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Automatic control and adaptive time-stepping

Söderlind, Gustaf LU (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:
author
organization
publishing date
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
id
41378d55-ee2b-4139-af52-f5811cc93404 (old id 323359)
date added to LUP
2007-11-14 12:59:56
date last changed
2017-06-11 03:45:46
@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},
  keyword      = {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},
  volume       = {31},
  year         = {2002},
}