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

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.