On modified runge-kutta trees and methods

dc.contributor.author	Τσίτουρας, Χαράλαμπος	el
dc.contributor.author	Φαμέλης, Ιωάννης Θ.	el
dc.contributor.author	Σίμος, Θεόδωρος	el
dc.date.accessioned	2015-02-14T11:06:12Z
dc.date.available	2015-02-14T11:06:12Z
dc.date.issued	2015-02-14
dc.identifier.uri	http://hdl.handle.net/11400/6223
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	Integer partitions
dc.subject	Initial value problems
dc.subject	Ακέραιος χωρίσματα
dc.subject	Προβλήματα αρχικών τιμών
dc.title	On modified runge-kutta trees and methods	en
heal.type	journalArticle
heal.classification	Mathematics
heal.classification	Mathematical physics
heal.classification	Μαθηματικά
heal.classification	Εφαρμοσμένα μαθηματικά
heal.classificationURI	http://id.loc.gov/authorities/subjects/sh85082139
heal.classificationURI	http://id.loc.gov/authorities/subjects/sh85082129
heal.classificationURI	N/A-Μαθηματικά
heal.classificationURI	N/A-Εφαρμοσμένα μαθηματικά
heal.keywordURI	http://id.loc.gov/authorities/subjects/sh85066415
heal.identifier.secondary	doi:10.1016/j.camwa.2011.06.058
heal.language	en
heal.access	campus
heal.recordProvider	Τ.Ε.Ι. Αθήνας. Σχολή Τεχνολογικών Εφαρμογών. Τμήμα Ηλεκτρονικών Μηχανικών Τ.Ε.	el
heal.publicationDate	2011
heal.bibliographicCitation	Tsitouras, Ch., Famelis, I. and Simos, F. (August 2011). On modified runge-kutta trees and methods. Computers and Mathematics with Applications. 62(4). pp. 2101–2111. Elsevier Science Ltd: 2011. Available from: http://www.sciencedirect.com [Accessed 23/07/2011]	en
heal.abstract	Modified Runge–Kutta (mRK) methods can have interesting properties as their coefficients may depend on the step length. By a simple perturbation of very few coefficients we may produce various function-fitted methods and avoid the overload of evaluating all the coefficients in every step. It is known that, for Runge–Kutta methods, each order condition corresponds to a rooted tree. When we expand this theory to the case of mRK methods, some of the rooted trees produce additional trees, called mRK rooted trees, and so additional conditions of order. In this work we present the relative theory including a theorem for the generating function of these additional mRK trees and explain the procedure to determine the extra algebraic equations of condition generated for a major subcategory of these methods. Moreover, efficient symbolic codes are provided for the enumeration of the trees and the generation of the additional order conditions. Finally, phase-lag and phase-fitted properties are analyzed for this case and specific phase-fitted pairs of orders 8(6) and 6(5) are presented and tested.	en
heal.publisher	Elsevier Science Ltd	en
heal.journalName	Computers & Mathematics with Applications	en
heal.journalType	peer-reviewed
heal.fullTextAvailability	true