Numerical scheme for a model of shallow water waves in (2+1)-dimensions

A nonlinear difference scheme is considered for the two-dimensional Rosenau-Burgers equation. Some priori estimates, existence and uniqueness of the difference solution have been shown. A second-order convergence in the uniform norm and stability are proved. Also a convergent iterative algorithm is presented. All results are obtained without any restrictions on the meshsizes. At last numerical experiments are carried out to support the theoretical claims.