Convergence analysis of a L1‐ADI scheme for two‐dimensional multiterm reaction‐subdiffusion equation

Abstract

In this paper, we consider the numerical approximation for a two‐dimensional multiterm reaction‐subdiffusion equation, where we adopt an alternating direction implicit (ADI) method combined with the L1 approximation for the multiterm time Caputo fractional derivatives of orders between 0 and 1. Stability and convergence of the full‐discrete L1‐ADI scheme are established. The final convergence in time direction is point‐wise, that is, at . Numerical results are given to confirm our theoretical results.