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Adaptive Time-Stepping and Computational Stability

Söderlind, Gustaf LU and Wang, Lina LU (2006) In Journal of Computational and Applied Mathematics 185. p.225-243
Abstract
We investigate the effects of adaptive time-stepping and other algorithmic strategies on the computational stability of ODE codes. We show that carefully designed adaptive algorithms have a most significant impact on computational stability and reliability. A series of computational experiments with the standard implementation of Dassl and a modified version, including stepsize control based on digital filters, is used to demonstrate that relatively small algorithmic changes are able to extract a vastly better computational stability at no extra expense. The inherent performance and stability of Dassl are therefore much greater than the standard implementation seems to suggest.
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author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Computational stability stepsize control adaptive time-stepping PI control digital filters Dassl mathematical software algorithm analysis
in
Journal of Computational and Applied Mathematics
volume
185
pages
225 - 243
publisher
Elsevier
external identifiers
  • wos:000232549600005
  • scopus:25144512384
ISSN
0377-0427
DOI
10.1016/j.cam.2005.03.008
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
1395eea8-af07-41b7-925e-25a2a2c2780c (old id 633841)
date added to LUP
2016-04-01 16:22:51
date last changed
2022-04-22 21:35:44
@article{1395eea8-af07-41b7-925e-25a2a2c2780c,
  abstract     = {{We investigate the effects of adaptive time-stepping and other algorithmic strategies on the computational stability of ODE codes. We show that carefully designed adaptive algorithms have a most significant impact on computational stability and reliability. A series of computational experiments with the standard implementation of Dassl and a modified version, including stepsize control based on digital filters, is used to demonstrate that relatively small algorithmic changes are able to extract a vastly better computational stability at no extra expense. The inherent performance and stability of Dassl are therefore much greater than the standard implementation seems to suggest.}},
  author       = {{Söderlind, Gustaf and Wang, Lina}},
  issn         = {{0377-0427}},
  keywords     = {{Computational stability
stepsize control
adaptive time-stepping
PI control 
digital filters
Dassl
mathematical software
algorithm analysis}},
  language     = {{eng}},
  pages        = {{225--243}},
  publisher    = {{Elsevier}},
  series       = {{Journal of Computational and Applied Mathematics}},
  title        = {{Adaptive Time-Stepping and Computational Stability}},
  url          = {{http://dx.doi.org/10.1016/j.cam.2005.03.008}},
  doi          = {{10.1016/j.cam.2005.03.008}},
  volume       = {{185}},
  year         = {{2006}},
}