Highly efficient strong stability preserving Runge-Kutta methods with Low-Storage Implementations

Handle URI:
http://hdl.handle.net/10754/136932
Title:
Highly efficient strong stability preserving Runge-Kutta methods with Low-Storage Implementations
Authors:
Ketcheson, David I. ( 0000-0002-1212-126X )
Abstract:
Strong stability-preserving (SSP) Runge–Kutta methods were developed for time integration of semidiscretizations of partial differential equations. SSP methods preserve stability properties satisfied by forward Euler time integration, under a modified time-step restriction. We consider the problem of finding explicit Runge–Kutta methods with optimal SSP time-step restrictions, first for the case of linear autonomous ordinary differential equations and then for nonlinear or nonautonomous equations. By using alternate formulations of the associated optimization problems and introducing a new, more general class of low-storage implementations of Runge–Kutta methods, new optimal low-storage methods and new low-storage implementations of known optimal methods are found. The results include families of low-storage second and third order methods that achieve the maximum theoretically achievable effective SSP coefficient (independent of stage number), as well as low-storage fourth order methods that are more efficient than current full-storage methods. The theoretical properties of these methods are confirmed by numerical experiment.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Numerical Mathematics Group
Publisher:
Society for Industrial and Applied Mathematics
Journal:
Society for Industrial and Applied Mathematics
Issue Date:
2008
DOI:
10.1137/07070485X
Type:
Article
ISSN:
1064-8275
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.date.accessioned2011-07-26T08:34:22Z-
dc.date.available2011-07-26T08:34:22Z-
dc.date.issued2008en
dc.identifier.issn1064-8275en
dc.identifier.doi10.1137/07070485Xen
dc.identifier.urihttp://hdl.handle.net/10754/136932en
dc.description.abstractStrong stability-preserving (SSP) Runge–Kutta methods were developed for time integration of semidiscretizations of partial differential equations. SSP methods preserve stability properties satisfied by forward Euler time integration, under a modified time-step restriction. We consider the problem of finding explicit Runge–Kutta methods with optimal SSP time-step restrictions, first for the case of linear autonomous ordinary differential equations and then for nonlinear or nonautonomous equations. By using alternate formulations of the associated optimization problems and introducing a new, more general class of low-storage implementations of Runge–Kutta methods, new optimal low-storage methods and new low-storage implementations of known optimal methods are found. The results include families of low-storage second and third order methods that achieve the maximum theoretically achievable effective SSP coefficient (independent of stage number), as well as low-storage fourth order methods that are more efficient than current full-storage methods. The theoretical properties of these methods are confirmed by numerical experiment.en
dc.language.isoenen
dc.publisherSociety for Industrial and Applied Mathematicsen
dc.subjectmethod of lineen
dc.subjectstrong stability-preservingen
dc.subjectmonotonicityen
dc.subjectlow-storageen
dc.subjectRunge-Kutta methodsen
dc.titleHighly efficient strong stability preserving Runge-Kutta methods with Low-Storage Implementationsen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentNumerical Mathematics Groupen
dc.identifier.journalSociety for Industrial and Applied Mathematicsen
dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)en
kaust.authorKetcheson, David I.en
kaust.authorKetcheson, David I.en
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