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.|
|Issue Date:||15 January 2016|
|Open Access Date:||15 January 2018|
|This document was published in:||Journal of Computational and Applied Mathematics, Vol. 292, 654-673 (2016)|
|Collection:||Articles publiés dans des revues avec comité de lecture|
All documents in CorpusUL are protected by Copyright Act of Canada.