Time-step selection algorithms: Adaptivity, control, and signal processing

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Abstract

The efficiency of numerical time-stepping methods for dynamical systems is greatly enhanced by automatic time step variation. In this paper we present and discuss three different approaches to step size selection: (i) control theory (to keep the error in check); (ii) signal processing (to produce smooth step size sequences and improve computational stability); and (iii) adaptivity, in the sense that the time step should be covariant or contravariant with some prescribed function of the dynamical system's solution. Examples are used to demonstrate the different advantages in different applications. The main ideas are further developed to approach some open problems that are subject to special requirements. (c) 2005 IMACS. Published by Elsevier B.V. All rights reserved.
Original languageEnglish
Title of host publicationApplied Numerical Mathematics
PublisherElsevier
Pages488-502
Volume56
DOIs
Publication statusPublished - 2006

Publication series

Name
Number3-4
Volume56
ISSN (Print)0168-9274

Bibliographical note

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

  • reversible
  • step size selection
  • systems
  • adaptivity
  • signal processing
  • control

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