Finite difference scheme on graded meshes to the time-fractional neutron diffusion equation with non-smooth solutions

作者：

Highlights：

• In this paper, the time-fractional neutron diffusion equation with single group delayed neutrons is derived in detail, which leads to a multi-term time-fractional subdiffusion equation.

• 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 (2−2α) instead of 2α under non-smooth solutions.

摘要

•In this paper, the time-fractional neutron diffusion equation with single group delayed neutrons is derived in detail, which leads to a multi-term time-fractional subdiffusion equation.•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 (2−2α) instead of 2α under non-smooth solutions.

论文关键词：Fractional neutron diffusion equation,Delayed neutrons,Weak singularity,Graded meshes

论文评审过程：Received 7 March 2022, Revised 2 August 2022, Accepted 5 August 2022, Available online 14 August 2022, Version of Record 14 August 2022.

论文官网地址：https://doi.org/10.1016/j.amc.2022.127474