[1]贺增甲,孔令华*,符芳芳.2维Gross-Pitaevskii方程的分裂高阶紧致差分格式[J].江西师范大学学报(自然科学版),2020,(06):599-603.[doi:10.16357/j.cnki.issn1000-5862.2020.06.09]
　HE Zengjia,KONG Linghua*,FU Fangfang.The Splitting High-Order Compact Difference Scheme for Two-Dimensional Gross-Pitaevskii Equation[J].Journal of Jiangxi Normal University:Natural Science Edition,2020,(06):599-603.[doi:10.16357/j.cnki.issn1000-5862.2020.06.09]
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2维Gross-Pitaevskii方程的分裂高阶紧致差分格式()
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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:
2020年06期
页码:
599-603
栏目:
数学与应用数学
出版日期:
2020-12-20

文章信息/Info

Title:
The Splitting High-Order Compact Difference Scheme for Two-Dimensional Gross-Pitaevskii Equation
文章编号:
1000-5862(2020)06-0599-05
作者:
贺增甲1; 孔令华1*; 符芳芳2
1.江西师范大学数学与统计学院,江西 南昌 330022; 2.南昌工学院基础部,江西 南昌 330108
Author(s):
HE Zengjia1; KONG Linghua1*; FU Fangfang2
1.School of Mathematics and Statistics,Jiangxi Normal University,Nanchang Jiangxi 330022,China; 2.Department of Fundamental Education,Nanchang Institute of Science and Technology,Nanchang Jiangxi 330108,China
关键词:
Gross-Pitaevskii方程;  旋转效应;  分裂方法;  高阶紧致格式;  质量守恒
Keywords:
Gross-Pitaevskii equation;  rotating effect;  splitting method;  high-order compact scheme;  mass conservation law
分类号:
O 241.8
DOI:
10.16357/j.cnki.issn1000-5862.2020.06.09
文献标志码:
A
摘要:
该文为带有旋转角动量的Gross-Pitaevskii方程构造了分裂高阶紧致差分格式.首先通过时间分裂将其分为线性方程和非线性方程,非线性方程可以通过质量守恒定律进行精确求解,线性方程通过高阶紧致格式和局部1维方法进行离散,最终得到的格式时间方向2阶收敛和空间方向4阶收敛,并保持质量守恒.最后用数值算例验证了格式的收敛阶以及质量守恒性.
Abstract:
The splitting high-order compact difference scheme for the Gross-Pitaevskii equation with angular momentum rotation term is constructed.Firstly,the equation is divided into linear equations and nonlinear equations by time splitting method.Secondly,the nonlinear equations can be accurately solved by the conservation law of mass,and the linear equation is discretized by a high-order compact scheme and a local one-dimensional method.The resulting scheme converges second-order in time and fourth-order in space while maintaining mass conservation.Finally,numerical experiments verify the convergence orders and mass conservation of the scheme.

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期:2020-08-11
基金项目:国家自然科学基金(11961036)和江西省教育厅基金(GJJ200310)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: 2020-12-20