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Sliced-Time Computations with Re-scaling for Blowing-Up Solutions to Initial Value Differential Equations
Lebanese University, Beirut, Lebanon.
2005 (English)In: Computational Science – ICCS 2005 / [ed] Sunderam, Vaidy S.; van Albada, Geert Dick; Sloot, Peter M. A.; Dongarra, Jack J., Springer Berlin/Heidelberg, 2005, p. 58-65Conference paper, Published paper (Refereed)
Abstract [en]

In this paper, we present a new approach to simulate time-dependent initial value differential equations which solutions have a common property of blowing-up in a finite time. For that purpose, we introduce the concept of “sliced-time computations”, whereby, a sequence of time intervals (slices) {[Tn − 1, Tn]| n ≥ 1} is defined on the basis of a change of variables (re-scaling), allowing the generation of computational models that share symbolically or numerically “similarity” criteria. One of these properties is to impose that the re-scaled solution computed on each slice do not exceed a well-defined cut-off value (or threshold) S. In this work we provide fundamental elements of the method, illustrated on a scalar ordinary differential equation y′ = f(y) where f(y) verifies $\int_0^\infty {f(y)dy} < \infty$. Numerical results on various ordinary and partial differential equations are available in [7], some of which will be presented in this paper.

Place, publisher, year, edition, pages
Springer Berlin/Heidelberg, 2005. p. 58-65
Series
Lecture Notes in Computer Science, ISSN 0302-9743, E-ISSN 1611-3349 ; 3514
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:du-30071DOI: 10.1007/11428831_8ISBN: 978-3-540-32111-8 (electronic)ISBN: 978-3-540-26032-5 (print)OAI: oai:DiVA.org:du-30071DiVA, id: diva2:1316715
Conference
ICCS 2005, 5th International Conference, Atlanta, GA, USA, May 22-25, 2005
Available from: 2019-05-20 Created: 2019-05-20 Last updated: 2019-05-20Bibliographically approved

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Cortas Nordlander, Maria

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CiteExportLink to record
Permanent link

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Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • chicago-author-date
  • chicago-note-bibliography
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf