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dc.contributor.authorHigueras, Inmaculada
dc.contributor.authorKetcheson, David I.
dc.contributor.authorKocsis, Tihamér A.
dc.date.accessioned2018-02-15T09:55:08Z
dc.date.available2018-02-15T09:55:08Z
dc.date.issued2018-02-14
dc.identifier.citationHigueras I, Ketcheson DI, Kocsis TA (2018) Optimal Monotonicity-Preserving Perturbations of a Given Runge–Kutta Method. Journal of Scientific Computing. Available: http://dx.doi.org/10.1007/s10915-018-0664-3.
dc.identifier.issn0885-7474
dc.identifier.issn1573-7691
dc.identifier.doi10.1007/s10915-018-0664-3
dc.identifier.urihttp://hdl.handle.net/10754/627136
dc.description.abstractPerturbed Runge–Kutta methods (also referred to as downwind Runge–Kutta methods) can guarantee monotonicity preservation under larger step sizes relative to their traditional Runge–Kutta counterparts. In this paper we study the question of how to optimally perturb a given method in order to increase the radius of absolute monotonicity (a.m.). We prove that for methods with zero radius of a.m., it is always possible to give a perturbation with positive radius. We first study methods for linear problems and then methods for nonlinear problems. In each case, we prove upper bounds on the radius of a.m., and provide algorithms to compute optimal perturbations. We also provide optimal perturbations for many known methods.
dc.description.sponsorshipMinisterio de Economía y Competitividad[MTM2016-77735-C3-2-P, MTM2014-53178-P]
dc.description.sponsorshipKing Abdullah University of Science and Technology[FIC/2010/05-2000000231]
dc.description.sponsorshipHungarian Government[TÁMOP-4.2.2.A-11/1/KONV-2012-0012]
dc.publisherSpringer Nature
dc.relation.urlhttps://link.springer.com/article/10.1007%2Fs10915-018-0664-3
dc.rightsThe final publication is available at Springer via http://dx.doi.org/10.1007/s10915-018-0664-3
dc.subjectStrong stability preserving
dc.subjectMonotonicity
dc.subjectRunge–Kutta methods
dc.subjectTime discretization
dc.titleOptimal Monotonicity-Preserving Perturbations of a Given Runge–Kutta Method
dc.typeArticle
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.identifier.journalJournal of Scientific Computing
dc.eprint.versionPost-print
dc.contributor.institutionPublic University of Navarre, Pamplona, Spain
dc.contributor.institutionSzéchenyi István University, Győr, Hungary
dc.identifier.arxividarXiv:1505.04024
kaust.personKetcheson, David I.
kaust.grant.numberFIC/2010/05-2000000231


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