CONTROL-THEORETIC TECHNIQUES FOR STEPSIZE SELECTION IN IMPLICIT RUNGE-KUTTA METHODS

Authors
Citation
K. Gustafsson, CONTROL-THEORETIC TECHNIQUES FOR STEPSIZE SELECTION IN IMPLICIT RUNGE-KUTTA METHODS, ACM transactions on mathematical software, 20(4), 1994, pp. 496-517
Citations number
15
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Computer Sciences",Mathematics
ISSN journal
0098-3500
Volume
20
Issue
4
Year of publication
1994
Pages
496 - 517
Database
ISI
SICI code
0098-3500(1994)20:4<496:CTFSSI>2.0.ZU;2-C
Abstract
The problem of stepsize selection in implicit Runge-Kutta schemes is a nalyzed from a feedback control point of view. This approach leads to a better understanding of the relation between stepsize and error. A n ew dynamical model describing this relation is derived. The model is u sed as a basis for a new stepsize selection rule. This rule achieves b etter error control at little extra expense. The properties of the new model and the improved performance of the new error control are demon strated using both analysis and numerical examples.