Automatic control and adaptive time-stepping
(2002) In Numerical Algorithms 31(1-4). p.281-310- Abstract
- Adaptive time-stepping is central to the efficient solution of initial value problems in ODEs and DAEs. The error committed in the discretization method primarily depends on the time-step size h, which is varied along the solution in order to minimize the computational effort subject to a prescribed accuracy requirement. This paper reviews the recent advances in developing local adaptivity algorithms based on well established techniques from linear feedback control theory, which is introduced in a numerical context. Replacing earlier heuristics, this systematic approach results in a more consistent and robust performance. The dynamic behaviour of the discretization method together with the controller is analyzed. We also review some basic... (More)
- Adaptive time-stepping is central to the efficient solution of initial value problems in ODEs and DAEs. The error committed in the discretization method primarily depends on the time-step size h, which is varied along the solution in order to minimize the computational effort subject to a prescribed accuracy requirement. This paper reviews the recent advances in developing local adaptivity algorithms based on well established techniques from linear feedback control theory, which is introduced in a numerical context. Replacing earlier heuristics, this systematic approach results in a more consistent and robust performance. The dynamic behaviour of the discretization method together with the controller is analyzed. We also review some basic techniques for the coordination of nonlinear equation solvers with the primary stepsize controller in implicit time-stepping methods. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/323359
- author
- Söderlind, Gustaf LU
- organization
- publishing date
- 2002
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- control theory, ordinary differential equations, adaptivity, error, control, stepsize control
- in
- Numerical Algorithms
- volume
- 31
- issue
- 1-4
- pages
- 281 - 310
- publisher
- Springer
- external identifiers
-
- wos:000179313300019
- scopus:0036441379
- ISSN
- 1572-9265
- DOI
- 10.1023/A:1021160023092
- 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
- 41378d55-ee2b-4139-af52-f5811cc93404 (old id 323359)
- date added to LUP
- 2016-04-01 12:11:21
- date last changed
- 2022-04-29 01:45:13
@article{41378d55-ee2b-4139-af52-f5811cc93404,
abstract = {{Adaptive time-stepping is central to the efficient solution of initial value problems in ODEs and DAEs. The error committed in the discretization method primarily depends on the time-step size h, which is varied along the solution in order to minimize the computational effort subject to a prescribed accuracy requirement. This paper reviews the recent advances in developing local adaptivity algorithms based on well established techniques from linear feedback control theory, which is introduced in a numerical context. Replacing earlier heuristics, this systematic approach results in a more consistent and robust performance. The dynamic behaviour of the discretization method together with the controller is analyzed. We also review some basic techniques for the coordination of nonlinear equation solvers with the primary stepsize controller in implicit time-stepping methods.}},
author = {{Söderlind, Gustaf}},
issn = {{1572-9265}},
keywords = {{control theory; ordinary differential equations; adaptivity; error; control; stepsize control}},
language = {{eng}},
number = {{1-4}},
pages = {{281--310}},
publisher = {{Springer}},
series = {{Numerical Algorithms}},
title = {{Automatic control and adaptive time-stepping}},
url = {{http://dx.doi.org/10.1023/A:1021160023092}},
doi = {{10.1023/A:1021160023092}},
volume = {{31}},
year = {{2002}},
}