Advanced

Evaluating Numerical ODE/DAE Methods, Algorithms and Software

Söderlind, Gustaf LU and Wang, Lina LU (2006) In Journal of Computational and Applied Mathematics 185(2). p.244-260
Abstract
Until recently, the testing of ODE/DAE software has been limited to simple comparisons and benchmarking. The process of developing software from a mathematically specified method is complex: it entails constructing control structures and objectives, selecting iterative methods and termination criteria, choosing norms and many more decisions. Most software constructors have taken a heuristic approach to these design choices, and as a consequence two different implementations of the same method may show significant differences in performance. Yet it is common to try to deduce from software comparisons that one method is better than another. Such conclusions are not warranted, however, unless the testing is carried out under true ceteris... (More)
Until recently, the testing of ODE/DAE software has been limited to simple comparisons and benchmarking. The process of developing software from a mathematically specified method is complex: it entails constructing control structures and objectives, selecting iterative methods and termination criteria, choosing norms and many more decisions. Most software constructors have taken a heuristic approach to these design choices, and as a consequence two different implementations of the same method may show significant differences in performance. Yet it is common to try to deduce from software comparisons that one method is better than another. Such conclusions are not warranted, however, unless the testing is carried out under true ceteris paribus conditions. Moreover, testing is an empirical science and as such requires a formal test protocol; without it conclusions are questionable, invalid or even false.



We argue that ODE/DAE software can be constructed and analyzed by proven, ''standard'' scientific techniques instead of heuristics. The goals are computational stability, reproducibility, and improved software quality. We also focus on different error criteria and norms, and discuss modifications to Daspk and Radau5. Finally, some basic principles of a test protocol are outlined and applied to testing these codes on a variety of problems. (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
Software testing Test protocols Computational stability ODE software DAE software work/precision adaptive time-stepping mathematical software algorithm analysis
in
Journal of Computational and Applied Mathematics
volume
185
issue
2
pages
244 - 260
publisher
Elsevier
external identifiers
  • wos:000232549600006
  • scopus:25144523380
ISSN
0377-0427
DOI
10.1016/j.cam.2005.03.009
language
English
LU publication?
yes
id
1c6013f2-3795-44df-a100-653f34d9cabc (old id 633884)
date added to LUP
2007-12-11 15:35:52
date last changed
2019-03-12 02:46:12
@article{1c6013f2-3795-44df-a100-653f34d9cabc,
  abstract     = {Until recently, the testing of ODE/DAE software has been limited to simple comparisons and benchmarking. The process of developing software from a mathematically specified method is complex: it entails constructing control structures and objectives, selecting iterative methods and termination criteria, choosing norms and many more decisions. Most software constructors have taken a heuristic approach to these design choices, and as a consequence two different implementations of the same method may show significant differences in performance. Yet it is common to try to deduce from software comparisons that one method is better than another. Such conclusions are not warranted, however, unless the testing is carried out under true ceteris paribus conditions. Moreover, testing is an empirical science and as such requires a formal test protocol; without it conclusions are questionable, invalid or even false.<br/><br>
<br/><br>
We argue that ODE/DAE software can be constructed and analyzed by proven, ''standard'' scientific techniques instead of heuristics. The goals are computational stability, reproducibility, and improved software quality. We also focus on different error criteria and norms, and discuss modifications to Daspk and Radau5. Finally, some basic principles of a test protocol are outlined and applied to testing these codes on a variety of problems.},
  author       = {Söderlind, Gustaf and Wang, Lina},
  issn         = {0377-0427},
  keyword      = {Software testing
Test protocols
Computational stability
ODE software
DAE software
work/precision
adaptive time-stepping
mathematical software
algorithm analysis},
  language     = {eng},
  number       = {2},
  pages        = {244--260},
  publisher    = {Elsevier},
  series       = {Journal of Computational and Applied Mathematics},
  title        = {Evaluating Numerical ODE/DAE Methods, Algorithms and Software},
  url          = {http://dx.doi.org/10.1016/j.cam.2005.03.009},
  volume       = {185},
  year         = {2006},
}