High order PDE-convergence of AMF-W methods for 2D-linear parabolic problems

Abstract

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−ϵ for every ϵ>0 can be obtained. In the case of time-dependent boundary conditions the order reduction is more dramatic, but order p=2.25−ϵ for every ϵ>0 can be achieved.