Maximum Norm Error Estimates of ADI Methods for a Two-Dimensional Fractional Subdiffusion Equation

Abstract

This paper is concerned with two alternating direction implicit (ADI) finite difference methods for solving a two-dimensional fractional subdiffusion equation. An explicit error estimate for each of the two methods is provided in the discrete maximum norm. It is shown that the methods have the same order as their truncation errors with respect to the discrete maximum norm. Numerical results are given to confirm the theoretical analysis results.