Continuous extensions to high order Runge-Kutta methods

Papageorgiou, G; Tsitouras, Ch

dc.contributor.author	Papageorgiou, G	en
dc.contributor.author	Tsitouras, Ch	en
dc.date.accessioned	2014-03-01T01:12:43Z
dc.date.available	2014-03-01T01:12:43Z
dc.date.issued	1997	en
dc.identifier.issn	0020-7160	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/12212
dc.subject	Hermite interpolation	en
dc.subject	ODE's	en
dc.subject	Runge-Kutta	en
dc.subject	Scaling	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.other	Approximation theory	en
dc.subject.other	Computational complexity	en
dc.subject.other	Differential equations	en
dc.subject.other	Function evaluation	en
dc.subject.other	Integration	en
dc.subject.other	Interpolation	en
dc.subject.other	Hermite interpolation	en
dc.subject.other	High order Runge Kutta methods	en
dc.subject.other	Computational methods	en
dc.title	Continuous extensions to high order Runge-Kutta methods	en
heal.type	journalArticle	en
heal.identifier.primary	10.1080/00207169708804616	en
heal.identifier.secondary	http://dx.doi.org/10.1080/00207169708804616	en
heal.language	English	en
heal.publicationDate	1997	en
heal.abstract	Computer assisted derivation and improved techniques have led to effective explicit Runge-Kutta methods of higher order. These methods become inefficient when the step size must be reduced often to produce approximations at specified points. Considerable effort has been devoted to providing Runge-Kutta methods with an interpolation capability, so that approximations can be produced inexpensively at intermediate points of a successful step. New high order Hermite interpolants for two well known embedded Runge-Kutta methods of orders 7 and 8 are presented. These interpolants are constructed using values from two successive integration steps, are locally of O(h(8)) or O(h(9)), and require only one or four extra function evaluations per step respectively.	en
heal.publisher	GORDON BREACH SCI PUBL LTD	en
heal.journalName	International Journal of Computer Mathematics	en
dc.identifier.doi	10.1080/00207169708804616	en
dc.identifier.isi	ISI:000071481100010	en
dc.identifier.volume	65	en
dc.identifier.issue	3-4	en
dc.identifier.spage	273	en
dc.identifier.epage	291	en