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

Abstract

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.