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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
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
id
1395eea8-af07-41b7-925e-25a2a2c2780c (old id 633841)
date added to LUP
2007-12-10 11:20:02
date last changed
2019-09-11 02:37:47
@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},
  keyword      = {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},
  volume       = {185},
  year         = {2006},
}