[1]姚梦丽,田朝薇,翁智峰.非线性Schr?dinger方程的算子分裂配点格式[J].华侨大学学报(自然科学版),2023,44(5):645-653.[doi:10.11830/ISSN.1000-5013.202209015]
　YAO Mengli,TIAN Zhaowei,WENG Zhifeng.Operator Splitting Collocation Scheme for Nonlinear Schr?dinger Equation[J].Journal of Huaqiao University(Natural Science),2023,44(5):645-653.[doi:10.11830/ISSN.1000-5013.202209015]
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非线性Schr?dinger方程的算子分裂配点格式()
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《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第44卷
期数:
2023年第5期
页码:
645-653
栏目:
出版日期:
2023-09-20

文章信息/Info

Title:
Operator Splitting Collocation Scheme for Nonlinear Schr?dinger Equation
文章编号:
1000-5013(2023)05-0645-09
作者:
姚梦丽;  田朝薇;  翁智峰
华侨大学 数学科学学院, 福建 泉州 362021
Author(s):
YAO Mengli;  TIAN Zhaowei;  WENG Zhifeng
School of Mathematical Science, Huaqiao University, Quanzhou 362021, China
关键词:
非线性Schr? dinger方程;  算子分裂格式;  重心Lagrange插值配点法;  Crank-Nicolson格式
Keywords:
nonlinear Schr? dinger equation;  operator splitting scheme;  barycentric Lagrange interpolation collocation method;  Crank-Nicolson scheme
分类号:
O241.82
DOI:
10.11830/ISSN.1000-5013.202209015
文献标志码:
A
摘要:
采用算子分裂格式结合重心Lagrange插值配点法求解非线性Schr?dinger方程.首先,将非线性Schr?dinger方程分解为线性部分和非线性部分,线性部分在空间方向上采用重心Lagrange插值配点格式进行离散,在时间方向上采用Crank-Nicolson格式进行离散,非线性部分采用解析求解;然后,对线性子问题空间半离散技术进行相容性分析.最后,采用数值算例进行验证.结果表明:算子分裂配点格式具有高精度,且满足离散的质量守恒和能量守恒.
Abstract:
The operator splitting scheme combined with the barycentric Lagrange interpolation collocation method is used to solve the nonlinear Schr?dinger equation. Firstly, the nonlinear Schr?dinger equation is decomposed into linear and nonlinear parts. The linear part is discretized by the barycentric Lagrange interpolation collocation scheme in the spatial direction, and the Crank-Nicolson scheme is used for discretization in the time direction, the nonlinear part is solved analytically. Then, the consistency analysis of space semi discrete technique for linear subquestion is proved. Finally, numerical experiments are used for verification. The results show that the operator splitting collocation scheme has high accuracy and satisfies discrete conservation of mass and conservation of energy.

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期: 2022-09-29
通信作者: 翁智峰(1985-),男,副教授,博士,主要从事偏微分方程数值解的研究.E-mail:zfwmath@163.com.
基金项目: 国家自然科学基金资助项目(11701197); 福建省自然科学基金面上资助项目(2022J01308); 中央高校基本科研业务费专项基金资助项目(ZQN702)
更新日期/Last Update: 2023-09-20