Time-step selection algorithms: Adaptivity, control, and signal processing
(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:
https://lup.lub.lu.se/record/414938
- author
- Söderlind, Gustaf LU
- organization
- publishing date
- 2006
- 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
- additional info
- The information about affiliations in this record was updated in December 2015. The record was previously connected to the following departments: Numerical Analysis (011015004)
- id
- 7ffaee31-c609-4d6b-bf04-2fd06bcdb7de (old id 414938)
- date added to LUP
- 2016-04-01 16:00:30
- date last changed
- 2022-04-22 18:59:23
@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}},
booktitle = {{Applied Numerical Mathematics}},
issn = {{0168-9274}},
keywords = {{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}},
doi = {{10.1016/j.apnum.2005.04.026}},
volume = {{56}},
year = {{2006}},
}