An efficient numerical method for fractional neutron diffusion equation in the presence of different types of reactivities

Abstract In this paper, we construct an efficient numerical technique for solving a fractional neutron diffusion equation with step, ramp and sinusoidal reactivity effects combined with one group of delayed neutron precursor concentration equation. This problem describes neutron transport in a nuclear reactor. We use L 1 approximation technique for discretization of time derivative and a collocation method based on quintic B-spline (QBS) basis function for discretization of space derivative. Some numerical experiments are performed to show the accuracy and efficiency of the method. The effects of order of fractional derivative, relaxation time and radioactive decay constant on the neutron flux profile are examined. It is shown that the suggested method is of order O ( k 1 + h 4 ) convergence, where k and h represent the step size for time and space, respectively. The numerical result of fractional model is compared with that of classic one. The CPU time is provided to show the computational efficiency of the method.