A family of fifth-order Runge-Kutta pairs

Papakostas, SN; Papageorgiou, G

dc.contributor.author	Papakostas, SN	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	0025-5718	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/11723
dc.subject	Initial value problems	en
dc.subject	Pairs of embedded methods	en
dc.subject	Phase-lag	en
dc.subject	Runge-Kutta	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.other	Convergence of numerical methods	en
dc.subject.other	Differential equations	en
dc.subject.other	Nonlinear equations	en
dc.subject.other	Equation system	en
dc.subject.other	Initial value problem	en
dc.subject.other	Numerical integration	en
dc.subject.other	Runge Kutta method	en
dc.subject.other	Truncation error	en
dc.subject.other	Numerical methods	en
dc.title	A family of fifth-order Runge-Kutta pairs	en
heal.type	journalArticle	en
heal.identifier.primary	10.1090/S0025-5718-96-00718-1	en
heal.identifier.secondary	http://dx.doi.org/10.1090/S0025-5718-96-00718-1	en
heal.language	English	en
heal.publicationDate	1996	en
heal.abstract	The construction of a Runge-Kutta pair of order 5(4) with the minimal number of stages requires the solution of a nonlinear system of 25 order conditions in 27 unknowns. We define a new family of pairs which includes pairs using 6 function evaluations per integration step as well as pairs which additionally use the first function evaluation from the next step. This is achieved by making use of Kutta's simplifying assumption on the original system of the order conditions, i.e., that all the internal nodes of a method contributing to the estimation of the endpoint solution provide, at these nodes, cost-free second-order approximations to the true solution of any differential equation. In both cases the solution of the resulting system of nonlinear equations is completely classified and described in terms of five free parameters. Optimal Runge-Kutta pairs with respect to minimized truncation error coefficients, maximal phase-lag order and various stability characteristics are presented. These pairs were selected under the assumption that they are used in Local Extrapolation Mode (the propagated solution of a problem is the one provided by the fifth-order formula of the pair). Numerical results obtained by testing the new pairs over a standard set of test problems suggest a significant improvement in efficiency when using a specific pair of the new family with minimized truncation error coefficients, instead of some other existing pairs.	en
heal.publisher	AMER MATHEMATICAL SOC	en
heal.journalName	Mathematics of Computation	en
dc.identifier.doi	10.1090/S0025-5718-96-00718-1	en
dc.identifier.isi	ISI:A1996UR11400013	en
dc.identifier.volume	65	en
dc.identifier.issue	215	en
dc.identifier.spage	1165	en
dc.identifier.epage	1181	en