[1]罗奕杨,王 兰*,万 隆,等.含阻尼效应的非线性薛定谔方程的共形分裂高阶紧致差分格式[J].江西师范大学学报(自然科学版),2022,(02):210-214.[doi:10.16357/j.cnki.issn1000-5862.2022.02.14]
　LUO Yiyang,WANG Lan*,WAN Long,et al.The Conformal Splitting High-Order Compact Difference Scheme for Damped Nonlinear Schrdinger Equation[J].Journal of Jiangxi Normal University:Natural Science Edition,2022,(02):210-214.[doi:10.16357/j.cnki.issn1000-5862.2022.02.14]
点击复制

含阻尼效应的非线性薛定谔方程的共形分裂高阶紧致差分格式()
分享到：

《江西师范大学学报》（自然科学版）[ISSN:1006-6977/CN:61-1281/TN]

卷:
期数:
2022年02期
页码:
210-214
栏目:
数学与应用数学
出版日期:
2022-03-25

文章信息/Info

Title:
The Conformal Splitting High-Order Compact Difference Scheme for Damped Nonlinear Schrödinger Equation
文章编号:
1000-5862(2022)02-0210-05
作者:
罗奕杨1; 王 兰1*; 万 隆2; 孔令华1
1.江西师范大学数学与统计学院,江西 南昌 330022; 2.豫章师范学院小学教育学院,江西 南昌 330103
Author(s):
LUO Yiyang1; WANG Lan1*; WAN Long2; KONG Linghua1
1.School of Mathematics and Statistics,Jiangxi Normal University,Nanchang Jiangxi 330022,China; 2.School of Primary Education,Yuzhang Normal University,Nanchang Jiangxi 330103,China
关键词:
含阻尼效应的非线性薛定谔方程;  分裂方法;  高阶紧致格式;  共形守恒律
Keywords:
damped nonlinear Schrö; dinger equation;  splitting method;  high-order compact scheme;  conformal conservation law
分类号:
O 241.8
DOI:
10.16357/j.cnki.issn1000-5862.2022.02.14
文献标志码:
A
摘要:
该文对含有阻尼效应的非线性薛定谔方程提出了一个新的共形分裂高阶紧致差分格式.首先利用分裂技巧,将复杂方程分裂为3个子问题; 然后对于其中的非线性子问题,利用其逐点质量守恒的性质可以精确求解,避免了迭代,提高了计算效率; 再利用了高阶紧致方法对空间进行离散,在基本不提高成本的情况下,提升了空间精度; 最后通过理论分析与数值实验证明了该格式的高精度、稳定性以及保持共形质量守恒律.
Abstract:
The new conformal splitting high-order compact difference scheme for damped nonlinear Schrödinger equation is proposed in this paper.Firstly,the complex equation is divided into three subproblems by using the splitting technique.Then,the nonlinear subproblem can be solved precisely by using the property of point-by-point mass conservation,which avoids iteration and improves computational efficiency.In addition,the high-order compact method is applied to discretize the space,which improves the spatial accuracy without increasing the cost.Finally,the high accuracy,stability and two conformal conservation laws of the scheme are proved by theoretical analysis and numerical experiments.

参考文献/References:

[1] ELPHICK C,MERON E.Localized structures in surface waves[J].Physical Review A:General Physics,Atomic and Molecular Structure,1989,40(6):3226-3229.
[2] DEUTSC I H,ABRAM I.Reduction of quantum noise in soliton propagation by phase-sensitive amplification[J].Journal of the Optical Society of America B:Optical Physics,1994,11(11):2303-2313.
[3] MCLACHLAN R,PERLMUTTER M.Conformal Hamiltonian systems[J].Journal of Geometry and Physics,2001,39(4):276-300.
[4] BAO Weizhu,JAKSCH D.An explicit unconditionally stable numerical method for solving damped nonlinear Schrödinger equations with a focusing nonlinearity[J].SIAM Journal on Numerical Analysis,2003,41(4):1406-1426.
[5] JIANG Chaolong,CAI Wenjun,WANG Yushun.Optimal error estimate of a conformal Fourier pseudo-spectral method for the damped nonlinear Schrödinger equation[J].Numerical Methods for Partial Differential Equations,2018,34(4):1422-1454.
[6] JIANG Chaolong,SONG Yongzhong,WANG Yushun.A linearly implicit structure-preserving Fourier pseudo-spectral scheme for the damped nonlinear Schrödinger equation in three dimensions[J].Advances in Computational Mathematics,2020,46(2):2621-2633.
[7] CAI Jiaxiang,ZHANG Haihui.Efficient schemes for the damped nonlinear Schrödinger equation in high dimensions[J].Applied Mathematics Letters,2020,102:106158.
[8] HU Weipeng,DENG Zichen,YIN Tingting.Almost structure-preserving analysis for weakly linear damping nonlinear Schrödinger equation with periodic perturbation[J].Communications in Nonlinear Science and Numerical Simulation,2017,42:298-312.
[9] STRANG G.On the construction and comparison of difference schemes[J].SIAM Journal on Numerical Analysis,1968,5(3):506-517.
[10] MCLACHLAN R I,QUISPEL G R W.Splitting methods[J].Acta Numerica,2002,11:341-434.
[11] LELE S K.Compact finite difference schemes with spectral-like resolution[J].Journal of Computational Physics,1992,103(1):16-42.
[12] 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),2020,44(6):599-603.
[13] 陈萌,孔令华,王兰.Burgers方程的跳点紧致格式[J].江西师范大学学报(自然科学版),2017,41(5):526-530.
[14] KONG Linghua,LUO Yiyang,WANG Lan,et al.HOC-ADI schemes for two-dimensional Ginzburg-Landau equation in superconductivity[J].Mathematics and Computers in Simulation,2021,190:494-507.
[15] KONG Linghua,KUANG Liqun,WANG Tingchun.Efficient numerical schemes for two-dimensional Ginzburg-Landau equation in superconductivity[J].Discrete and Continuous Dynamical Systems:B,2019,24(12):6325-6347.
[16] 孙志忠.偏微分方程数值解法[M].2版.北京:科学出版社,2012.

相似文献/References:

[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.[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,(02):599.[doi:10.16357/j.cnki.issn1000-5862.2020.06.09]

备注/Memo

备注/Memo:
收稿日期:2021-12-28
基金项目:国家自然科学基金(11961036)和江西师范大学研究生创新基金(YJS2021068)的资助项目.
通信作者:王 兰(1979—),女,安徽池州人,副教授,博士,主要从事微分方程数值方法的研究.E-mail:wl0908@yeah.net
更新日期/Last Update: 2022-03-25