Strong Stability Preserving Two-step Runge–Kutta Methods

Handle URI:
http://hdl.handle.net/10754/333597
Title:
Strong Stability Preserving Two-step Runge–Kutta Methods
Authors:
Ketcheson, David I. ( 0000-0002-1212-126X ) ; Gottlieb, Sigal; Macdonald, Colin B.
Abstract:
We investigate the strong stability preserving (SSP) property of two-step Runge–Kutta (TSRK) methods. We prove that all SSP TSRK methods belong to a particularly simple subclass of TSRK methods, in which stages from the previous step are not used. We derive simple order conditions for this subclass. Whereas explicit SSP Runge–Kutta methods have order at most four, we prove that explicit SSP TSRK methods have order at most eight. We present explicit TSRK methods of up to eighth order that were found by numerical search. These methods have larger SSP coefficients than any known methods of the same order of accuracy and may be implemented in a form with relatively modest storage requirements. The usefulness of the TSRK methods is demonstrated through numerical examples, including integration of very high order weighted essentially non-oscillatory discretizations.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Numerical Mathematics Group
Citation:
Strong Stability Preserving Two-step Runge–Kutta Methods 2011, 49 (6):2618 SIAM Journal on Numerical Analysis
Publisher:
Society for Industrial & Applied Mathematics (SIAM)
Journal:
SIAM Journal on Numerical Analysis
Issue Date:
22-Dec-2011
DOI:
10.1137/10080960X
Type:
Article
ISSN:
0036-1429; 1095-7170
Additional Links:
http://epubs.siam.org/doi/abs/10.1137/10080960X; http://davidketcheson.info/assets/papers/2011_tsrk.pdf; http://arxiv.org/abs/1106.3626
Appears in Collections:
Articles; Numerical Mathematics Group; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorKetcheson, David I.en
dc.contributor.authorGottlieb, Sigalen
dc.contributor.authorMacdonald, Colin B.en
dc.date.accessioned2014-11-03T16:17:00Z-
dc.date.available2014-11-03T16:17:00Z-
dc.date.issued2011-12-22en
dc.identifier.citationStrong Stability Preserving Two-step Runge–Kutta Methods 2011, 49 (6):2618 SIAM Journal on Numerical Analysisen
dc.identifier.issn0036-1429en
dc.identifier.issn1095-7170en
dc.identifier.doi10.1137/10080960Xen
dc.identifier.urihttp://hdl.handle.net/10754/333597en
dc.description.abstractWe investigate the strong stability preserving (SSP) property of two-step Runge–Kutta (TSRK) methods. We prove that all SSP TSRK methods belong to a particularly simple subclass of TSRK methods, in which stages from the previous step are not used. We derive simple order conditions for this subclass. Whereas explicit SSP Runge–Kutta methods have order at most four, we prove that explicit SSP TSRK methods have order at most eight. We present explicit TSRK methods of up to eighth order that were found by numerical search. These methods have larger SSP coefficients than any known methods of the same order of accuracy and may be implemented in a form with relatively modest storage requirements. The usefulness of the TSRK methods is demonstrated through numerical examples, including integration of very high order weighted essentially non-oscillatory discretizations.en
dc.language.isoenen
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.relation.urlhttp://epubs.siam.org/doi/abs/10.1137/10080960Xen
dc.relation.urlhttp://davidketcheson.info/assets/papers/2011_tsrk.pdfen
dc.relation.urlhttp://arxiv.org/abs/1106.3626en
dc.rightsArchived with thanks to SIAM Journal on Numerical Analysisen
dc.subjectstrong stability preservingen
dc.subjectmonotonicityen
dc.subjecttwo-step Runge–Kutta methodsen
dc.titleStrong Stability Preserving Two-step Runge–Kutta Methodsen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentNumerical Mathematics Groupen
dc.identifier.journalSIAM Journal on Numerical Analysisen
dc.eprint.versionPublisher's Version/PDFen
dc.contributor.institutionDepartment of Mathematics, University of Massachusetts Dartmouth, North Dartmouth, MAen
dc.contributor.institutionMathematical Institute, University of Oxford, Oxford OX1 3LB, UKen
dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)en
kaust.authorKetcheson, David I.en
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