Novel numerical solution to the fractional neutron point kinetic equation in nuclear reactor dynamics

•Numerical solution to nonlinear multi-term fractional differential-integral equations.•Differential-integral operators of fractional order are numerically solved.•The impact of the order of the operators were assessed.•Time derivative of the reactivity is takes into account to obtain the general mo...

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Bibliographic Details
Published in:Annals of nuclear energy Vol. 137; p. 107173
Main Authors: Polo-Labarrios, M.A., Quezada-García, S., Espinosa-Paredes, G., Franco-Pérez, L., Ortiz-Villafuerte, J.
Format: Journal Article
Language:English
Published: Elsevier Ltd 01.03.2020
Subjects:
Anomalous diffusion coefficient
Fractional neutron point kinetic equations
Multi term higher-order linear approximation
Reactor dynamics
Sinusoidal reactivity
Fractional neutron point kinetic equations
Reactor dynamics
Anomalous diffusion coefficient
Sinusoidal reactivity
Multi term higher-order linear approximation
ISSN:0306-4549, 1873-2100
Online Access:Get full text
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Summary:•Numerical solution to nonlinear multi-term fractional differential-integral equations.•Differential-integral operators of fractional order are numerically solved.•The impact of the order of the operators were assessed.•Time derivative of the reactivity is takes into account to obtain the general model of the FNPK equation.•The form and the quantity of additional terms on FNPK equation depend on the reactivity parameter. In this work, a novel numerical solution to modified Fractional Neutron Point Kinetic (FNPK) equations is presented. The method is based on a numerical solution to linear multi-term fractional differential equations taking from scientific literature. Differential-integral operators of fractional order are numerically solved with the novel method. The impact of the order of the operators has been assessed during the process of order reduction of the fractional differential-integral equation. The numerical solution is applied to case with sinusoidal reactivity, and different values of the anomalous diffusion order are used to study the effect on the neutron density. The results of the neutron density behavior obtained with this proposed numerical novel solution were compared against the classical neutron point kinetics equations and with other results from scientific literature. The comparison showed a clear improvement of the numerical results when using a fractional differential-integral operator instead of an only fractional differential operator.
ISSN:0306-4549
1873-2100
DOI:10.1016/j.anucene.2019.107173