求解隐式差分方程的并行迭代法

本文研究了求解隐式差分方程的并行迭代方法，其基本思想是把隐式差分方程组划分为若干个子方程组来分别同时进行迭代求解。本文给出了构造隐式方程组并行迭代法的一般过程－－分段隐式迭代法，推导论证了它的收敛性，并阐明了它处理子方程组的优越之处。同时，据其本身特点，把它推广到二维情形。为说明此迭代法的有效性，本中针对具体例子给出了数值试验结果。

Parallel iterative algorithms for solving the implicit difference equations

The parallel algorithms for solving the implicit difference equations have been studied in the paper. The basic idea is to divide the system of implicit difference equations into a set of subsystems which can be solved individually in parallel. The segment implicit iterative(SII) algorithm is set up and the convergence theorem on the iteration is proved. And more, we have showed that they have good property. According to the property, this method is extended to the case of the two-space dimensional problem. To show the deficiency of the segment implicit iteration, the paper gives the numerical experiments for examples of the diffusion equation.