Discrete Dynamics in Nature and Society
Volume 2009 (2009), Article ID 283959, 27 pages
doi:10.1155/2009/283959

Large time-stepping spectral methods for the semiclassical limit of the defocusing nonlinear Schrödinger equation

Abstract

We analyze a class of large time-stepping Fourier spectral methods for the semiclassical limit of the defocusing Nonlinear Schrödinger equation and provide highly stable methods which allow much larger time step than for a standard implicit-explicit approach. An extra term, which is consistent with the order of the time discretization, is added to stabilize the numerical schemes. Meanwhile, the first-order and second-order semi-implicit schemes are constructed and analyzed. Finally the numerical experiments are performed to demonstrate the effectiveness of the large time-stepping approaches.