A 2N order compact finite difference method for solving the generalized regularized long wave (GRLW) equation

The generalized regularized long wave (GRLW) equation is solved by fully different numerical scheme. The equation is discretized in space by 2N order compact finite difference method and in time by a backward finite difference method. At the inner and the boundary nodes, the first and the second order derivatives with 2N order of accuracy are obtained. To determine the conservation properties of the GRLW equation three invariants of motion are evaluated. The single solitary wave and the interaction of two and three solitary waves are presented to validate the efficiency and the accuracy of the proposed scheme.