A high-order and efficient numerical technique for the nonlocal neutron diffusion equation representing neutron transport in a nuclear reactor

Abstract

In this paper, a high-order and efficient numerical technique is constructed to solve nonlocal neutron diffusion equation with delayed neutrons representing neutron transport in a nuclear reactor. The method is based on approximating the temporal derivative by L1-2 technique, in combination with a space discretization by using compact difference method. The convergence of this method are studied using energy analysis and Cholesky decomposition. The error convergence order is shown to be O(k3−2α+h4), where α is the order of fractional derivative, k and h represent the parameters for the time and space meshes, respectively. Further, two numerical experiments are presented to validate the sharpness of our theoretical error bounds.