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dc.contributor.authorBresten, Christopher
dc.contributor.authorGottlieb, Sigal
dc.contributor.authorGrant, Zachary
dc.contributor.authorHiggs, Daniel
dc.contributor.authorKetcheson, David I.
dc.contributor.authorNémeth, Adrian
dc.date.accessioned2017-01-29T13:51:35Z
dc.date.available2017-01-29T13:51:35Z
dc.date.issued2015-10-15
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.
dc.identifier.issn0025-5718
dc.identifier.issn1088-6842
dc.identifier.doi10.1090/mcom/3115
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.
dc.description.sponsorshipThis research was supported by AFOSR grant number FA-9550-12-1-0224 and KAUST grant FIC/2010/05.
dc.publisherAmerican Mathematical Society (AMS)
dc.relation.urlhttp://www.ams.org/journals/mcom/2017-86-304/S0025-5718-2016-03115-4/
dc.relation.urlhttp://arxiv.org/pdf/1307.8058.pdf
dc.rightsFirst published in Mathematics of Computation in 86 (2017), 747-769, published by the American Mathematical Society
dc.rightsThis file is an open access version redistributed from: http://arxiv.org/pdf/1307.8058.pdf
dc.titleExplicit strong stability preserving multistep Runge–Kutta methods
dc.typeArticle
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.identifier.journalMathematics of Computation
dc.eprint.versionPost-print
dc.contributor.institutionDepartment of Mathematics, University of Massachusetts, Dartmouth, 285 Old Westport Road, North Dartmouth, MA, 02747, United States
dc.contributor.institutionDepartment of Mathematics and Computational Sciences, Széchenyi István University, Gyor, Hungary
kaust.personKetcheson, David I.
kaust.grant.numberFIC/2010/05
refterms.dateFOA2020-06-30T13:49:38Z
dc.date.published-online2015-10-15
dc.date.published-print2016-06-02


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