Probabilistic evolution theory for the solution of explicit autonomous ordinary differential equations: squarified telescope matrices

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dc.contributor.authorGozukirmizi, Cosar
dc.contributor.authorKirkin, Melike Ebru
dc.contributor.authorDemiralp, Metin
dc.date.accessioned2024-03-13T10:30:46Z
dc.date.available2024-03-13T10:30:46Z
dc.date.issued2017
dc.departmentİstanbul Beykent Üniversitesien_US
dc.description.abstractProbabilistic evolution theory (PREVTH) is used for the solution of initial value problems of first order explicit autonomous ordinary differential equation sets with second degree multinomial right hand side functions. It is an approximation method based on Kronecker power series: a rewriting of multivariate Taylor series using matrices having certain flexible parameters. Kronecker power series have matrices which are called telescope matrices: matrices where j is the index of summation. The additive terms of each telescope matrix is formed through Kronecker product from both sides by Kronecker powers of identity matrices. Recently, squarification is proposed in order to avoid the growing of the matrices in size at each additive term of the series. This paper explains the squarification procedure: the procedure used in order to avoid Kronecker multiplications within PREVTH so that the sizes of the matrices do not grow and so that the amount of necessary computation is reduced. The recursion between squarified matrices is also given. As a numerical application, the solution of a H,non-Heiles system is provided.en_US
dc.identifier.doi10.1007/s10910-016-0678-8
dc.identifier.endpage194en_US
dc.identifier.issn0259-9791
dc.identifier.issn1572-8897
dc.identifier.issue1en_US
dc.identifier.scopus2-s2.0-84982298216en_US
dc.identifier.scopusqualityQ2en_US
dc.identifier.startpage175en_US
dc.identifier.urihttps://doi.org/10.1007/s10910-016-0678-8
dc.identifier.urihttps://hdl.handle.net/20.500.12662/3533
dc.identifier.volume55en_US
dc.identifier.wosWOS:000392430300011en_US
dc.identifier.wosqualityQ2en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherSpringeren_US
dc.relation.ispartofJournal Of Mathematical Chemistryen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectProbabilistic evolution theoryen_US
dc.subjectSquarificationen_US
dc.subjectKronecker power seriesen_US
dc.subjectInitial value problemen_US
dc.titleProbabilistic evolution theory for the solution of explicit autonomous ordinary differential equations: squarified telescope matricesen_US
dc.typeArticleen_US

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