A High-Order Conservative Numerical Method for Gross–Pitaevskii Equation with Time-Varying Coefficients in Modeling BEC
Xiang Li1 , Xu Qian1,2** , Ling-Yan Tang1 , Song-He Song1
1 College of Science and State Key Laboratory of High Performance Computing, National University of Defense Technology, Changsha 4100732 Academy of Ocean Science and Engineering, National University of Defense Technology, Changsha 410073
Abstract ：We propose a high-order conservative method for the nonlinear Schrödinger/Gross–Pitaevskii equation with time-varying coefficients in modeling Bose–Einstein condensation (BEC). This scheme combined with the sixth-order compact finite difference method and the fourth-order average vector field method, finely describes the condensate wave function and physical characteristics in some small potential wells. Numerical experiments are presented to demonstrate that our numerical scheme is efficient by the comparison with the Fourier pseudo-spectral method. Moreover, it preserves several conservation laws well and even exactly under some specific conditions.
收稿日期: 2017-01-05
出版日期: 2017-05-23
:
02.60.Lj
(Ordinary and partial differential equations; boundary value problems)
02.70.Bf
(Finite-difference methods)
02.60.Cb
(Numerical simulation; solution of equations)
02.60.Jh
(Numerical differentiation and integration)
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2017, Vol. 34 
