Adaptive Time-Stepping and Computational Stability
(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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/633841
- author
- Söderlind, Gustaf LU and Wang, Lina LU
- organization
- publishing date
- 2006
- 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
- 2024-09-14 14:06:47
@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}}, 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}}, }