytical solution.