Probabilistic Evolution Theory for Explicit Autonomous ODEs: Simplifying the Factorials, Cauchy Product Folding and Kronecker Product Decomposition

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dc.contributor.authorGozukirmizi, Cosar
dc.date.accessioned2024-03-13T10:30:19Z
dc.date.available2024-03-13T10:30:19Z
dc.date.issued2018
dc.departmentİstanbul Beykent Üniversitesien_US
dc.description12th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences (ICNPAA) -- JUL 03-06, 2018 -- Amer Univ Armenia, ARMENIAen_US
dc.description.abstractProbabilistic evolution theory forms a framework for the solution of explicit ODEs. The squarification concept and the recursion between the squarified telescope matrices (or the images of initial vectors under the squarified telescope matrices) make the method efficient in terms of time and space necessities. This work is designed for further improvements. The new concepts in this work are simplifying the factorials, Cauchy product folding, the use of Kronecker product decomposition within Probabilistic evolution theory (PREVTH) and condensation. Simplifying the factorials is about embedding the factorial that is appearing in the series expansion into the recursion so that number of calculations is reduced and numerical stability is improved. Cauchy product folding is about the Cauchy Kronecker product of two vectors. If the vectors change places in Kronecker product, the new result is a permutation of the original result. This property is used so that the number of terms in the series is halved. Also, the possibilities of the use of Kronecker product decomposition on the rectangular matrix are investigated in detail. Lastly, in condensation, the effect of Cauchy product folding which causes equivalent columns in the rectangular matrix is utilized so that smaller matrices and vectors may be used in the recursion.en_US
dc.description.sponsorshipAmer Inst Aeronaut & Astronaut,Int Federat Nonlinear Analysts,Int Federat Informat Proc,Fdn Armenian Sci & Technolen_US
dc.identifier.doi10.1063/1.5081554
dc.identifier.isbn978-0-7354-1772-4
dc.identifier.issn0094-243X
dc.identifier.scopus2-s2.0-85058695928en_US
dc.identifier.scopusqualityN/Aen_US
dc.identifier.urihttps://doi.org/10.1063/1.5081554
dc.identifier.urihttps://hdl.handle.net/20.500.12662/3255
dc.identifier.volume2046en_US
dc.identifier.wosWOS:000468353100034en_US
dc.identifier.wosqualityN/Aen_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherAmer Inst Physicsen_US
dc.relation.ispartofIcnpaa 2018 World Congress: 12th International Conference On Mathematical Problems In Engineering, Aerospace And Sciencesen_US
dc.relation.publicationcategoryKonferans Öğesi - Uluslararası - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.titleProbabilistic Evolution Theory for Explicit Autonomous ODEs: Simplifying the Factorials, Cauchy Product Folding and Kronecker Product Decompositionen_US
dc.typeConference Objecten_US

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