两步Runge-Kutta法求解延迟微分方程的GPL_m-稳定性(英文)

GPL_m-stability of Two-Step Runge-Kutta Methods for Delay Differential Equations

讨论了两步Runge-Kutta方法求解延迟微分方程的数值稳定性,分析了求解线性试验方程的两步Runge-Kutta方法的稳定性态。证明了两步Runge-Kutta方法是GPLm-稳定的,当且仅当它求解常微分方程是L-稳定的。

The stability of two-step Runge-Kutta methods for delay differential equations（DDEs） with many delays was dealt with,and the stability for the test equation was analyzed.It is shown that a two-step Runge-Kutta method is GPLm-stable if and only if the corresponding method for ordinary differential equation is L-stable.