A Stability Analysis of Modified Patankar–Runge–Kutta methods for a nonlinear Production–Destruction System

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dc.date.accessioned2023-04-24T09:57:36Z
dc.date.available2023-04-24T09:57:36Z
dc.date.issued2023-03-24
dc.description.sponsorshipGefördert im Rahmen des Projekts DEALger
dc.identifierdoi:10.17170/kobra-202304057781
dc.identifier.urihttp://hdl.handle.net/123456789/14624
dc.language.isoengeng
dc.relation.doidoi:10.1002/pamm.202200083
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 International*
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/*
dc.subject.ddc510
dc.subject.swdRunge-Kutta-Verfahrenger
dc.subject.swdDifferentialgleichungger
dc.subject.swdStabilitätger
dc.subject.swdPhysikalische Eigenschaftger
dc.subject.swdAnalyseger
dc.titleA Stability Analysis of Modified Patankar–Runge–Kutta methods for a nonlinear Production–Destruction Systemeng
dc.typeAufsatz
dc.type.versionpublishedVersion
dcterms.abstractModified Patankar–Runge–Kutta (MPRK) methods preserve the positivity as well as conservativity of a production–destruction system (PDS) of ordinary differential equations for all time step sizes. As a result, higher order MPRK schemes do not belong to the class of general linear methods, i. e. the iterates are generated by a nonlinear map g even when the PDS is linear. Moreover, due to the conservativity of the method, the map g possesses non-hyperbolic fixed points. Recently, a new theorem for the investigation of stability properties of non-hyperbolic fixed points of a nonlinear iteration map was developed. We apply this theorem to understand the stability properties of a family of second order MPRK methods when applied to a nonlinear PDS of ordinary differential equations. It is shown that the fixed points are stable for all time step sizes and members of the MPRK family. Finally, experiments are presented to numerically support the theoretical claims.eng
dcterms.accessRightsopen access
dcterms.creatorIzgin, Thomas
dcterms.creatorKopecz, Stefan
dcterms.creatorMeister, Andreas
dcterms.source.articlenumbere202200083
dcterms.source.identifiereissn:1617-7061
dcterms.source.issueIssue 1
dcterms.source.journalProceedings in Applied Mathematics and Mechanics (PAMM)eng
dcterms.source.volumeVolume 22
kup.iskupfalse

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