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dc.contributor.authorRanocha, Hendrik
dc.contributor.authorKetcheson, David I.
dc.date.accessioned2020-11-25T11:59:01Z
dc.date.available2019-11-13T00:16:22Z
dc.date.available2020-11-25T11:59:01Z
dc.date.issued2020-11-24
dc.date.submitted2019-09-30
dc.identifier.citationRanocha, H., & Ketcheson, D. I. (2020). Energy Stability of Explicit Runge--Kutta Methods for Nonautonomous or Nonlinear Problems. SIAM Journal on Numerical Analysis, 58(6), 3382–3405. doi:10.1137/19m1290346
dc.identifier.issn0036-1429
dc.identifier.issn1095-7170
dc.identifier.doi10.1137/19m1290346
dc.identifier.urihttp://hdl.handle.net/10754/659989
dc.description.abstractMany important initial value problems have the property that energy is nonincreasing in time. Energy stable methods, also referred to as strongly stable methods, guarantee the same property discretely. We investigate requirements for conditional energy stability of explicit Runge--Kutta methods for nonlinear or nonautonomous problems. We provide both necessary and sufficient conditions for energy stability over these classes of problems. Examples of conditionally energy stable schemes are constructed, and an example is given in which unconditional energy stability is obtained with an explicit scheme.
dc.description.sponsorshipResearch reported in this publication was supported by the King Abdullah University of Scienceand Technology (KAUST). The first author was partially supported by the German Research Foundation (DFG, Deutsche Forschungsgemeinschaft) under Grant SO 363/14-1.
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)
dc.relation.urlhttps://epubs.siam.org/doi/10.1137/19M1290346
dc.rightsArchived with thanks to SIAM Journal on Numerical Analysis
dc.titleEnergy Stability of Explicit Runge--Kutta Methods for Nonautonomous or Nonlinear Problems
dc.typeArticle
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.identifier.journalSIAM Journal on Numerical Analysis
dc.eprint.versionPublisher's Version/PDF
dc.identifier.volume58
dc.identifier.issue6
dc.identifier.pages3382-3405
dc.identifier.arxivid1909.13215
kaust.personRanocha, Hendrik
kaust.personKetcheson, David I.
dc.date.accepted2020-09-09
refterms.dateFOA2019-11-13T00:16:56Z
dc.date.published-online2020-11-24
dc.date.published-print2020-01
dc.date.posted2019-09-29


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