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PDE-convergence in euclidean norm of AMF-W methods for multidimensional linear parabolic problems
dc.contributor.author | Hernández Abreu, Domingo | |
dc.contributor.author | González Pinto, Severiano | |
dc.contributor.author | Hairer, Ernst | |
dc.contributor.other | Análisis Matemático | |
dc.contributor.other | Grupo de investigación ULL: "Métodos numéricos en ecuaciones diferenciales" | |
dc.date.accessioned | 2024-12-04T21:05:12Z | |
dc.date.available | 2024-12-04T21:05:12Z | |
dc.date.issued | 2024 | |
dc.identifier.uri | http://riull.ull.es/xmlui/handle/915/40424 | |
dc.description.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 [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. | en |
dc.description.abstract | Ce travail consid` ere des probl` emes paraboliques discr´ etis´ es en espace sur un domaine rectangulaire soumis ` a conditions aux limites de Dirichlet. Pour l’int´egration temporelle, on consid` ere les m´ ethodes AMF-W ` a s ´ etages qui sont des int´ egrateurs de type ADI (implicites dans des directions alternantes). Ces m´ ethodes sont particuli` erement efficaces lorsque la dimension spatiale m du probl`eme est grande. Des r´ esultats optimaux sur la convergence ind´ ependamment de la r´esolution spatiale ont r´ ecemment ´ et´ e obtenus dans [J. Calcul. Appl. Math., 417:114642, 2023] pour le cas m = 2. L’objectif du pr´esent travail est d’´ etendre ces r´ esultats ` a la dimension arbitraire m ≥ 3. Nous expliquons quels r´ esultats sur l’ordre de convergence persistent ou non en dimension m ≥ 3 en comparaison avec la dimension m = 2. | fr |
dc.format.mimetype | application/pdf | |
dc.language.iso | en | |
dc.relation.ispartofseries | Mathematical Modelling and Numerical Analysis Volume 58, Number 6 | |
dc.rights | Licencia Creative Commons (Reconocimiento-No comercial-Sin obras derivadas 4.0 Internacional) | |
dc.rights | info:eu-repo/semantics/openAccess | |
dc.rights.uri | https://creativecommons.org/licenses/by-nc-nd/4.0/deed.es_ES | |
dc.title | PDE-convergence in euclidean norm of AMF-W methods for multidimensional linear parabolic problems | en |
dc.type | info:eu-repo/semantics/article | |
dc.identifier.doi | 10.1051/m2an/2023094 | |
dc.subject.keyword | multidimensional parabolic problem | en |
dc.subject.keyword | ADI-type AMF-W method | en |
dc.subject.keyword | PDE-convergence | en |
dc.subject.keyword | order conditions | en |
dc.subject.keyword | fractional order | en |