High phase-lag-order Runge-Kutta and Nystrom pairs

Papakostas, SN; Tsitouras, CH

dc.contributor.author	Papakostas, SN	en
dc.contributor.author	Tsitouras, CH	en
dc.date.accessioned	2014-03-01T01:14:42Z
dc.date.available	2014-03-01T01:14:42Z
dc.date.issued	1999	en
dc.identifier.issn	1064-8275	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/13192
dc.relation.uri	http://www.scopus.com/inward/record.url?eid=2-s2.0-0033297038&partnerID=40&md5=709b4508eab24260af0e16365f950583	en
dc.subject	Runge-Kutta	en
dc.subject	Nystrom methods	en
dc.subject	periodic initial value problems	en
dc.subject	pairs of embedded methods	en
dc.subject	hyperbolic equations	en
dc.subject	phase-lag	en
dc.subject	dispersion order	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.other	Hyperbolic equations	en
dc.subject.other	Nystrom methods	en
dc.subject.other	Pairs of embedded methods	en
dc.subject.other	Phase lag order	en
dc.subject.other	Algorithms	en
dc.subject.other	Approximation theory	en
dc.subject.other	Function evaluation	en
dc.subject.other	Initial value problems	en
dc.subject.other	Integration	en
dc.subject.other	Optimization	en
dc.subject.other	Parameter estimation	en
dc.subject.other	Runge Kutta methods	en
dc.title	High phase-lag-order Runge-Kutta and Nystrom pairs	en
heal.type	journalArticle	en
heal.language	English	en
heal.publicationDate	1999	en
heal.abstract	We exploit the freedom in the selection of the free parameters of one family of eighth-algebraic-order Runge-Kutta (RK) pairs and of three families of fourth-, sixth-, and eighth-order RK Nystrom (RKN) pairs with the purpose of obtaining specific pairs of the highest possible phase-lag order, which are also characterized by minimized principal truncation error coefficients. We present a method for the analytic derivation of the dissipation-order conditions for RK methods and the phase-lag- and dissipation-order conditions for Nystrom methods. The RK pairs we study here are based on a one-parameter generalization of some older families of pairs. An algorithm and specific optimized 8(6) Nystrom pairs are also provided. For a class of initial value problems, whose solution is known to be described by free oscillations or free oscillations of low frequency with forced oscillations of high frequency superimposed, over long integration intervals, these new pairs seem to offer some advantages with respect to some older pairs. The latter are of the same algebraic orders as the new ones but are characterized by the minimal phase-lag order according to their algebraic order and number of stages.	en
heal.publisher	SIAM PUBLICATIONS	en
heal.journalName	SIAM Journal on Scientific Computing	en
dc.identifier.isi	ISI:000083608100017	en
dc.identifier.volume	21	en
dc.identifier.issue	2	en
dc.identifier.spage	747	en
dc.identifier.epage	763	en