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

Dujardin, Guillaume; Lacroix-Violet, Ingrid

Document type :

Compte-rendu et recension critique d'ouvrage

DOI :

10.48550/arXiv.2304.09672

Title :

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

Author(s) :

Dujardin, Guillaume [Auteur]

Systèmes de particules et systèmes dynamiques [Paradyse]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Lacroix-Violet, Ingrid [Auteur]
Institut Élie Cartan de Lorraine [IECL]

Journal title :

Applied Numerical Mathematics: an IMACS journal

Pages :

158-172

Publisher :

Elsevier

Publication date :

2024-08

ISSN :

0168-9274

English keyword(s) :

Numerical analysis
Runge-Kutta methods
collocation methods
stability

HAL domain(s) :

Mathématiques [math]/Analyse numérique [math.NA]

English abstract : [en]

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 ...
Show more >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.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :