[1]林周瑾,汪佳玲,霍昱安.Klein-Gordon-Schr?dinger方程的几种差分格式及比较[J].华侨大学学报(自然科学版),2024,45(1):108-120.[doi:10.11830/ISSN.1000-5013.202306029]
　LIN Zhoujin,WANG Jialing,HUO Yuan.Several Difference Schemes and Comparisons for Klein-Gordon-Schr?dinger Equation[J].Journal of Huaqiao University(Natural Science),2024,45(1):108-120.[doi:10.11830/ISSN.1000-5013.202306029]
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Klein-Gordon-Schr?dinger方程的几种差分格式及比较()
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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1期
页码:
108-120
栏目:
出版日期:
2024-01-11

文章信息/Info

Title:
Several Difference Schemes and Comparisons for Klein-Gordon-Schr?dinger Equation
文章编号:
1000-5013(2024)01-0108-13
作者:
林周瑾;  汪佳玲;  霍昱安
南京信息工程大学 数学与统计学院, 江苏 南京 210044
Author(s):
LIN Zhoujin;  WANG Jialing;  HUO Yu’an
School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China
关键词:
Klein-Gordon-Schr? dinger方程;  向前Euler格式;  Crank-Nicolson格式;  紧差分格式;  电荷守恒;  能量守恒
Keywords:
Klein-Gordon-Schr? dinger equation;  forward Euler scheme;  Crank-Nicolson scheme;  compact difference scheme;  charge conservation;  energy conservation
分类号:
O241.82
DOI:
10.11830/ISSN.1000-5013.202306029
文献标志码:
A
摘要:
探究在特定的初值和边界条件下一维Klein-Gordon-Schr?dinger方程的几种差分格式并进行比较。利用经典的向前差分算子、中心差分算子、Crank-Nicolson方法和紧差分算子分别为Klein-Gordon-Schr?dinger方程构造向前Euler式、Crank-Nicolson格式及紧差分格式。结果表明:Crank-Nicolson格式及紧差分格式能够精确地保持离散电荷和能量守恒。数值实验验证了理论结果的正确性。
Abstract:
Several difference schemes of one-dimensional Klein-Gordon-Schr?dinger equation under specific initial value and boundary conditions are investigated and contrasted. The classical forward difference operator, central difference operator, Crank-Nicolson method and compact difference operator are used to construct forward Euler scheme, Crank-Nicolson scheme and compact difference scheme respectively. Results show that Crank-Nicolson scheme and the compact difference scheme can accurately conserve the discrete charge and energy conservation. The correctness of the theoretical result has been verified by numerical experiments.

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期: 2023-06-30
通信作者: 汪佳玲(1990-),女,副教授,博士,主要从事微分方程数值解的研究。E-mail:wangjialing@nuist.edu.cn。
基金项目: 国家自然科学基金青年基金资助项目(11801277)
更新日期/Last Update: 2024-01-20