一类求解常微分方程数值解的块方法

A Class of Parallel Algorithms for the Numerical Integration of Ordinary Differential Equations

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的块隐式混合单步方法,这种方法可以在K台处理机上并行进行数值计算,本文对方法的一般性质及收敛性进行了讨论,得知该方法的阶数为2l+1,并且指出当l=1,2时,方法是A-稳定的。最后给出了一个数值例子。

This paper, introduces a class of block implicit: hybrid one-step methods with higher order derivative for the numerical integration of initial value problems in ordinary differential e-quations. By the methods, a block K new values can be obtained simultaneously on K-processors. The derivation of the methods is given and the theorem of convergence is proved. It is shown that there exist the methods of order 2L+1 and they are A-stable for L=1,2. One numerical example is given.