An efficient computational approach for two-dimensional variant of nonlinear-dispersive model of shallow water wave

Abstract

A three-level linearized difference scheme for two-dimensional dispersive shallow water wave that is governed by the Rosenau-RLW equation is considered. It is proved that the proposed difference scheme is conservative, uniquely solvable and unconditionally convergent. The convergence order in maximum norm is $$O(\tau ^2+h_1^2+h_2^2)$$, where $$\tau$$ is the temporal grid size and $$h_1, h_2$$ are spatial grid sizes in the x- and y-directions, respectively. Some numerical examples are provided to demonstrate the efficiency and applicability of the method and to verify its rate of convergence. The numerical results are compared with exact solutions and other existing method. Comparison reveals that our method improves the accuracy of the space and time direction and shortens computation time largely.