Error estimate of GL‐ADI scheme for 2D multiterm nonlinear time‐fractional subdiffusion equation

Abstract

In this paper, a 2D multiterm nonlinear problem of the form is considered, where each Caputo fractional derivative is of order . We use the Grünwald–Letnikov(GL) scheme on uniform mesh to discretize the multiterm Caputo fractional derivative and finite difference scheme is used for spatial discretization, and then we construct a fully discrete GL‐ADI scheme. A discrete Gronwall inequality is introduced for getting the sharp pointwise‐in‐time error estimate on uniform mesh. Numerical examples are provided to verify the sharpness of our error estimate.