An efficient computational technique for solving a fractional-order model describing dynamics of neutron flux in a nuclear reactor

Abstract

This paper focuses on the development of a computational technique for numerical solution of the time-fractional neutron diffusion (FND) equation, which describes dynamics of neutron flux in a nuclear reactor. The time-fractional derivatives are discretized by means of L1 scheme, while the space derivative is discretized by employing a collocation method based on quartic B-spline (QUBS) basis functions. Numerical experiments are presented to illustrate the performance of proposed technique. Results reveal that the proposed technique yields a reliable approximation to the solution of the underlying model problem and has O(k+h4)−order convergence, with k and h representing the step sizes in time and space directions, respectively. It is important to point out that the numerical method for the underlying problem has not yet been discussed in the literature. The effect of fractional order derivative on the behavior of neutron flux is investigated.