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

Lina Wang

Research output: ThesisDoctoral Thesis (monograph)

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.

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.
Original languageEnglish
QualificationDoctor
Awarding Institution
  • Mathematics (Faculty of Engineering)
Supervisors/Advisors
  • [unknown], [unknown], Supervisor, External person
Award date2003 Jun 2
Publisher
ISBN (Print)91-628-5318-X
Publication statusPublished - 2003

Bibliographical note

Defence details

Date: 2003-06-02
Time: 10:15
Place: E-house E:1406

External reviewer(s)

Name: Kvaernö, Anne
Title: Dr.
Affiliation: Trondheim, Norge

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The information about affiliations in this record was updated in December 2015.
The record was previously connected to the following departments: Numerical Analysis (011015004)

Subject classification (UKÄ)

  • Mathematics

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

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