Probabilistic evolution theory for explicit autonomous ordinary differential equations: recursion of squarified telescope matrices and optimal space extension

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dc.contributor.authorGozukirmizi, Cosar
dc.contributor.authorDemiralp, Metin
dc.date.accessioned2024-03-13T10:30:19Z
dc.date.available2024-03-13T10:30:19Z
dc.date.issued2018
dc.departmentİstanbul Beykent Üniversitesien_US
dc.description17th International Conference on Computational and Mathematical Methods in Science and Engineering (CMMSE) -- JUL, 2017 -- Cadiz, SPAINen_US
dc.description.abstractProbabilistic evolution theory facilitates the solution of initial value problem of explicit autonomous ordinary differential equations with second degree multinomial right hand side functions. Its formulation has components we call telescope matrices. The matrices grow in size very rapidly and has many zeroes and repeating structures. In order to avoid the computational complexity coming from telescope matrices, squarified telescope matrices are utilized. Their calculation is through a recursion. This recursion has been used in several works by the authors and their colleagues but its proof was not given. This work gives the proof of the recursion and all the surrounding details. A second purpose of this work is to provide a method for most facilitative (optimal) space extension. Space extension is needed for using probabilistic evolution theory when degree of multinomiality of the right hand side functions is more than two. For this purpose, an approach using method of exhaustion (brute-force) is proposed.en_US
dc.identifier.doi10.1007/s10910-017-0849-2
dc.identifier.endpage1848en_US
dc.identifier.issn0259-9791
dc.identifier.issn1572-8897
dc.identifier.issue7en_US
dc.identifier.scopus2-s2.0-85038351642en_US
dc.identifier.scopusqualityQ2en_US
dc.identifier.startpage1826en_US
dc.identifier.urihttps://doi.org/10.1007/s10910-017-0849-2
dc.identifier.urihttps://hdl.handle.net/20.500.12662/3263
dc.identifier.volume56en_US
dc.identifier.wosWOS:000438284000003en_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.publicationcategoryKonferans Öğesi - Uluslararası - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectProbabilistic evolution theoryen_US
dc.subjectSquarificationen_US
dc.subjectKronecker multiplicationen_US
dc.subjectTelescope matricesen_US
dc.subjectSpace extensionen_US
dc.titleProbabilistic evolution theory for explicit autonomous ordinary differential equations: recursion of squarified telescope matrices and optimal space extensionen_US
dc.typeConference Objecten_US

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