Numerical analysis report

dc.contributor.author	Higham, Desmond J.	en
dc.contributor.author	Φαμέλης, Ιωάννης Θ.	el
dc.date.accessioned	2014-12-24T11:59:44Z
dc.date.available	2014-12-24T11:59:44Z
dc.date.issued	2014-12-24
dc.identifier.uri	http://hdl.handle.net/11400/3158
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	University of Dundee	en
dc.subject	Computer science--Mathematics--Congresses
dc.subject	Soft computing
dc.subject	Αλγόριθμοι
dc.subject	Runge-Kutta method
dc.subject	error control
dc.subject	Fixed point theory--Congresses
dc.subject	delay
dc.subject	Μαθηματικά
dc.subject	Πληροφορική
dc.title	Numerical analysis report	en
heal.type	conferenceItem
heal.secondaryTitle	stability of adaptive algoritms for delay differential equation	el
heal.classification	Computer science
heal.classification	Computer programming
heal.classification	Πληροφορική
heal.classification	Προγραμματισμός
heal.classificationURI	http://data.seab.gr/concepts/77de68daecd823babbb58edb1c8e14d7106e83bb
heal.classificationURI	http://skos.um.es/unescothes/C00749
heal.classificationURI	N/A-Πληροφορική
heal.classificationURI	N/A-Προγραμματισμός
heal.keywordURI	http://id.loc.gov/authorities/subjects/sh2008101221
heal.keywordURI	http://id.loc.gov/authorities/subjects/sh96004789
heal.keywordURI	http://id.loc.gov/authorities/subjects/sh2009124398
heal.language	en
heal.access	campus
heal.recordProvider	ΤΕΙ Αθήνας, Σχολή Τεχνολογικών Εφαρμογών, Τμήμα Μηχανικών Πληροφορικής	el
heal.publicationDate	1992-12
heal.bibliographicCitation	Higham, D. J. & Famelis, I.TH. (1992) Numerical analysis report:stability of adaptive algoritms for delay differential equation. December 1992. Dundee:University of Dundee	el
heal.abstract	This work examines the performance of explicit, adaptive, Runge-Kutta based algorithms for solving delay differential equations. The results of Hall [ACM Trans. Math. Soft. 11 (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 oither 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. Further, 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 that guarantees the existence of equilibrium states for a large class of algorithms.	el
heal.publisher	University of Dundee	en
heal.fullTextAvailability	true
heal.conferenceName	Numerical analysis report:stability of adaptive algoritms for delay differential equation	en
heal.conferenceItemType	full paper