Abstract The main purpose of this work is to construct and analyze an efficient numerical scheme for solving the fractional neutron diffusion equation with delayed neutrons, which describes neutron transport in a nuclear reactor. The L1 approximation is used for discretization of time derivative and finite difference method is used for discretization of space derivative. The stability and convergence analysis of the proposed method are studied. The method is shown to be second-order convergent in space and ( 2 − 2 α ) -th order convergent in time, where α is the order of fractional derivative. Numerical experiments are carried out to demonstrate the performance of the method and theoretical analysis. The effects of fractional order derivative, relaxation time and radioactive decay constant on the neutron flux behaviour are investigated. Moreover, the CPU time of the present method is provided.

中文翻译：

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一种含延迟中子的分数阶中子扩散方程数值方法的设计与分析

摘要 这项工作的主要目的是构建和分析一个有效的数值方案，用于求解具有延迟中子的分数式中子扩散方程，该方程描述了核反应堆中的中子输运。L1 近似用于时间导数的离散化，有限差分法用于空间导数的离散化。研究了该方法的稳定性和收敛性分析。该方法在空间上是二阶收敛的，在时间上是 ( 2 − 2 α ) 阶收敛，其中 α 是分数阶导数。进行数值实验以证明该方法和理论分析的性能。研究了分数阶导数、弛豫时间和放射性衰变常数对中子通量行为的影响。而且，