Analysis of a temporal discretization for a semilinear fractional diffusion equation

Abstract

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 L2(0,T;L2(Ω)) is derived by a new discrete Grönwall’s inequality, and then first-order temporal accuracy in the norm of L∞(0,T;L2(Ω)) is established for 1∕2<α<1. Finally, numerical results are provided to verify the theoretical results.