Compact finite difference schemes with high accuracy for one-dimensional nonlinear Schrodinger equation

In this paper, two compact finite difference schemes are presented for the numerical solution of the one-dimensional nonlinear Schrodinger equation. The discrete L-2-norm error estimates show that convergence rates of the present schemes are of order O(h(4) + r(2)). Numerical experiments on some model problems show that the present schemes preserve the conservation laws of charge and energy and are of high accuracy. (C) 2008 Elsevier B.V. All rights reserved.