Continuous Runge-Kutta(-nyström) methods with reduced phase-errors

Papageorgiou, G; Tsitouras, Ch

dc.contributor.author	Papageorgiou, G	en
dc.contributor.author	Tsitouras, Ch	en
dc.date.accessioned	2014-03-01T01:11:48Z
dc.date.available	2014-03-01T01:11:48Z
dc.date.issued	1996	en
dc.identifier.issn	0377-0427	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/11818
dc.subject	Phase-error	en
dc.subject	Phase-lag interpolants	en
dc.subject	Runge-Kutta(-Nyström) methods	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.other	Computational methods	en
dc.subject.other	Differential equations	en
dc.subject.other	Integration	en
dc.subject.other	Numerical analysis	en
dc.subject.other	Phase-error	en
dc.subject.other	Runge-Kutta methods	en
dc.subject.other	Approximation theory	en
dc.title	Continuous Runge-Kutta(-nyström) methods with reduced phase-errors	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/0377-0427(95)00027-5	en
heal.identifier.secondary	http://dx.doi.org/10.1016/0377-0427(95)00027-5	en
heal.language	English	en
heal.publicationDate	1996	en
heal.abstract	An explicit Runge-Kutta (RK) or Runge-Kutta-Nyström (RKN) method, for the numerical approximation of the initial value problem, can be expanded by the addition of a ""dense"" formula which provides solutions at points within or outside the normal step intervals. In this paper, we are concerned with the construction of continuous extensions for RK and RKN methods, intended to approximate first- and second-order differential equations, respectively. First we derive the required equations of conditions that the coefficients of these extensions have to satisfy in order to produce reduced phase-errors, when applied to a linear homogeneous test equation. Moreover some particular continuous extensions of an explicit 6(5) RK and 8(6) RKN pair, respectively, are proposed and tested numerically.	en
heal.publisher	ELSEVIER SCIENCE BV	en
heal.journalName	Journal of Computational and Applied Mathematics	en
dc.identifier.doi	10.1016/0377-0427(95)00027-5	en
dc.identifier.isi	ISI:A1996UQ49100001	en
dc.identifier.volume	69	en
dc.identifier.issue	1	en
dc.identifier.spage	1	en
dc.identifier.epage	11	en