Show simple item record

dc.contributor.authorBader, Philipp
dc.contributor.authorMcLaren, David I.
dc.contributor.authorQuispel, G. R. W.
dc.contributor.authorWebb, Marcus
dc.date.accessioned2016-08-12T08:58:42Z
dc.date.available2016-08-12T08:58:42Z
dc.date.issued2016-07-12
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/257255
dc.descriptionThis is the final version of the article. It first appeared from Elsevier via http://dx.doi.org/10.1016/j.apnum.2016.06.010en
dc.description.abstractIt is a classical theorem of Liouville that Hamiltonian systems preserve volume in phase space. Any symplectic Runge–Kutta method will respect this property for such systems, but it has been shown by Iserles, Quispel and Tse and independently by Chartier and Murua that no B-Series method can be volume preserving for all volume preserving vector fields. In this paper, we show that despite this result, symplectic Runge–Kutta methods can be volume preserving for a much larger class of vector fields than Hamiltonian systems, and discuss how some Runge–Kutta methods can preserve a modified measure exactly.en
dc.description.sponsorshipThis research was supported by the Marie Curie International Research Staff Exchange Scheme, grant number DP140100640, within the 7th European Community Framework Programme; by the Australian Research Council grant number 269281; and by the UK Engineering and Physical Sciences Research Council grant EP/H023348/1 for the Cambridge Centre for Analysis.en
dc.language.isoenen
dc.publisherElsevieren
dc.rightsAttribution 4.0 International*
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/*
dc.subjectvolume preservationen
dc.subjectRunge–Kutta methoden
dc.subjectmeasure preservationen
dc.subjectKahan’s methoden
dc.titleVolume preservation by Runge–Kutta methodsen
dc.typeArticleen
prism.endingPage137en
prism.publicationNameApplied Numerical Mathematicsen
prism.startingPage123en
prism.volume109en
dc.identifier.doi10.17863/CAM.1184
pubs.declined2017-10-11T13:54:42.95+0100
dcterms.dateAccepted2016-06-29
rioxxterms.versionofrecord10.1016/j.apnum.2016.06.010en
rioxxterms.versionVoRen
cam.orpheus.successThu Jan 30 12:57:19 GMT 2020 - The item has an open VoR version.*
rioxxterms.freetoread.startdate2100-01-01


Files in this item

Thumbnail
Thumbnail
Thumbnail

This item appears in the following Collection(s)

Show simple item record

Attribution 4.0 International
Except where otherwise noted, this item's licence is described as Attribution 4.0 International