具有高阶导数的块隐式混合单步并行计算方法

Parallel Block Implicit Hybrid One-Step Methods with Higher Order Derivative

该文讨论了一类求解常微分方程初值问题的具有高阶导数项的块隐式混合单步并行计算方法．这种算法的块数为k，价数为（l十1）（d＋1），可以在s台处理机上进行并行计算，其中l是高阶导数的阶数，k＝s·d.该文讨论了方法的一般性质及数值稳定性，最后给数值例子。

In this paper, a class of K-block implicit hybrid methods with higher orderderivative 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 (1 + 1 ) (d + 1 ) exist, where K = s· d. The theorems of convergence and numerical stability are presented, and one numerical experiment is also given.