[1]李 羽,孔令华*,罗奕杨.耦合Gross-Pitaevskii方程的高效保质量守恒格式[J].江西师范大学学报(自然科学版),2023,(02):194-198.[doi:10.16357/j.cnki.issn1000-5862.2023.02.12]
　LI Yu,KONG Linghua*,LUO Yiyang.The Efficient Mass-Preserving Scheme for Coupled Gross-Pitaevskii Equations[J].Journal of Jiangxi Normal University:Natural Science Edition,2023,(02):194-198.[doi:10.16357/j.cnki.issn1000-5862.2023.02.12]
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耦合Gross-Pitaevskii方程的高效保质量守恒格式()
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《江西师范大学学报》（自然科学版）[ISSN:1006-6977/CN:61-1281/TN]

卷:
期数:
2023年02期
页码:
194-198
栏目:
出版日期:
2023-03-25

文章信息/Info

Title:
The Efficient Mass-Preserving Scheme for Coupled Gross-Pitaevskii Equations
文章编号:
1000-5862(2023)02-0194-05
作者:
李 羽1; 孔令华1; 2*; 罗奕杨1
(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)
Author(s):
LI Yu1; KONG Linghua1; 2*; LUO Yiyang1
(1.School of Mathematics and Statistic,Jiangxi Normal University,Nanchang Jiangxi 330022,China; 2.Jiangxi Provincial Center for Applied Mathematics,Nanchang Jiangxi 330022,China)
关键词:
耦合Gross-Pitaevskii方程;  投影法;  高阶紧致格式;  质量守恒
Keywords:
coupled Gross-Pitaevskii equation;  projection method;  high order compact scheme;  mass conservation law.
分类号:
O 241.8
DOI:
10.16357/j.cnki.issn1000-5862.2023.02.12
文献标志码:
A
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.
Abstract:
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.

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期:2022-08-27
基金项目:国家自然科学基金(11961036),江西省自然科学基金(20224ACB201001)和江西师范大学研究生创新基金(YJ2021068)资助项目.
通信作者: 孔令华(1977—),男,江西石城人, 教授,博士, 博士生导师, 主要从事微分方程数值方法的研究.E-mail:konglh@mail.ustc.edu.cn
更新日期/Last Update: 2023-03-25