A compact finite difference scheme for the nonlinear Schrodinger equation with wave operator

In this paper, a compact finite difference scheme is presented for an periodic initial value problem of the nonlinear Schrodinger (NLS) equation with wave operator. This is a scheme of three levels with a discrete conservation law. The unconditional stability and convergence in maximum norm with order O(h(4) + tau(2)) are proved by the energy method. A numerical experiment is presented to support our theoretical results. (C) 2012 Elsevier Inc. All rights reserved.