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A Logic Based Approach to Finding Real Singularities of Implicit Ordinary Differential Equations

dc.date.accessioned2021-05-25T10:29:42Z
dc.date.available2021-05-25T10:29:42Z
dc.date.issued2020-06-17
dc.identifierdoi:10.17170/kobra-202105203943
dc.identifier.urihttp://hdl.handle.net/123456789/12847
dc.description.sponsorshipGefördert im Rahmen des Projekts DEALger
dc.language.isoengeng
dc.rightsNamensnennung 4.0 International*
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/*
dc.subjectimplicit differential equationseng
dc.subjectgeometric singularitieseng
dc.subjectvessiot distributioneng
dc.subjectreal algebraic computationseng
dc.subjectlogic computationeng
dc.subject.ddc510
dc.titleA Logic Based Approach to Finding Real Singularities of Implicit Ordinary Differential Equationseng
dc.typeAufsatz
dcterms.abstractWe discuss the effective computation of geometric singularities of implicit ordinary differential equations over the real numbers using methods from logic. Via the Vessiot theory of differential equations, geometric singularities can be characterised as points where the behaviour of a certain linear system of equations changes. These points can be discovered using a specifically adapted parametric generalisation of Gaussian elimination combined with heuristic simplification techniques and real quantifier elimination methods. We demonstrate the relevance and applicability of our approach with computational experiments using a prototypical implementation in Reduce.eng
dcterms.accessRightsopen access
dcterms.creatorSeiler, Werner M.
dcterms.creatorSeiß, Matthias
dcterms.creatorSturm, Thomas
dc.relation.doidoi:10.1007/s11786-020-00485-x
dc.subject.swdImplizite Differentialgleichungger
dc.subject.swdGeometrieger
dc.subject.swdSingularität <Mathematik>ger
dc.subject.swdReelle algebraische Geometrieger
dc.subject.swdComputational logicger
dc.type.versionpublishedVersion
dcterms.source.identifiereissn:1661-8289
dcterms.source.issueIssue 2
dcterms.source.journalMathematics in Computer Science (MCS)eng
dcterms.source.pageinfo333-352
dcterms.source.volumeVolume 15
kup.iskupfalse


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Namensnennung 4.0 International
Except where otherwise noted, this item's license is described as Namensnennung 4.0 International