A stability property of \(A\)-stable natural Runge-Kutta methods for systems of delay differential equations (Q1334998)

This article investigates the asymptotic stability of implicit Runge- Kutta methods applied to systems of the form \(u'(t)=Lu(t)+Mu(t-\tau)\) with constant delay \(\tau\). Under natural assumptions on the problem asymptotic stability is obtained, if \(\tau\) is an integer multiple of the stepsize, if previous stage values are used for the approximation of \(u(t-\tau)\) and if the method is \(A\)-stable.