Error analysis of an L2-type method on graded meshes for semilinear subdiffusion equations

Abstract

A semilinear initial-boundary value problem with a Caputo time derivative of fractional order $\alpha \in (0,1)$ is considered, solutions of which typically exhibit a singular behaviour at an initial time. For an L2-type discretization of order $3-\alpha$, we give sharp pointwise-in-time error bounds on graded temporal meshes with arbitrary degree of grading.