Â-and Î-stability of collocation Runge-Kutta methods - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2023

Â-and Î-stability of collocation Runge-Kutta methods

Résumé

This paper deals with stability of classical Runge-Kutta collocation methods. When such methods are embedded in linearly implicit methods as developed in [12] and used in [13] for the time integration of nonlinear evolution PDEs, the stability of these methods has to be adapted to this context. For this reason, we develop in this paper several notions of stability, that we analyze. We provide sufficient conditions that can be checked algorithmically to ensure that these stability notions are fulfilled by a given Runge-Kutta collocation method. We also introduce examples and counterexamples used in [13] to highlight the necessity of these stability conditions in this context.
Fichier principal
Vignette du fichier
main.pdf (294.89 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-04074151 , version 1 (19-04-2023)
hal-04074151 , version 2 (10-10-2023)

Licence

Paternité

Identifiants

Citer

Guillaume Dujardin, Ingrid Lacroix-Violet. Â-and Î-stability of collocation Runge-Kutta methods. 2023. ⟨hal-04074151v2⟩
70 Consultations
48 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More