A new conservation finite 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 also obtained.It is proved that the finite difference scheme is convergent with order 2 and stable without condition.The numerical examples show this scheme is feasible and its accuracy is better than usual difference scheme of two levels.