Conservative and Nonconservative Schemes for the Solution of the Nonlinear Schroedinger Equation

摘要

Schema for the integration in time of a space discretization of the nonlinear Schroedinger equation are studied. Five methods (implicit point, pseudo linear midpoint, scheme of Griffiths, and two splitting procedures) for the time integration of the resulting system of ordinary differential equations are discussed. The partly explicit scheme of Griffiths and splitting procedures are found to perform poorly. Drawbacks and advantages of using time integrators which exactly conserve energy are discussed.