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

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Severiano González-Pinto, Ernst Hairer, and Domingo Hernández-Abreu,

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Abstract.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 \cite{gonzalez23hop} for the case $m=2$. The aim of the present work is to extend these results to arbitrary space dimension $m\ge 3$. It is explained which order statements carry over from the case $m=2$ to $m\ge 3$, and which do not.

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Key Words. multidimensional parabolic problem, ADI-type AMF-W method, PDE-convergence, order conditions, fractional order

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