On the relation between stability and contractivity

This paper concerns the rate of growth of numerical approximations obtained by one-step methods for solving linear stiff initial value problems. For some of these methods weak stability with respect to arbitrary norms is shown to be equivalent to contractivity. This kind of stability is also proved to entail a barrierp1 for the order of accuracyp within a broad class of methods, including general Runge-Kutta methods withm1 stages.Dedicated to Professor Germund Dahlquist on the occasion of his sixtieth birthday.