临界Schrödinger映射非齐次初边值问题的有限差分格式

数学物理学报 ›› 2021, Vol. 41 ›› Issue (5): 1311-1322.

临界Schrödinger映射非齐次初边值问题的有限差分格式

邓海云¹(),刘辉^2,*(),宋文静³()

¹ 南京审计大学应用数学系南京 211815
² 曲阜师范大学数学科学学院山东曲阜 273165
³ 西安工程大学理学院西安 710048

收稿日期:2020-08-13 出版日期:2021-10-26 发布日期:2021-10-08
通讯作者: 刘辉 E-mail:haiyundengmath1989@njust.edu.cn;liuhuinanshi@qfnu.edu.cn;wenjingsong1@163.com
作者简介:邓海云, E-mail: haiyundengmath1989@njust.edu.cn|宋文静, E-mail: wenjingsong1@163.com
基金资助:
国家自然科学基金(12001276);国家自然科学基金(12001275);国家自然科学基金(12071219);国家自然科学基金(11901342);国家自然科学基金(12001415);山东省自然科学基金(ZR2018QA002);中国博士后科学基金(2019M652350)

Finite Difference Scheme for the Nonhomogeneous Initial Boundary Value Problem of Critical Schrödinger Map

Haiyun Deng¹(),Hui Liu^2,*(),Wenjing Song³()

¹ Department of Applied Mathematics, Nanjing Audit University, Nanjing 211815
² School of Mathematical Sciences, Qufu Normal University, Shandong Qufu 273165
³ College of Science, Xi'an Polytechnic University, Xi'an 710048

Received:2020-08-13 Online:2021-10-26 Published:2021-10-08
Contact: Hui Liu E-mail:haiyundengmath1989@njust.edu.cn;liuhuinanshi@qfnu.edu.cn;wenjingsong1@163.com
Supported by:
the NSFC(12001276);the NSFC(12001275);the NSFC(12071219);the NSFC(11901342);the NSFC(12001415);the NSF of Shandong Province(ZR2018QA002);the China Postdoctoral Science Foundation(2019M652350)

摘要/Abstract

摘要：

利用有限差分格式考虑了具有非齐次初边值条件的临界Schrödinger映射的数值解，证明了其收敛性及稳定性，并通过数值实验表明，格式具有较好的有效性和稳定性.

关键词: Schrödinger映射, 差分格式, 收敛性, 稳定性

Abstract:

In this paper, we study finite difference scheme for the nonhomgeneous initial boundary value problem of critical Schrödinger map in two-dimensional space. We get the convergence and stability of the difference scheme. At the same time, we prove that this difference scheme has good effectiveness and stability by numerical experiments.

Key words: Schrödinger map, Difference scheme, Convergence, Stability

中图分类号:

O241.82

邓海云,刘辉,宋文静. 临界Schrödinger映射非齐次初边值问题的有限差分格式[J]. 数学物理学报, 2021, 41(5): 1311-1322.

Haiyun Deng,Hui Liu,Wenjing Song. Finite Difference Scheme for the Nonhomogeneous Initial Boundary Value Problem of Critical Schrödinger Map[J]. Acta mathematica scientia,Series A, 2021, 41(5): 1311-1322.

图/表 3

图 1

图 2

表 1

参考文献 28

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时间层	精确解	差分格式解	误差值	所需时间(s)
1	1.00+e00	1.00-4.44089e-16	4.44089e-16	0.017160
2	1.00+e00	1.00-3.33067e-16	3.33067e-16	0.012998
3	1.00+e00	1.00-3.33067e-16	3.33067e-16	0.011783
4	1.00+e00	1.00-4.44089e-16	4.44089e-16	0.011667
5	1.00+e00	1.00-6.66134e-16	6.66134e-16	0.011951
6	1.00+e00	1.00-4.44089e-16	4.44089e-16	0.011711
7	1.00+e00	1.00-3.33067e-16	3.33067e-16	0.011630
8	1.00+e00	1.00-4.44089e-16	4.44089e-16	0.011647
9	1.00+e00	1.00-5.55112e-16	5.55112e-16	0.011787
10	1.00+e00	1.00-5.55112e-16	5.55112e-16	0.011690
11	1.00+e00	1.00-4.44089e-16	4.44089e-16	0.011579
12	1.00+e00	1.00-4.44089e-16	4.44089e-16	0.011576
13	1.00+e00	1.00-3.33067e-16	3.33067e-16	0.011611
14	1.00+e00	1.00-3.33067e-16	3.33067e-16	0.011501
15	1.00+e00	1.00-4.44089e-16	4.44089e-16	0.011609
16	1.00+e00	1.00-4.44089e-16	4.44089e-16	0.011973
17	1.00+e00	1.00-4.44089e-16	4.44089e-16	0.011524
18	1.00+e00	1.00-3.33067e-16	3.33067e-16	0.012638
19	1.00+e00	1.00-4.44089e-16	4.44089e-16	0.011606
20	1.00+e00	1.00-3.33067e-16	3.33067e-16	0.011690

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