Characterization of allA-stable methods of order 2m-4

The characterization ofA-stable methods is often considered as a very difficult task (see e.g. 1]). In recent years, simple proofs have been found for methods of orderp2m-2 (see 2], 3], 7]). In this paper, we characterize theA-acceptable approximations of orderp 2m-4 and apply the result to 12-parameter families of implicit Runge-Kutta methods.