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 d...

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Bibliographic Details
Authors: Hernández Abreu, Domingo, González Pinto, Severiano, Hairer, Ernst
Format: article
Publication Date:2024
Country:España
Institution:Universidad de La Laguna (ULL)
Repository:RIULL. Repositorio Institucional de la Universidad de La Laguna
OAI Identifier:oai:riull.ull.es:915/40424
Online Access:http://riull.ull.es/xmlui/handle/915/40424
Access Level:Open access
Keyword:multidimensional parabolic problem
ADI-type AMF-W method
PDE-convergence
order conditions
fractional order
Description
Summary: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 [J. Comput. Appl. Math., 417:114642, 2023] 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.