Klein-Gordon-Schrodinger方程的几种差分格式及比较  

Several Difference Schemes and Comparisons for Klein-Gordon-Schrodinger Equation

作　　者：林周瑾 汪佳玲 霍昱安 LIN Zhoujin;WANG Jialing;HUO Yu′an(School of Mathematics and Statistics,Nanjing University of Information Science and Technology,Nanjing 210044,China)

机构地区：[1]南京信息工程大学数学与统计学院,江苏南京210044

出　　处：《华侨大学学报（自然科学版）》2024年第1期108-120,共13页Journal of Huaqiao University(Natural Science)

基　　金：国家自然科学基金青年基金资助项目(11801277)。

摘　　要：探究在特定的初值和边界条件下一维Klein-Gordon-Schrodinger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-Schrodinger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。Several difference schemes of one-dimensional Klein-Gordon-Schrodinger 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.

关 键 词：Klein-Gordon-Schrodinger方程 向前Euler格式 CRANK-NICOLSON格式 紧差分格式 电荷守恒 能量守恒 

分 类 号：O241.82[理学—计算数学]