Large Time-Stepping Spectral Methods for the Semiclassical Limit of the Defocusing Nonlinear Schrödinger Equation

Zongqi Liang

Discrete Dynamics in Nature and Society, 2009, vol. 2009, 1-27

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.

Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:283959

DOI: 10.1155/2009/283959

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