Using enchanted features of Constancy Adding Space Extension (CASE) to reduce the dimension of evolver dynamics: Single Monomial Probabilistic Evolution Theory

Özdemir, Semra Bayat; Demіralp, Metin

doi:10.1007/s10910-018-0854-0

Cited by 3 publications

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“…Second degree multinomial functions may be formed from multinomial functions [20,21]. Single monomial functions may be formed from multinomial functions [19,25,26]: obtaining purely second degree multinomials from second degree multinomials is a special case of this. Putting it together, it is always possible to obtain purely second degree multinomial functions from multinomial functions.…”

Section: Methodsmentioning

confidence: 99%

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

Gözükırmızı

Demіralp

2019

Mathematics

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Probabilistic 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.

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