Stability Criteria for Implicit Runge–Kutta Methods

A comparison is made of two stability criteria. The first is a modification to nonautonomous problems of A-stability and the second is a similar modification of B-stability. It is shown that under certain mild conditions these two concepts are equivalent. A number of examples are given of methods that satisfy these new stability properties and it is also shown that the growth of errors can be estimated by an extension of this theory.