PDE-convergence in euclidean norm of AMF-W methods for multidimensional linear parabolic problems

This work considers space-discretised parabolic problems on a rectangular domain subject to Dirichlet boundary conditions. For the time integration s-stage AMF-W-methods, which are ADI (alternating direction implicit) type integrators, are considered. They are particularly efficient when the space dimension m of the problem is large. Optimal results on PDE-convergence have recently been obtained in [S. González-Pinto, E. Hairer and D. Hernández-Abreu, J. Comput. Appl. Math. 417 (2023) 114642.] for the case m = 2. The aim of the present work is to extend these results to arbitrary space dimension m ≥ 3. It is explained which order statements carry over from the case m = 2 to m ≥ 3, and which do not.