Numerical analysis for fourth-order compact conservative difference scheme to solve the 3D Rosenau-RLW equation

In this paper, a fourth-order compact and energy conservative difference scheme for three-dimensional Rosenau-RLW equation is proposed. The scheme is a two-level and nonlinear-implicit scheme. It is proved by the discrete energy method that the compact scheme is solvable, the convergence and stability of the difference scheme is obtained, and its numerical convergence order is O(τ2+h4) in the L∞-norm. We discuss an iterative algorithm for solving the nonlinear algebraical system generated by the nonlinear compact scheme and prove its convergence. Numerical experiment results show that the theory is accurate and the method is efficient and reliable.