Rosenbrock-type `Peer' two-step methods

Abstract

It is well-known that one-step Rosenbrock methods may suffer from order reduction for very stiff problems. By considering two-step methods we construct $s$-stage methods where all stage values have stage order $s-1$. The proposed class of methods is stable in the sense of zero-stability for arbitrary stepsize sequences. Furthermore there exist L($alpha$)-stable methods with large $alpha$ for $s=4ldots8$. Using the concept of emph{effective order} we derive methods having order $s$ for constant stepsizes. Numerical experiments show an efficiency superior to RODAS for more stringent tolerances.