Numerical solution of fractional stochastic neutron point kinetic equation for nuclear reactor dynamics

Abstract

In the present article, we have used a numerical procedure which is efficiently calculating the solution for fractional stochastic neutron point kinetic equation (FSNPK) in the dynamical system of nuclear reactor. The explicit finite difference method is applied to solve the fractional stochastic neutron point kinetic equation with the Grunwald–Letnikov (GL) definition (Podlubny, 1999; Oldham and Spanier, 1974). Fractional stochastic neutron point kinetic model has been analyzed for the dynamic behavior of the neutron. The method is investigated over the experimental data, with given initial conditions and step reactivity. The computational results designate that this numerical approximation method is straightforward, effective and easy for solving fractional stochastic point kinetic equations. Numerical results for showing the behavior of neutron density and precursor concentration have been presented graphically for different values of fractional order.