On implicit Runge-Kutta methods with high stage order

It is well known that high stage order is a desirable property for implicit Runge-Kutta methods. In this paper it is shown that it is always possible to construct ans-stage IRK method with a given stability function and stage orders−1 if the stability function is an approximation to the exponential function of at least orders. It is further indicated how to construct such methods as well as in which cases the constructed methods will be stiffly accurate.