Rosenbrock-type `Peer' two-step methods

H. Podhaisky, R. Weiner, B.A. Schmitt


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.

Stiff ODEs, Rosenbrock methods, general linear methods, peer method

Math Review Classification
Primary 65L05

Last Updated
1 Dec 2003

13 pages

This article is available in: