The orders of PDE-convergence in the Euclidean norm of s-stage AMF-W-methods for two-dimensional
parabolic problems on rectangular domains are considered for the case of Dirichlet boundary conditions and
an initial condition. The classical algebraic conditions for order p with p ≤ 3 are shown to be sufficient
for PDE-convergence of order p (independently of the spatial resolution) in the case of time-independent
Dirichlet boundary conditions. Under additional conditions, PDE-convergence of order p = 3.25 − for
every > 0 can be obtained. In the case of time-dependent boundary conditions the order reduction is more
dramatic, but order p = 2.25 − for every > 0 can be achieved.
