| Issue |
ESAIM: M2AN
Volume 58, Number 6, November-December 2024
Special issue - To commemorate Assyr Abdulle
|
|
|---|---|---|
| Page(s) | 2119 - 2133 | |
| DOI | https://doi.org/10.1051/m2an/2023094 | |
| Published online | 04 December 2024 | |
PDE-convergence in euclidean norm of AMF-W methods for multidimensional linear parabolic problems*
1
Departamento de Análisis Matemático, Universidad de La Laguna, 38071 La Laguna, Spain
2
Section de Mathématiques, Université de Genève, 1205 Genève, Switzerland
** Corresponding author: Ernst.Hairer@unige.ch
Received:
29
December
2022
Accepted:
15
November
2023
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.
Mathematics Subject Classification: 65M12 / 65M15 / 65M20
Key words: Multidimensional parabolic problem / ADI-type AMF-W method / PDE-convergence / order conditions / fractional order
© The authors. Published by EDP Sciences, SMAI 2024
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.