Show simple item record

Volume preservation by Runge–Kutta methods

dc.creatorBader, Philipp
dc.creatorMcLaren, David I.
dc.creatorQuispel, G. R. W.
dc.creatorWebb, Marcus
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.
dc.publisherApplied Numerical Mathematics
dc.rightsAttribution 4.0 International
dc.subjectvolume preservation
dc.subjectRunge–Kutta method
dc.subjectmeasure preservation
dc.subjectKahan’s method
dc.titleVolume preservation by Runge–Kutta methods

Files in this item

Bader_et_al-201 ... merical_Mathematics-AM.pdf166.2Kbapplication/pdfView/Open
Bader_et_al-201 ... erical_Mathematics-VoR.pdf412.5Kbapplication/pdfView/Open

This item appears in the following Collection(s)

Show simple item record