Equilibrium states of adaptive algorithms for delay differential equations

dc.contributor.author	Higham, Desmond J.	en
dc.contributor.author	Φαμέλης, Ιωάννης Θ.	el
dc.date.accessioned	2015-02-13T15:38:17Z
dc.date.available	2015-02-13T15:38:17Z
dc.date.issued	2015-02-13
dc.identifier.uri	http://hdl.handle.net/11400/6151
dc.rights	Αναφορά Δημιουργού-Μη Εμπορική Χρήση-Όχι Παράγωγα Έργα 3.0 Ηνωμένες Πολιτείες	*
dc.rights.uri	http://creativecommons.org/licenses/by-nc-nd/3.0/us/	*
dc.source	http://www.elsevier.com	en
dc.subject	Delay
dc.subject	Fixed point theory
dc.subject	Καθυστέρηση
dc.subject	Σταθερό σημείο
dc.title	Equilibrium states of adaptive algorithms for delay differential equations	en
heal.type	journalArticle
heal.classification	Electronics
heal.classification	Ηλεκτρονική
heal.classification	Applied mathematics
heal.classification	Εφαρμοσμένα μαθηματικά
heal.classificationURI	http://zbw.eu/stw/descriptor/10455-2
heal.classificationURI	N/A-Ηλεκτρονική
heal.classificationURI	http://id.loc.gov/authorities/subjects/sh93002523
heal.classificationURI	N/A-Εφαρμοσμένα μαθηματικά
heal.keywordURI	http://id.loc.gov/authorities/subjects/sh85048934
heal.identifier.secondary	doi:10.1016/0377-0427(93)E0268-Q
heal.language	en
heal.access	campus
heal.recordProvider	Τ.Ε.Ι. Αθήνας. Σχολή Τεχνολογικών Εφαρμογών. Τμήμα Ηλεκτρονικών Μηχανικών Τ.Ε.	el
heal.publicationDate	1995
heal.bibliographicCitation	Higham, D. & Famelis, I.TH (1995) Equilibrium states of adaptive algorithms for delay differential equations. "Journal of Computational and Applied Mathematics". 58 (2). p. 151-169. Elsevier Science Ltd: 1995. Available from: http://www.sciencedirect.com [Accessed 13-02-2015]	en
heal.abstract	This work examines the performance of explicit, adaptive, Runge-Kutta based algorithms for solving delay differential equations. The results of Hall (1985) for ordinary differential equation (ODE) solvers are extended by adding a constant-delay term to the test equation. It is shown that by regarding an algorithm as a discrete nonlinear map, fixed points or equilibrium states can be identified and their stability can be determined numerically. Specific results are derived for a low order Runge-Kutta pair coupled with either a linear or cubic interpolant. The qualitative performance is shown to depend upon the interpolation process, in addition to the ODE formula and the error control mechanism. Furthermore, and in contrast to the case for standard ODEs, it is found that the parameters in the test equation also influence the behaviour. This phenomenon has important implications for the design of robust algorithms. The choice of error tolerance, however, is shown not to affect the stability of the equilibrium states. Numerical tests are used to illustrate the analysis. Finally, a general result is given which guarantees the existence of equilibrium states for a large class of algorithms.	en
heal.publisher	Elsevier Science Ltd	en
heal.journalName	Journal of Computational and Applied Mathematics	en
heal.journalType	peer-reviewed
heal.fullTextAvailability	true