线性Schrdinger方程的两个时间分裂差分格式

Two time-splitting difference schemes for linear Schrdinger equation

针对物理问题中常常需要求解一类线性Schrdinger方程的问题,本文中提出两个构造简单、精度高、便于计算的时间分裂差分格式.用方程的平面波解证明两个格式的精度都为O(τ2+h2),并用线性化的分析方法证明两个格式的稳定性和收敛性.数值实验表明,在计算量较大的情况下,要保证相当的精度,提出的两个格式可以有效地节省计算时间.

To solve a linear Schrdinger equation in the physical problems,two time-splitting difference schemes were presented which were simple structure,high precision and computational efficiency.The truncation error of the schemes was O(τ2+h2)which was obtained by the plane wave solution.The stability and convergence of the two schemes were obtained by the linearized method.The numerical experiments showed that these schemes had the higher accuracy and shorter time in case of large amount of calculation.