Picard iteration and Padé approximations for stiff fractional point kinetics equations

A model of stiff point kinetics equations is one of the important models in the nuclear reactor dynamics. This model describes the neutron density and the precursor concentrations of delayed neutrons into nuclear reactors. In this work, a fractional model of the stiff point kinetics equations is studied to describe the neutron density behavior by the fractional order. Picard iteration and Padé approximations are presented to solve the stiff fractional point kinetics equations with multi-group of delayed neutrons. The validity of the fractional model is tested for different cases of step, ramp and sinusoidal reactivities. The numerical results of Picard iteration and Padé approximations are computed for various fractional order. The results of Padé11 approximation are in good agreement with the results of Picard iteration than Padé01 approximation. In addition, the numerical results confirm that the neutron density for a positive (negative) reactivity is increasing (decreasing) quicker with decreases the fractional order.