Rigorous numerics for piecewise-smooth systems : a functional analytic approach based on Chebyshev series

Auteur(s): Gameiro, Marcio; Lessard, Jean-Philippe; Ricaud, Yann
Résumé: In this paper, a rigorous computational method to compute solutions of piecewise-smooth systems using a functional analytic approach based on Chebyshev series is introduced. A general theory, based on the radii polynomial approach, is proposed to compute crossing periodic orbits for continuous and discontinuous (Filippov) piecewise-smooth systems. Explicit analytic estimates to carry the computer-assisted proofs are presented. The method is applied to prove existence of crossing periodic orbits in a model nonlinear Filippov system and in the Chua’s circuit system. A general formulation to compute rigorously crossing connecting orbits for piecewise-smooth systems is also introduced.
Date de publication: 15 janvier 2016
Date de la mise en libre accès: 15 janvier 2018
Version du document: Accepted Manuscript
Lien permanent: http://hdl.handle.net/20.500.11794/1342
Ce document a été publié dans: Journal of Computational and Applied Mathematics, Vol. 292, 654-673 (2016)
http://dx.doi.org/10.1016/j.cam.2015.05.016
Elsevier
Autre version disponible: 10.1016/j.cam.2015.05.016
Collection(s) :Articles publiés dans des revues avec comité de lecture

Fichier(s) :
TailleFormat 
Piecewise_smooth.pdf521.17 kBAdobe PDF    Demander une copie
Tous les documents dans CorpusUL sont protégés par la Loi sur le droit d'auteur du Canada.