Schrdinger型方程的显式差分格式

Exiplicit Difference schemes for Schrodinger Type Equation

本文讨论了 Schrdinger 型方程 u_t=iu_(xx)的显式差分格式。跳点格式(2.7)-(2.8),格式(2.10)与(2.11)是本文的结果。格式(2.7)-(2.8)恒稳定,格式(2.10)与(2.11)的稳定条件分别是 R≤1,R≤2(R=△t/△x^2),均比[1]的 R≤1/2有大的改进。

A number of explicit difference schemes for Schrodinger type equ- ation u_t=iu_(xx) are discussed.The Hopscotch scheme (2.7)-(2.8) and the schemes (2.10),(2.11) are worked out by us.We have proved the sch- emes (2.7)-(2.8) to be always stable and the stability conditions of the schemes (2.10) and (2.11) are R≤1 and R≤2,respectively.These res- ults are much better than the condition R≤0.5 in the literature[1].