Some stability results for explicit Runge-Kutta methods

The theory of positive real functions is used to provide bounds for the largest possible disk to be inscribed in the stability region of an explicit Runge-Kutta method. In particular, we show that the closed disk |+r| r can be contained in the stability region of an explicitm-stage Runge-Kutta method of order two if and only ifr m – 1.