耦合Gross-Pitaevskii方程的高效保质量守恒格式  

The Efficient Mass-Preserving Scheme for Coupled Gross-Pitaevskii Equations

作　　者：李羽 孔令华 罗奕杨 LI Yu;KONG Linghua;LUO Yiyang(School of Mathematics and Statistic,Jiangxi Normal University,Nanchang Jiangxi 330022,China;Jiangxi Provincial Center for Applied Mathematics,Nanchang Jiangxi 330022,China)

机构地区：[1]江西师范大学数学与统计学院,江西南昌330022 [2]江西省应用数学中心,江西南昌330022

出　　处：《江西师范大学学报（自然科学版）》2023年第2期194-198,共5页Journal of Jiangxi Normal University(Natural Science Edition)

基　　金：国家自然科学基金(11961036);江西省自然科学基金(20224ACB201001);江西师范大学研究生创新基金(YJ2021068)资助项目。

摘　　要：该文为耦合Gross-Pitaevskii方程提出了一个新的保质量守恒格式.首先对空间导数利用高阶紧致格式离散得到半离散格式;然后在时间方向上利用基于外推的Crank-Nicolson格式离散,得到一个半显式的数值格式,然而此格式不能保持GP方程固有的质量守恒,因此,对格式得到的数值解利用投影方法进行修正,使其满足离散质量守恒;最后通过数值实验验证了该格式具有高精度以及保持质量守恒.In this paper,the new mass-preserving scheme is proposed for the coupled Gross-Pitaevskii equation.Firstly,the spatial derivative is approximated by high order compact scheme and a semi-discrete scheme is obtained.The temporal derivative is approximated by Crank-Nicolson based extrapolation.Thus,a semi-implicit scheme is obtained.Unforunately this scheme is not mass-preserving.To make up for this,a projection method is used to pull solution back the mass-preserving space.Finaly,some numerical experiments are presented to illustrate high accuracy and mass-presering of the new scheme.

关 键 词：耦合Gross-Pitaevskii方程 投影法 高阶紧致格式 质量守恒 

分 类 号：O241.8[理学—计算数学]