Strong Stability Preserving Explicit Runge--Kutta Methods of Maximal Effective Order

Handle URI:
http://hdl.handle.net/10754/333578
Title:
Strong Stability Preserving Explicit Runge--Kutta Methods of Maximal Effective Order
Authors:
Hadjimichael, Yiannis ( 0000-0003-3517-8557 ) ; Macdonald, Colin B.; Ketcheson, David I. ( 0000-0002-1212-126X ) ; Verner, James H.
Abstract:
We apply the concept of effective order to strong stability preserving (SSP) explicit Runge--Kutta methods. Relative to classical Runge--Kutta methods, methods with an effective order of accuracy are designed to satisfy a relaxed set of order conditions but yield higher order accuracy when composed with special starting and stopping methods. We show that this allows the construction of four-stage SSP methods with effective order four (such methods cannot have classical order four). However, we also prove that effective order five methods---like classical order five methods---require the use of nonpositive weights and so cannot be SSP. By numerical optimization, we construct explicit SSP Runge--Kutta methods up to effective order four and establish the optimality of many of them. Numerical experiments demonstrate the validity of these methods in practice.
KAUST Department:
Numerical Mathematics Group; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Citation:
Strong Stability Preserving Explicit Runge--Kutta Methods of Maximal Effective Order 2013, 51 (4):2149 SIAM Journal on Numerical Analysis
Publisher:
Society for Industrial and Applied Mathematics
Journal:
SIAM Journal on Numerical Analysis
Issue Date:
23-Jul-2013
DOI:
10.1137/120884201
ARXIV:
arXiv:1207.2902
Type:
Article
ISSN:
0036-1429; 1095-7170
Additional Links:
http://epubs.siam.org/doi/abs/10.1137/120884201; http://arxiv.org/abs/1207.2902
Appears in Collections:
Articles; Numerical Mathematics Group; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorHadjimichael, Yiannisen
dc.contributor.authorMacdonald, Colin B.en
dc.contributor.authorKetcheson, David I.en
dc.contributor.authorVerner, James H.en
dc.date.accessioned2014-11-03T16:17:40Z-
dc.date.available2014-11-03T16:17:40Z-
dc.date.issued2013-07-23en
dc.identifier.citationStrong Stability Preserving Explicit Runge--Kutta Methods of Maximal Effective Order 2013, 51 (4):2149 SIAM Journal on Numerical Analysisen
dc.identifier.issn0036-1429en
dc.identifier.issn1095-7170en
dc.identifier.doi10.1137/120884201en
dc.identifier.urihttp://hdl.handle.net/10754/333578en
dc.description.abstractWe apply the concept of effective order to strong stability preserving (SSP) explicit Runge--Kutta methods. Relative to classical Runge--Kutta methods, methods with an effective order of accuracy are designed to satisfy a relaxed set of order conditions but yield higher order accuracy when composed with special starting and stopping methods. We show that this allows the construction of four-stage SSP methods with effective order four (such methods cannot have classical order four). However, we also prove that effective order five methods---like classical order five methods---require the use of nonpositive weights and so cannot be SSP. By numerical optimization, we construct explicit SSP Runge--Kutta methods up to effective order four and establish the optimality of many of them. Numerical experiments demonstrate the validity of these methods in practice.en
dc.language.isoenen
dc.publisherSociety for Industrial and Applied Mathematicsen
dc.relation.urlhttp://epubs.siam.org/doi/abs/10.1137/120884201en
dc.relation.urlhttp://arxiv.org/abs/1207.2902en
dc.rightsArchived with thanks to SIAM Journal on Numerical Analysisen
dc.subjectstrong stability preserving (SSP)en
dc.subjecteffective orderen
dc.subjectmonotonicityen
dc.subjectRunge–Kutta methodsen
dc.subjecttime integrationen
dc.subjecthigh-order accuracyen
dc.titleStrong Stability Preserving Explicit Runge--Kutta Methods of Maximal Effective Orderen
dc.typeArticleen
dc.contributor.departmentNumerical Mathematics Groupen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalSIAM Journal on Numerical Analysisen
dc.eprint.versionPublisher's Version/PDFen
dc.contributor.institutionMathematical Institute, University of Oxford, Oxford OX1 3LB, UKen
dc.contributor.institutionDepartment of Mathematics, Simon Fraser University, Burnaby V5A 1S6, BC, Canadaen
dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)en
dc.identifier.arxividarXiv:1207.2902en
kaust.authorHadjimichael, Yiannisen
kaust.authorKetcheson, David I.en
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