Operator-compensation methods with mass and energy conservation for solving the Gross-Pitaevskii equation
Operator-compensation methods with mass and energy conservation for solving the Gross-Pitaevskii equation
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用于求解 Gross-Pitaevskii 方程的具有质量和能量守恒的算子补偿方法
DOI：
10.1016/j.apnum.2020.01.004
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发表时间：
2020-05
影响因子：
2.8
通讯作者：
Pengde Wang
中科院分区：
文献类型：
--
作者：
Xiang-Gui Li;Yongyong Cai;Pengde Wang
In this work, operator-compensation based high order methods are presented to solve the Gross-Pitaevskii equation modeling Bose-Einstein condensation (BEC). We begin with the high-order approximation to the Laplacian by the central finite difference method combined with operator-compensation technique, and the Crank-Nicolson and time-splitting methods are then proposed for the time discretization. We show that the Crank-Nicolson operator-compensation method keeps the mass and energy conservation, while the time-splitting operator-compensation method only conserves the mass. Then by extending the high-order operator-compensation methods for the first order derivative, the time-splitting finite difference method is developed to solve the Gross-Pitaevskii equation with an angular momentum rotation term. Numerical results are given to test accuracy and verify the conservation properties.
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