Pseudo-compact conservation difference scheme for generalized regularized long wave equation

The numerical solution for an initial-boundary value problem of generalized regularized long wave equation is considered.An implicit pseudo-compact finite difference of two levels is proposed.This scheme simulates the conservation properties of the problem well.And the existence and uniqueness of the solution are obtained.It is proved that the finite difference scheme is convergent with order 2 and stable without condition by the energy method.The numerical examples show that the accuracy of this scheme is better than usual difference scheme of two levels.