Finite difference methods for 2D shallow water equations with dispersion

Basic properties of some finite difference schemes for two-dimensional nonlinear dispersive equations for hydrodynamics of surface waves are considered. It is shown that stability conditions for difference schemes of shallow water equations are qualitatively different in the cases the dispersion is taken into account, or not. The difference in the behavior of phase errors in one- and two-dimensional cases is pointed out. Special attention is paid to the numerical algorithm based on the splitting of the original system of equations into a nonlinear hyperbolic system and a scalar linear equation of elliptic type.