Analysis of a temporal discretization for a semilinear fractional diffusion equation

This paper considers a temporal discretization of a semilinear fractional diffusion equation with nonsmooth initial data. With appropriately graded temporal grids, first-order temporal accuracy in the norm of L-2(0, T; L-2(Omega)) is derived by a new discrete Gronwall's inequality, and then first-order temporal accuracy in the norm of L-infinity(0, T; L-2(Omega)) is established for 1/2 < alpha < 1. Finally, numerical results are provided to verify the theoretical results. (c) 2020 Elsevier Ltd. All rights reserved.