An implicit finite difference method for solving the corrected fractional neutron point kinetics equations

Abstract

It is well known that Espinosa-parades et al. (Espinosa-Paredes et al., 2011) proposed a fractional neutron point kinetic (FNPK) model with multi-group of delayed neutrons to describe dynamic behavior in a nuclear reactor. In (Aboanber and Nahla, 2016b), Aboanber and Nahla presented an extension of Espinosa-parades et al. FNPK model. This new model is called as the corrected fractional neutron point kinetic (CFNPK) model. The present study is concerned with the numerical solution of the CFNPK model (Aboanber and Nahla, 2016b) with six groups of delayed neutron precursors. The fractional derivative is described in the sense of Grünwald-Letnikov. An implicit finite difference method (FDM) is constructed for the solution of CFNPK model. The stability analysis of the method is carried out. We analyze the results of neutron density for different values of anomalous diffusion order, reactivity function, relaxation time and time step size. In addition, we compare the results corresponding to CFNPK model (Aboanber and Nahla, 2016b) with the results corresponding to the FNPK model proposed by Espinosa-parades et al. (Espinosa-Paredes et al., 2011). It is shown that as anomalous diffusion order decreases or simulation time increases the difference between the values of neutron density increases. We have investigated the effects of each term of the CFNPK.