Solving ODEs by Obtaining Purely Second Degree Multinomials via Branch and Bound with Admissible Heuristic

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dc.authorid20015en_US
dc.authorid13434en_US
dc.contributor.authorGözükırmızı, Coşkun
dc.contributor.authorDemiralp, Metin
dc.date.accessioned2019-12-31T11:22:06Z
dc.date.available2019-12-31T11:22:06Z
dc.date.issued2019
dc.departmentİstanbul Beykent Üniversitesien_US
dc.description.abstractProbabilistic evolution theory (PREVTH) forms a framework for the solution of explicit ODEs. The purpose of the paper is two-fold: (1) conversion of multinomial right-hand sides of the ODEs to purely second degree multinomial right-hand sides by space extension; (2) decrease the computational burden of probabilistic evolution theory by using the condensed Kronecker product. A first order ODE set with multinomial right-hand side functions may be converted to a first order ODE set with purely second degree multinomial right-hand side functions at the expense of an increase in the number of equations and unknowns. Obtaining purely second degree multinomial right-hand side functions is important because the solution of such equation set may be approximated by probabilistic evolution theory. A recent article by the authors states that the ODE set with the smallest number of unknowns can be found by searching. This paper gives the details of a way to search for the optimal space extension. As for the second purpose of the paper, the computational burden can be reduced by considering the properties of the Kronecker product of vectors and how the Kronecker product appears within the recursion of PREVTH: as a Cauchy product structure.en_US
dc.identifier.citationMathematics 2019, 7, 367en_US
dc.identifier.doi10.3390/math7040367
dc.identifier.issn2227-7390
dc.identifier.scopus2-s2.0-85066427982en_US
dc.identifier.scopusqualityQ2en_US
dc.identifier.urihttps://doi.org/10.3390/math7040367
dc.identifier.wosWOS:000467495500060en_US
dc.identifier.wosqualityQ1en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherMDPIen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.subjectspace extensionen_US
dc.subjectbranch and bounden_US
dc.subjectordinary differential equationsen_US
dc.subjectKronecker producten_US
dc.titleSolving ODEs by Obtaining Purely Second Degree Multinomials via Branch and Bound with Admissible Heuristicen_US
dc.typeArticleen_US

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