常微分方程组中典型环节的数值处理

The Numerical Treatment for a Typical Link in ODEs

由控制系统形成的大型常微分方程组中,经常出现一些典型环节,例如惯性环节、振荡环节等,它们一般具有很小的时间常数,因而使系统呈现高度的刚性,任何类型的数值方法处理此类都会引起巨大的困难。本文给出了一种数值方法,它可以大大减轻问题的刚性程度,方法的优越性已被数值实验所证明。

A large scale ODEs, arising from control system, always have some typical links, e.g. Inertial link and oscillation link, which have very small time constant and the system is very stiff. Any kind numerical method for this system will meet serious difficulty. In this paper a special treatment is given, which can relieve the stiffness of the system enormously. The efficiency of this treatment is proved by numerical test.