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

Authors: Gameiro, Marcio; Lessard, Jean-Philippe; Ricaud, Yann
Abstract: 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.
Document Type: Article de recherche
Issue Date: 15 January 2016
Open Access Date: 15 January 2018
Document version: AM
Permalink: http://hdl.handle.net/20.500.11794/1342
This document was published in: Journal of Computational and Applied Mathematics, Vol. 292, 654-673 (2016)
https://doi.org/10.1016/j.cam.2015.05.016
Elsevier
Alternative version: 10.1016/j.cam.2015.05.016
Collection:Articles publiés dans des revues avec comité de lecture

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