并行计算的带有高阶导数的块隐式单步法

PARALLEL ALGORITHMS OF BLOCK IMPLICIT HYBRID ONE—STEP METHODS WITH HIGHER ORDER DERIVATIVE

本文讨论了一类并行计算常微分方程初值问题的带有高阶导数项的块隐式单步方法,这种方法可以在 K 台处理机上并行进行数值处理.本文对方法的一般性质及方法收敛的条件进行了讨沦,得到方法的阶数为2l,并且指出适 l≤4时方法是 A-稳定的,最后给出了一个数值例子.

In this paper,a class of block implicit one-step methods with higher orderderivative for the numerical integration of initial value problems in ordinarydifferential equations is derived.By the methods,a block K new values can beobtained simultaneously on K-processors.It is shown that,when K≥2L,themethods of order 2L exist,and methods are A-ttable for L=1,2,3,4.One nu-merical example is given.