NUMERICAL APPROACH OF DISPERSIVE SHALLOW WATER WAVES WITH ROSENAU-KDV-RLW EQUATION IN (2+1)-DIMENSIONS

. A linearized conservative finite difference scheme for a model of regularised long wave (Rosenau-KdV-RLW) equation is proposed. It is shown that the difference scheme is conservative, unique solvable and unconditionally stable. The numerical scheme is proved to be of second-order accurate both in time and space for the maximum norm. In order to validate the theoretical results, several numerical examples are presented. The numerical results obtained by the linearized finite difference scheme are compared with the exact solution and solutions of other published recent methods. All the numerical experiments show that present linearized conservative difference scheme is the most effective in terms of accuracy and time consumption and gives a summary of the advantages of our method over the existing numerical methods.