一类块隐式混合单步并行计算方法

Parallel Block Implicit Hybrid One-Step Methods

本文讨论了一类解常微分方程初值问题的块隐式混合单步并行算法，这种算法的块数为K，精度阶为2d＋2，可在S台处理机上进行并行计算，其中K＝S·d．本文讨论了方法的一般性质，给出了方法的稳定性定理，最后给出了一个数值例子．

In this paper, a class of K-block implicit hybrid methods for the numerical integration of initial value problems in ordinary differential equations are derived. By the methods, a block of K new values can be obtained simultaneously on s-processors. It is shown that the method of order 2d + 2 exists, where k = s. d. The theorems of convergence and numerical stability are presented, and one numerical experiment is also given.