In this paper, we construct and analyze an efficient numerical scheme based on graded meshes in time for solving the fractional neutron diffusion equation with delayed neutrons and non-smooth solutions, which can be found everywhere in nuclear reactors. Using the L1 discretization of each time fractional derivatives on graded meshes and the classical finite difference for the spatial derivatives on uniform meshes, we prove the order of convergence in time is at best $(2-2\alpha )$ instead of $2\alpha$ under non-smooth solutions, where $0<\alpha <1/2$ is the anomalous diffusion order. Numerical experiments are designed to verify our theoretical analysis. Although we can pick any mesh parameter $r$ provided $r\ge (2-2\alpha )/2\alpha$ to get the optimal order, we choose the minimum in consideration of both accuracy and convergence.

在本文中，我们构建并分析了一种基于分级网格的有效数值方案，用于求解在核反应堆中随处可见的具有延迟中子和非光滑解的分数中子扩散方程。使用梯度网格上每个时间分数导数的 L1 离散化和均匀网格上空间导数的经典有限差分，我们证明时间上的收敛顺序充其量是$(2-2\alpha )$代替$2\alpha$在非光滑解下，其中$0<\alpha <1/2$是异常扩散阶。数值实验旨在验证我们的理论分析。虽然我们可以选择任何网格参数$r$假如$r\ge (2-2\alpha )/2\alpha$为了得到最优的顺序，我们在考虑准确性和收敛性的情况下选择最小值。