[1]孙传志,汪佳玲.非线性薛定谔方程的几种差分格式[J].华侨大学学报(自然科学版),2021,42(4):551-560.[doi:10.11830/ISSN.1000-5013.202011019]
　SUN Chuanzhi,WANG Jialing.Several Difference Schemes for Nonlinear Schr?dinger Equation[J].Journal of Huaqiao University(Natural Science),2021,42(4):551-560.[doi:10.11830/ISSN.1000-5013.202011019]
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非线性薛定谔方程的几种差分格式()
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《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第42卷
期数:
2021年第4期
页码:
551-560
栏目:
出版日期:
2021-07-20

文章信息/Info

Title:
Several Difference Schemes for Nonlinear Schr?dinger Equation
文章编号:
1000-5013(2021)04-0551-10
作者:
孙传志;  汪佳玲
南京信息工程大学 数学与统计学院, 江苏 南京 210044
Author(s):
SUN Chuanzhi;  WANG Jialing
School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China
关键词:
非线性薛定谔方程;  向前Euler格式;  Crank-Nicolson格式;  紧致差分格式;  质量守恒;  能量守恒
Keywords:
nonlinear Schr? dinger equation;  forward Euler scheme;  Crank-Nicolson scheme;  compact difference scheme;  mass conservation;  energy conservation
分类号:
O241.81
DOI:
10.11830/ISSN.1000-5013.202011019
文献标志码:
A
摘要:
在满足一定的初值、边值条件下,结合不同的差分格式对非线性薛定谔(NLS)方程进行数值求解.分别利用经典的向前差分算子、二阶中心差分算子、Crank-Nicolson方法和紧致差分算子构造向前Euler格式、Crank-Nicolson格式和紧致差分格式,并证明Crank-Nicolson格式和紧致差分格式精确保持离散质量守恒和能量守恒.利用数学软件MATLAB进行实验计算,结果表明:所构造的3种格式具有合理性及有效性.
Abstract:
Under the condition of initial value and boundary value, the nonlinear Schr?dinger(NLS)equation numerical solution is solved by different difference schemes. The forward Euler scheme, the Crank-Nicolson scheme and the compact difference scheme are constructed by using the classical forward difference operator, the second-order central difference operator, the Crank-Nicolson method and the compact difference operator. It is proved that the Crank-Nicolson scheme and the compact difference scheme keep the conservation of discrete mass and energy accurately. Carrying out experimontal calculation by using mathematical software MATLAB, we find that the three schemes constructed are reasonable and effective.

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备注/Memo

备注/Memo:
收稿日期: 2020-11-12
通信作者: 汪佳玲(1990-),讲师,博士,主要从事微分方程数值解的研究.E-mail:wjl19900724@126.com.
基金项目: 国家自然科学基金青年基金资助项目(11801277); 南京信息工程大学科研启动项目(2017r090)
更新日期/Last Update: 2021-07-20