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Computational Stability and Adaptive Strategies - An Experimental Study of ODE Software

Wang, Lina LU (2003)
Abstract
The algorithmic content of adaptive ODE/DAE software is dominated by a considerable amount of control structures, support algorithms and logic. The control logic has been largely heuristic and lacking support by analysis. In this thesis we study adaptive time-stepping based on control theory, combined with other carefully selected control strategies. Thus we argue that ODE/DAE software can be constructed and analyzed by proven, "standard" scientific techniques instead of heuristics. We show that carefully designed adaptive algorithms have a most significant impact on the reliability and computational stability of ODE/DAE codes. The latter notion implies that minor changes of the computational setup must only lead to small changes in the... (More)
The algorithmic content of adaptive ODE/DAE software is dominated by a considerable amount of control structures, support algorithms and logic. The control logic has been largely heuristic and lacking support by analysis. In this thesis we study adaptive time-stepping based on control theory, combined with other carefully selected control strategies. Thus we argue that ODE/DAE software can be constructed and analyzed by proven, "standard" scientific techniques instead of heuristics. We show that carefully designed adaptive algorithms have a most significant impact on the reliability and computational stability of ODE/DAE codes. The latter notion implies that minor changes of the computational setup must only lead to small changes in the computed result: the software must be computationally well-conditioned.



A series of computational experiments with the standard implementations of DASSL and RADAU5 are compared to results obtained with modified versions of these codes, where the improved strategies build on the theory mentioned above. These include stepsize control based on digital filters. The experiments demonstrate that these "minor" algorithmic changes strongly improve computational stability at no extra computational expense. (Less)
Please use this url to cite or link to this publication:
author
supervisor
opponent
  • Dr. Kvaern√∂, Anne, Trondheim, Norge
organization
publishing date
type
Thesis
publication status
published
subject
keywords
algorithm analysis, Mathematical software, RADAU5, DASSL, digital filters, PI control, adaptive time-stepping, stepsize control, computational stability, test protocol, Computer science, numerical analysis, systems, control, Datalogi, numerisk analys, system, kontroll
pages
130 pages
publisher
Numerical Analysis, Lund University
defense location
E-house E:1406
defense date
2003-06-02 10:15
ISSN
1404-0034
ISBN
91-628-5318-X
language
English
LU publication?
yes
id
e2114144-388a-4f45-85a5-dfd26a721b66 (old id 27608)
date added to LUP
2007-06-08 08:39:40
date last changed
2018-05-29 09:26:54
@phdthesis{e2114144-388a-4f45-85a5-dfd26a721b66,
  abstract     = {The algorithmic content of adaptive ODE/DAE software is dominated by a considerable amount of control structures, support algorithms and logic. The control logic has been largely heuristic and lacking support by analysis. In this thesis we study adaptive time-stepping based on control theory, combined with other carefully selected control strategies. Thus we argue that ODE/DAE software can be constructed and analyzed by proven, "standard" scientific techniques instead of heuristics. We show that carefully designed adaptive algorithms have a most significant impact on the reliability and computational stability of ODE/DAE codes. The latter notion implies that minor changes of the computational setup must only lead to small changes in the computed result: the software must be computationally well-conditioned.<br/><br>
<br/><br>
A series of computational experiments with the standard implementations of DASSL and RADAU5 are compared to results obtained with modified versions of these codes, where the improved strategies build on the theory mentioned above. These include stepsize control based on digital filters. The experiments demonstrate that these "minor" algorithmic changes strongly improve computational stability at no extra computational expense.},
  author       = {Wang, Lina},
  isbn         = {91-628-5318-X},
  issn         = {1404-0034},
  keyword      = {algorithm analysis,Mathematical software,RADAU5,DASSL,digital filters,PI control,adaptive time-stepping,stepsize control,computational stability,test protocol,Computer science,numerical analysis,systems,control,Datalogi,numerisk analys,system,kontroll},
  language     = {eng},
  pages        = {130},
  publisher    = {Numerical Analysis, Lund University},
  school       = {Lund University},
  title        = {Computational Stability and Adaptive Strategies - An Experimental Study of ODE Software},
  year         = {2003},
}