Rosenbrock-type ‘Peer’ two-step methods Original Research Article

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−1s−1. The proposed class of methods is stable in the sense of zero-stability for arbitrary stepsize sequences. Furthermore there exist L(α)-stable methods with large α for s=4,…,8s=4,…,8. Using the concept of effective order we derive methods having order s for constant stepsizes. Numerical experiments show an efficiency superior to RODAS for more stringent tolerances.