High-order IMEX-spectral schemes for computing the dynamics of systems of nonlinear Schrodinger/Gross-Pitaevskii equations

JOURNAL OF COMPUTATIONAL PHYSICS

卷:327

Article

Antoine, Xavier¹  Besse, Christophe²  Rispoli, Vittorio² 

[1] Univ Lorraine, Inst Elie Cartan Lorraine, UMR 7502, Inria Nancy Grand Est SPHINX Team, F-54506 Vandoeuvre Les Nancy, France

[2] Univ Toulouse 3, Inst Math Toulouse, UMR CNRS 5219, 118 Route Narbonne, F-31062 Toulouse 9, France

关键词: Nonlinear Schrodinger equation;    Gross-Pitaevskii equation;    Bose-Einstein condensates;    Spin-orbit;    Dynamics;    High-order discretization;    IMplicit-EXplicit schemes;    Pseudo-spectral schemes;    Time-splitting;    Adaptive time stepping;   

DOI  :  10.1016/j.jcp.2016.09.020

来源: Elsevier

【 摘 要 】

The aim of this paper is to build and validate some explicit high-order schemes, both in space and time, for simulating the dynamics of systems of nonlinear Schrodinger/Gross-Pitaevskii equations. The method is based on the combination of high-order IMplicit-EXplicit (IMEX) schemes in time and Fourier pseudo-spectral approximations in space. The resulting IMEXSP schemes are highly accurate, efficient and easy to implement. They are also robust when used in conjunction with an adaptive time stepping strategy and appear as an interesting alternative to time-splitting pseudo-spectral (TSSP) schemes. Finally, a complete numerical study is developed to investigate the properties of the IMEXSP schemes, in comparison with TSSP schemes, for one-and two-components systems of Gross-Pitaevskii equations. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free