| 耦合Gross-Pitaevskii方程的高效保质量守恒格式 |
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| 引用本文： | 李 羽1,孔令华1,2,罗奕杨1. 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, 0(2): 194-198. DOI: 10.16357/j.cnki.issn1000-5862.2023.02.12 |
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| 作者姓名： | 李 羽1 孔令华1 2 罗奕杨1 |
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| 作者单位： | (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) |
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| 基金项目： | 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； |
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| 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.
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| 关 键 词： | 耦合Gross-Pitaevskii方程 投影法 高阶紧致格式 质量守恒 |
The Efficient Mass-Preserving Scheme for Coupled Gross-Pitaevskii Equations |
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| LI Yu1,KONG Linghua1,' target="_blank" rel="external">2,LUO Yiyang1. The Efficient Mass-Preserving Scheme for Coupled Gross-Pitaevskii Equations[J]. Journal of Jiangxi Normal University (Natural Sciences Edition), 2023, 0(2): 194-198. DOI: 10.16357/j.cnki.issn1000-5862.2023.02.12 |
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| Authors: | LI Yu1,KONG Linghua1,' target=" _blank" rel=" external" >2,LUO Yiyang1 |
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| Affiliation: | (1.School of Mathematics and Statistic,Jiangxi Normal University,Nanchang Jiangxi 330022,China; 2.Jiangxi Provincial Center for Applied Mathematics,Nanchang Jiangxi 330022,China) |
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| 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. |
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| Keywords: | coupled Gross-Pitaevskii equation projection method high order compact scheme mass conservation law. |
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