This is a joint work with Ernst Hairer

In this paper, asymptotic stability properties of implicit Runge Kutta methods for delay differential equations are considered with respect to the test equation y'(t) = a*y(t) + b*y(t-1) with a, b in (R) C.

In particular, we prove that symmetric methods cannot be unconditionally stable with respect to the considered test equation, while many of them are stable on problems where a in R and b in C. Furthermore, we prove that Radau-IIA methods are stable on the subclass of equations where a = alpha + i*gamma with alpha, gamma in R, gamma sufficiently small, and b in C.