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...

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Published inESAIM: Mathematical Modelling & Numerical Analysis (ESAIM: M2AN) Vol. 58; no. 6; pp. 2119 - 2133
Main Authors González-Pinto, Severiano, Hairer, Ernst, Hernández-Abreu, Domingo
Format Journal Article
LanguageEnglish
Published 01.11.2024
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ISSN2822-7840
2804-7214
DOI10.1051/m2an/2023094

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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 [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.
ISSN:2822-7840
2804-7214
DOI:10.1051/m2an/2023094