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Time-step selection algorithms: Adaptivity, control, and signal processing

Söderlind, Gustaf LU (2006) 56(3-4). p.488-502
Abstract
The efficiency of numerical time-stepping methods for dynamical systems is greatly enhanced by automatic time step variation. In this paper we present and discuss three different approaches to step size selection: (i) control theory (to keep the error in check); (ii) signal processing (to produce smooth step size sequences and improve computational stability); and (iii) adaptivity, in the sense that the time step should be covariant or contravariant with some prescribed function of the dynamical system's solution. Examples are used to demonstrate the different advantages in different applications. The main ideas are further developed to approach some open problems that are subject to special requirements. (c) 2005 IMACS. Published by... (More)
The efficiency of numerical time-stepping methods for dynamical systems is greatly enhanced by automatic time step variation. In this paper we present and discuss three different approaches to step size selection: (i) control theory (to keep the error in check); (ii) signal processing (to produce smooth step size sequences and improve computational stability); and (iii) adaptivity, in the sense that the time step should be covariant or contravariant with some prescribed function of the dynamical system's solution. Examples are used to demonstrate the different advantages in different applications. The main ideas are further developed to approach some open problems that are subject to special requirements. (c) 2005 IMACS. Published by Elsevier B.V. All rights reserved. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
keywords
reversible, step size selection, systems, adaptivity, signal processing, control
host publication
Applied Numerical Mathematics
volume
56
issue
3-4
pages
488 - 502
publisher
Elsevier
external identifiers
  • wos:000236425700018
  • scopus:33644628402
ISSN
0168-9274
DOI
10.1016/j.apnum.2005.04.026
language
English
LU publication?
yes
id
7ffaee31-c609-4d6b-bf04-2fd06bcdb7de (old id 414938)
date added to LUP
2007-10-19 12:24:00
date last changed
2019-09-04 02:52:19
@inproceedings{7ffaee31-c609-4d6b-bf04-2fd06bcdb7de,
  abstract     = {The efficiency of numerical time-stepping methods for dynamical systems is greatly enhanced by automatic time step variation. In this paper we present and discuss three different approaches to step size selection: (i) control theory (to keep the error in check); (ii) signal processing (to produce smooth step size sequences and improve computational stability); and (iii) adaptivity, in the sense that the time step should be covariant or contravariant with some prescribed function of the dynamical system's solution. Examples are used to demonstrate the different advantages in different applications. The main ideas are further developed to approach some open problems that are subject to special requirements. (c) 2005 IMACS. Published by Elsevier B.V. All rights reserved.},
  author       = {Söderlind, Gustaf},
  issn         = {0168-9274},
  keyword      = {reversible,step size selection,systems,adaptivity,signal processing,control},
  language     = {eng},
  number       = {3-4},
  pages        = {488--502},
  publisher    = {Elsevier},
  title        = {Time-step selection algorithms: Adaptivity, control, and signal processing},
  url          = {http://dx.doi.org/10.1016/j.apnum.2005.04.026},
  volume       = {56},
  year         = {2006},
}