YANN RICAUD, Laval University Rigorous numerics for periodic orbits of piecewise-smooth systems: a functional analytic approach based on Chebyshev series
نویسنده
چکیده
In this talk, we introduce a rigorous computational method for proving existence of periodic orbits of continuous and discontinuous (Filippov) piecewise-smooth differential equations. The computer-assisted proofs are obtained by combining a functional analytic approach based on Chebyshev series together with a Newton-Kantorovich type argument (the radii polynomial approach). Using this approach, we prove existence of crossing periodic orbits in a model nonlinear Filippov system and in the Chua’s circuit system. This is joint work with Marcio Gameiro (USP, Brazil) and Jean-Philippe Lessard (Université Laval, Canada).
منابع مشابه
Rigorous numerics for piecewise-smooth systems: A functional analytic approach based on Chebyshev series
In this paper, a rigorous computational method to compute solutions of piecewisesmooth 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 compute...
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