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

DC FieldValueLanguage
dc.contributor.authorGameiro, Marcio-
dc.contributor.authorLessard, Jean-Philippe-
dc.contributor.authorRicaud, Yann-
dc.date.accessioned2016-05-16T17:34:13Z-
dc.date.available2018-01-15-
dc.date.issued2016-01-15-
dc.identifier.issn0377-0427fr_CA
dc.identifier.urihttp://hdl.handle.net/20.500.11794/1342-
dc.description.abstractIn 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.fr_CA
dc.languageengfr_CA
dc.publisherElsevierfr_CA
dc.subjectRigorous numericsfr_CA
dc.subjectPiecewise smooth systemsfr_CA
dc.subjectPeriodic orbitsfr_CA
dc.subjectContraction mapping theoremfr_CA
dc.subjectChebyshev seriesfr_CA
dc.subjectFilippovfr_CA
dc.titleRigorous numerics for piecewise-smooth systems : a functional analytic approach based on Chebyshev seriesfr_CA
dc.typeCOAR1_1::Texte::Périodique::Revue::Contribution à un journal::Article::Article de recherche-
dcterms.bibliographicCitationJournal of Computational and Applied Mathematics, Vol. 292, 654-673 (2016)fr_CA
dc.audienceProfesseurs (Enseignement supérieur)fr_CA
dc.audienceÉtudiantsfr_CA
dc.audienceDoctorantsfr_CA
dc.audienceMathématiciensfr_CA
dc.identifier.doi10.1016/j.cam.2015.05.016fr_CA
dc.subject.rvmAnalyse numériquefr_CA
dc.subject.rvmSystèmes de Tchebychevfr_CA
dc.subject.rvmOrbites périodiques (Mathématiques)fr_CA
rioxxterms.versionAccepted Manuscriptfr_CA
rioxxterms.version_of_recordhttps://doi.org/10.1016/j.cam.2015.05.016fr_CA
rioxxterms.project.funder_nameNatural Sciences and Engineering Research Council of Canadafr_CA
bul.rights.periodeEmbargo2yfr_CA
Collection:Articles publiés dans des revues avec comité de lecture

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