摘要
[1]给出了解 Schrodinger型方程 u_t=iu_(xx)的两个三层显格式,其稳定条件分别为.r≤1和r≤1.2071.本文对更一般的N(≥1是自然数)维方程 ?u/?t=i sum from p=1 to N (?~2u/?x_p^2) (1)建立了一个三层显格式,并证明它是绝对稳定的. 为了建立差分格式,取时间步长τ=△t,空间步长h=△x_1=△x_2=…=△x_N;并记u_(j_1j_2…j_N)~k=u(j_1△x_1,J_2△x_2,…,j_N△x_N,k△_t).
In [1], two three-level explicit schemes for equations of the Schrodinger typeu_t=iu_(xx) are considered. The stability conditions of those schemes are r=τ/h^2≤1and r≤1.2071 respectively. In this paper, we give a three-level explicit scheme with absolute stability forsolving u/t=i∑from p=1 to n u/x_p^2, where N is a positive integer.
出处
《计算数学》
CSCD
北大核心
1990年第2期214-215,共2页
Mathematica Numerica Sinica
