On the Solution of the Nonlinear Fractional Neutron Point-Kinetics Equation with Newtonian Temperature Feedback Reactivity

Abstract

This technical note introduces a numerical procedure that is efficient for calculating the solution for the fractional order nonlinear neutron point-kinetics equation in nuclear reactor dynamics. The explicit finite difference method (EFDM) is applied to solve the fractional order nonlinear neutron point-kinetics equation with Newtonian temperature feedback reactivity. This nonlinear neutron point-kinetics model has been analyzed in the presence of temperature feedback reactivity. The numerical solution obtained by EFDM is an approximate solution that is based on neutron density, precursor concentrations of multigroup delayed neutrons, and the reactivity function. The method is investigated using experimental data, with given initial conditions along with Newtonian temperature feedback reactivity. From the computational results, it can be shown that this numerical approximation method is straightforward and effective for solving fractional order nonlinear neutron point-kinetics equations. Numerical results citing the behavior of neutron density for different types of fractional order are presented graphically.