Multi-step zero approximations for stepsize control

Authors
Butcher, JC Chan, TMH
Citation
Jc. Butcher et Tmh. Chan, Multi-step zero approximations for stepsize control, APPL NUM M, 34(2-3), 2000, pp. 167-177
Citations number
10
Categorie Soggetti
Mathematics
Journal title
APPLIED NUMERICAL MATHEMATICS
ISSN journal
01689274 → ACNP
Volume
34
Issue
2-3
Year of publication
2000
Pages
167 - 177
Database
ISI
SICI code
0168-9274(200007)34:2-3<167:MZAFSC>2.0.ZU;2-1
Abstract
The standard techniques for stepsize control for Runge-Kutta methods, based on embedding, typically use an error estimate which not only fails to be a symptotically correct but is even of the wrong order. We will refer to this sort of estimate as a "one-step zero approximation". Our aim in this paper is to consider also m-step error approximations for m greater than or equa l to 2. (C) 2000 IMACS. Published by Elsevier Science B.V. All rights reser ved.