[1]郭姣姣,庄清渠.求解耦合非线性Klein-Gordon-Schr?dinger方程的能量稳定方法[J].华侨大学学报(自然科学版),2023,44(4):533-540.[doi:10.11830/ISSN.1000-5013.202206030]
 GUO Jiaojiao,ZHUANG Qingqu.Energy Stable Method for Coupled Nonlinear Klein-Gordon-Schr?dinger Equation[J].Journal of Huaqiao University(Natural Science),2023,44(4):533-540.[doi:10.11830/ISSN.1000-5013.202206030]
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求解耦合非线性Klein-Gordon-Schr?dinger方程的能量稳定方法()
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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4期
页码:
533-540
栏目:
出版日期:
2023-07-17

文章信息/Info

Title:
Energy Stable Method for Coupled Nonlinear Klein-Gordon-Schr?dinger Equation
文章编号:
1000-5013(2023)04-0533-08
作者:
郭姣姣 庄清渠
华侨大学 数学科学学院, 福建 泉州 362021
Author(s):
GUO Jiaojiao ZHUANG Qingqu
School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China
关键词:
耦合非线性Klein-Gordon-Schr? dinger方程 指数标量辅助变量方法 修正能量 守恒律
Keywords:
coupled nonlinear Klein-Gordon-Schr? dinger equation exponential scalar auxiliary variable method modified energy conservation law
分类号:
O241.8
DOI:
10.11830/ISSN.1000-5013.202206030
文献标志码:
A
摘要:
研究基于指数标量辅助变量方法的耦合非线性Klein-Gordon-Schr?dinger方程有效数值方法.首先,采用指数标量辅助变量处理方程的非线性项,构造求解方程的无条件能量稳定格式;然后,对方程在时间方向上采用Crank-Nicolson格式进行离散,在空间方向上采用紧致差分格式进行离散,证明全离散格式的修正能量守恒律.最后,通过数值算例进行验证.结果表明:文中格式具有有效性,修正能量具有守恒性.
Abstract:
The efficient numerical method of coupled nonlinear Klein-Gordon-Schr?dinger equation based on exponential scalar auxiliary variable method is studied. Firstly, the nonlinear terms of the equation are treated with exponential scalar auxiliary variables, and an unconditional energy stable scheme is constructed to the solution of the equation. Then, the equation is discretized by Crank-Nicolson scheme in time direction and by compact difference scheme in space direction, the modified energy conservation law of the full discrete scheme is proved. Finally, it is verified by numerical examples that the proposed scheme is effective and the modified energy is conserved.

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期: 2022-06-22
通信作者: 庄清渠(1980-),男,副教授,博士,主要从事微分方程数值解法的研究.E-mail:qqzhuang@hqu.edu.cn.
基金项目: 国家自然科学基金资助项目(11771083); 福建省自然科学基金资助项目(2021J01306)
更新日期/Last Update: 2023-07-20