多步龙格-库塔方法的τ_1-稳定性

τ_1-stability of multistep Runge-Kutta methods

分析了标量延迟微分方程系统渐近稳定性的不同条件 ,给出了与延迟量τ有关及不依赖于延迟量τ的不同渐近稳定域 .在渐近稳定域与τ有关的条件下 ,对多步龙格 库塔方法的渐近稳定性进行了分析 ,定义了一种新的数值稳定性 ,即τ1 稳定性 ,在不同的条件下 。

This paper dealt with the stability conditions for the solution of delay differential equations, and gained different regions of asymptotic stability being independent or dependent of the value of τ. Under the condition making the stability regions are dependent of τ, the asymptotic stability of multistep Runge-Kutta methods called τ 1-stability, was investigated. It was proved that multistep Runge-Kutta method is stable under different conditions.