A general family of explicit Runge-Kutta pairs of orders 6(5)

Papakostas, SN; Tsitouras, Ch; Papageorgiou, G

dc.contributor.author	Papakostas, SN	en
dc.contributor.author	Tsitouras, Ch	en
dc.contributor.author	Papageorgiou, G	en
dc.date.accessioned	2014-03-01T01:11:35Z
dc.date.available	2014-03-01T01:11:35Z
dc.date.issued	1996	en
dc.identifier.issn	0036-1429	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/11727
dc.relation.uri	http://www.scopus.com/inward/record.url?eid=2-s2.0-0001394474&partnerID=40&md5=112e4de3ab691217d548163b5c595f1f	en
dc.subject	Initial value problems	en
dc.subject	Pairs of embedded methods	en
dc.subject	Runge-Kutta	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.other	FORMULA PAIRS	en
dc.title	A general family of explicit Runge-Kutta pairs of orders 6(5)	en
heal.type	journalArticle	en
heal.language	English	en
heal.publicationDate	1996	en
heal.abstract	Explicit Runge-Kutta formula pairs of different orders of accuracy form a class of efficient algorithms for treating nonstiff ordinary differential equations. So far, several Runge-Kutta pairs of order 6(5) have appeared in the literature. These pairs use 8 function evaluations per step and belong to certain families of solutions of a set of 54 nonlinear algebraic equations in 44 or 45 coefficients, depending on the use of the FSAL (first stage as last) device. These equations form a set of necessary and sufficient conditions that a 6(5) Runge-Kutta pair must satisfy. The solution of the latter is achieved by employing various types of simplifying assumptions. In this paper we make use of the fact that all these families of pairs satisfy a common set of simplifying assumptions. Using only these simplifying assumptions we define a new family of 6(5) Runge-Kutta pairs. Its main characteristic, which is also a property that no other known family shares, is that all of its nodes (except the last one, which equals 1) are free parameters of the resulting solution. A search has been carried out among the pairs of the new family and two nearly optimum pairs, with respect to accuracy and stability characteristics, have been constructed. The new pairs, as is exhibited by several numerical examples, compare favorably with all other currently known similar pairs.	en
heal.publisher	SIAM PUBLICATIONS	en
heal.journalName	SIAM Journal on Numerical Analysis	en
dc.identifier.isi	ISI:A1996UP95700005	en
dc.identifier.volume	33	en
dc.identifier.issue	3	en
dc.identifier.spage	917	en
dc.identifier.epage	936	en