Nonstandard finite difference schemes for numerical solution of the fractional neutron point kinetics equations

In this paper, our purpose is to find approximate solutions of fractional neutron point kinetic equations by using non-standard finite difference method. The fractional neutron point kinetic equations are modelled with average one group of delayed neutron precursors and the fractional derivative is given in the form of Grunwald-Letnikov. The efficiency and reliability of the suggested approach are proved by some numerical experiments for critical reactivity, supercritical reactivity and subcritical reactivity for various values of fractional order. It is found that the nonstandard finite difference method (NSFDM) is preferable than the standard finite difference method (SFDM). Also, the stability of the numerical scheme is investigated. The stability range of the step size is introduced for different values of the anomalous diffusion order (alpha) and of the relaxation time (tau). Numerical results and graphs for neutron flux for different values of the anomalous order and of the relaxation time are shown and compared with the classical solutions. (C) 2017 Elsevier Ltd. All rights reserved.