Hence for sufficiently small and we may conclude that the interval of absolute stability has the form .

Moreover, if the three-stage method has order three, then we have

A plot of this function against reveals that whenever . Since there are infinitely many such three-stage Runge-Kutta methods of order three, we conclude that all such methods have as the interval of absolute stability. Similarly, we can show that is the interval of absolute stability of all two-stage Runge-Kutta methods and is the interval of absolute stability of the classical fourth order Runge-Kutta method.