两步Runge-Kutta方法求解延迟微分方程的GPL-稳定性(英文)

The GPL-stability of the two-step Runge-Kutta methods for delay differential systems

主要研究了两步Runge-Kutta方法求解延迟系统方程的稳定性.首先讨论了两步Runge-Kutta方法求解常微分方程数值解的L-稳定性,给出L-稳定性的充分性条件,然后讨论延迟微分方程的GPL-稳定性,得到延迟微分方程是GPL-稳定的充要条件是它是L-稳定的.

This paper deals with the numerical stability of the two-step Runge-Kutta methods for delay differential equations（DDEs）.The conditions of L-stability of two-step Runge-Kutta methods for ordinary differential equation（ODE）are discussed,It is shown that two-step Runge-Kutta mthods is GPL-stable for DDEs if and only if the corresponding methods for ODE is L-stable.