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...
| Authors: | , , |
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| 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 |
| 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. |
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