A compact split-step finite difference method for solving the nonlinear Schrodinger equations with constant and variable coefficients

We propose a compact split-step finite difference method to solve the nonlinear Schrodinger equations with constant and variable coefficients. This method improves the accuracy of split-step finite difference method by introducing a compact scheme for discretization of space variable while this improvement does not reduce the stability range and does not increase the computational cost. This method also preserves some conservation laws. Numerical tests are presented to confirm the theoretical results for the new numerical method by using the cubic nonlinear Schrodinger equation with constant and variable coefficients and Gross-Pitaevskii equation. (C) 2009 Elsevier B.V. All rights reserved.