[1]姚梦丽,滕宇航,赖艺颖,等.非线性Schr?dinger方程的龙格库塔配点格式[J].华侨大学学报(自然科学版),2024,45(4):534-542.[doi:10.11830/ISSN.1000-5013.202308035]
　YAO Mengli,TENG Yuhang,LAI Yiying,et al.Runge-Kutta Collocation Scheme for Nonlinear Schr?dinger Equation[J].Journal of Huaqiao University(Natural Science),2024,45(4):534-542.[doi:10.11830/ISSN.1000-5013.202308035]
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非线性Schr?dinger方程的龙格库塔配点格式()
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《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第45卷
期数:
2024年第4期
页码:
534-542
栏目:
出版日期:
2024-07-20

文章信息/Info

Title:
Runge-Kutta Collocation Scheme for Nonlinear Schr?dinger Equation
文章编号:
1000-5013(2024)04-0534-09
作者:
姚梦丽;  滕宇航;  赖艺颖;  翁智峰
华侨大学 数学科学学院, 福建 泉州 362021
Author(s):
YAO Mengli;  TENG Yuhang;  LAI Yiying;  WENG Zhifeng
School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China
关键词:
非线性Schr? dinger方程;  4阶龙格库塔方法;  重心Lagrange插值配点;  相容性分析
Keywords:
nonlinear Schr? dinger equation;  fourth-order Runge-Kutta method;  barycentric Lagrange interpolation collocation;  consistency analysis
分类号:
O241.82
DOI:
10.11830/ISSN.1000-5013.202308035
文献标志码:
A
摘要:
采用4阶龙格库塔方法结合重心Lagrange插值配点法求解非线性Schr?dinger方程。首先,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4阶龙格库塔方法离散,从而得到非线性Schr?dinger方程的龙格库塔配点格式。其次,对全离散格式进行相容性分析。结果表明:龙格库塔配点格式具有高精度,且满足离散的质量和能量守恒。
Abstract:
The fourth order Runge-Kutta method and barycentric Lagrange interpolation collocation method are used to solve the nonlinear Schr?dinger equation. Firstly, the barycentric Lagrange interpolation collocation scheme is discreted in the spatial direction, and the fourth-order Runge-Kutta method is discreted in the temporal direction. The Runge-Kutta collocation scheme of the nonlinear Schr?dinger equation is obtained. Secondly, the consistency analysis of the fully discrete scheme is analyzed. The results show that the Runge-Kutta collocation scheme has the high accuracy and satisfies the conservation of discrete mass and energy.

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备注/Memo

备注/Memo:
收稿日期: 2023-08-29
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: 2024-07-20