Explicit strong stability preserving multistep Runge–Kutta methods

Handle URI:
http://hdl.handle.net/10754/622747
Title:
Explicit strong stability preserving multistep Runge–Kutta methods
Authors:
Bresten, Christopher; Gottlieb, Sigal; Grant, Zachary; Higgs, Daniel; Ketcheson, David I. ( 0000-0002-1212-126X ) ; Németh, Adrian
Abstract:
High-order spatial discretizations of hyperbolic PDEs are often designed to have strong stability properties, such as monotonicity. We study explicit multistep Runge-Kutta strong stability preserving (SSP) time integration methods for use with such discretizations. We prove an upper bound on the SSP coefficient of explicit multistep Runge-Kutta methods of order two and above. Numerical optimization is used to find optimized explicit methods of up to five steps, eight stages, and tenth order. These methods are tested on the linear advection and nonlinear Buckley-Leverett equations, and the results for the observed total variation diminishing and/or positivity preserving time-step are presented.
KAUST Department:
King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia
Citation:
Bresten C, Gottlieb S, Grant Z, Higgs D, Ketcheson DI, et al. (2016) Explicit strong stability preserving multistep Runge–Kutta methods. Mathematics of Computation 86: 747–769. Available: http://dx.doi.org/10.1090/mcom/3115.
Publisher:
American Mathematical Society (AMS)
Journal:
Mathematics of Computation
KAUST Grant Number:
FIC/2010/05
Issue Date:
15-Oct-2015
DOI:
10.1090/mcom/3115
Type:
Article
ISSN:
0025-5718; 1088-6842
Sponsors:
This research was supported by AFOSR grant number FA-9550-12-1-0224 and KAUST grant FIC/2010/05.
Additional Links:
http://www.ams.org/journals/mcom/2017-86-304/S0025-5718-2016-03115-4/
Appears in Collections:
Articles

Full metadata record

DC FieldValue Language
dc.contributor.authorBresten, Christopheren
dc.contributor.authorGottlieb, Sigalen
dc.contributor.authorGrant, Zacharyen
dc.contributor.authorHiggs, Danielen
dc.contributor.authorKetcheson, David I.en
dc.contributor.authorNémeth, Adrianen
dc.date.accessioned2017-01-29T13:51:35Z-
dc.date.available2017-01-29T13:51:35Z-
dc.date.issued2015-10-15en
dc.identifier.citationBresten C, Gottlieb S, Grant Z, Higgs D, Ketcheson DI, et al. (2016) Explicit strong stability preserving multistep Runge–Kutta methods. Mathematics of Computation 86: 747–769. Available: http://dx.doi.org/10.1090/mcom/3115.en
dc.identifier.issn0025-5718en
dc.identifier.issn1088-6842en
dc.identifier.doi10.1090/mcom/3115en
dc.identifier.urihttp://hdl.handle.net/10754/622747-
dc.description.abstractHigh-order spatial discretizations of hyperbolic PDEs are often designed to have strong stability properties, such as monotonicity. We study explicit multistep Runge-Kutta strong stability preserving (SSP) time integration methods for use with such discretizations. We prove an upper bound on the SSP coefficient of explicit multistep Runge-Kutta methods of order two and above. Numerical optimization is used to find optimized explicit methods of up to five steps, eight stages, and tenth order. These methods are tested on the linear advection and nonlinear Buckley-Leverett equations, and the results for the observed total variation diminishing and/or positivity preserving time-step are presented.en
dc.description.sponsorshipThis research was supported by AFOSR grant number FA-9550-12-1-0224 and KAUST grant FIC/2010/05.en
dc.publisherAmerican Mathematical Society (AMS)en
dc.relation.urlhttp://www.ams.org/journals/mcom/2017-86-304/S0025-5718-2016-03115-4/en
dc.titleExplicit strong stability preserving multistep Runge–Kutta methodsen
dc.typeArticleen
dc.contributor.departmentKing Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabiaen
dc.identifier.journalMathematics of Computationen
dc.contributor.institutionDepartment of Mathematics, University of Massachusetts, Dartmouth, 285 Old Westport Road, North Dartmouth, MA, 02747, United Statesen
dc.contributor.institutionDepartment of Mathematics and Computational Sciences, Széchenyi István University, Gyor, Hungaryen
kaust.authorKetcheson, David I.en
kaust.grant.numberFIC/2010/05en
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