An ADI Difference Scheme for the Three‐Dimensional Mobile/Immobile Transport Model With Weakly Singular Solutions

ABSTRACT In this study, we present a corresponding numerical approximation method for three‐dimensional mobile/immobile (MIM) transport problems with weakly singular solutions. The L1 scheme is used to estimate the Caputo fractional derivative, while the backward Euler method is used to approximate the first‐order temporal derivative. The fully discrete alternating direction implicit (ADI) difference scheme is constructed by incorporating a small term. The stability and convergence of the fully discrete ADI difference scheme are comprehensively investigated and verified in both the ‐norm and the maximum‐norm. Numerical experiments validate the robustness and accuracy of the proposed ADI method.