Publication

Abstract : This paper focuses on development of an efficient numerical technique for approximation of a fractional neutron diffusion equation with delayed neutrons for neutron flux profile in a nuclear reactor. The L 1 method is used to approximate the Caputo time-fractional derivatives in the governing equation. A collocation technique based on quintic B-spline (QBS) basis function is employed for discretization of space derivative. The proposed numerical scheme is applied to solve the considered fractional neutron diffusion equation in order to illustrate its applicability and efficiency. The influences of fractional order derivative ( α ), radioactive decay constant ( λ ) and relaxation time ( τ ) on the neutron flux profile are investigated. The numerical results of fractional neutron diffusion equation are compared with those of classical neutron diffusion equation. Further, the results obtained by the proposed approach are compared with the results obtained by the finite difference method to justify the superiority of our method. The CPU time (the execution time of the computer program) is given in order to demonstrate the method’s computational efficiency.