A corrected L1 scheme for solving a tempered subdiffusion equation with nonsmooth data

In this paper, we consider a time semi-discrete scheme for a tempered subdiffusion equation with nonsmooth data. Due to the low regularity of the solution, the optimal convergence rate cannot be achieved when the L1 time-stepping scheme is directly applied to discretize the tempered fractional derivative. By introducing a correction term at the initial time step, we propose a corrected L1 scheme which recover to the optimal convergence rate. Theoretical error estimates and numerical experiments validate the improvement.