Design and analysis of a numerical method for fractional neutron diffusion equation with delayed neutrons

Abstract

The main purpose of this work is to construct and analyze an efficient numerical scheme for solving the fractional neutron diffusion equation with delayed neutrons, which describes neutron transport in a nuclear reactor. The L1 approximation is used for discretization of time derivative and finite difference method is used for discretization of space derivative. The stability and convergence analysis of the proposed method are studied. The method is shown to be second-order convergent in space and (2−2α)-th order convergent in time, where α is the order of fractional derivative. Numerical experiments are carried out to demonstrate the performance of the method and theoretical analysis. The effects of fractional order derivative, relaxation time and radioactive decay constant on the neutron flux behaviour are investigated. Moreover, the CPU time of the present method is provided.