Error analysis of a high-order compact ADI method for two-dimensional fractional convection-subdiffusion equations (Q331792)

This paper focuses on the analysis of a high-order compact ADI scheme applied for a class of two-dimensional fractional convection-subdiffusion equations with time Caputo fractional derivative of order \(\alpha \in (0,1)\). The original equation is first transformed and then a fourth-order compact finite difference approximation in the spatial directions is introduced and for time advancing the alternating direction implicit (ADI) approximation is used. The optimal error estimates in \(L^2\), \(L^\infty\) and \(H^1\) norms are obtained. The compact ADI method is shown to be fourth order accurate in space and of order \(\min(1 + \alpha, 2 - \alpha)\) in time. The applicability of the method is tested on three benchmarks, which demonstrates the accuracy of the analyzed method.