Pointwise-in-time α-robust error estimate of the ADI difference scheme for three-dimensional fractional subdiffusion equations with variable coefficients

Abstract

In this paper, a fully-discrete alternating direction implicit (ADI) difference method is proposed for solving three-dimensional (3D) fractional subdiffusion equations with variable coefficients, whose solution presents a weak singularity at $ t = 0 $. The proposed method is established via the L1 scheme on graded mesh for the Caputo fractional derivative and central difference method for spatial derivative, and an ADI method is structured to change the 3D problem into three 1D problems. Using the modified Grönwall inequality we prove the stability and $ \alpha $-robust convergence. The results presented in numerical experiments are in accordance with the theoretical analysis.

Keywords

• three-dimensional fractional equation
• adi scheme
• variable coefficient
• $ \alpha $-robust
• l1 scheme
• stability and convergence