Numerical analysis of the conservative high-order compact scheme for 2D RLW equation in maximum norm

In this paper, a compact difference scheme is proposed for solving the two-dimensional regularized long wave (2D RLW) equation. The scheme adopts the fourth-order compact method in space and the Crank–Nicolson method in time. The discrete energy and mass conservations of the proposed scheme are verified via the discrete energy method. Prior estimates for the numerical solution are established in the maximum norm. The solvability of the scheme is proved based on the fixed-point theorem, and the uniqueness of the numerical solution is further obtained. Utilizing the prior estimates, the convergence and stability of the scheme in the maximum norm is proved, with a convergence order of second in time and fourth in space. Numerical tests validated the accuracy of the compact scheme.