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2016

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

4 years 3 months ago
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 computerassisted 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. Keywords Rigorous numerics · Piecewise smooth systems · Periodic orbits · Contraction mapping theorem · Chebyshev series · Filippov Mathematics Subject Classification (2010) 34A36 · 65P99 · 65L60 · 46B45 · 37M99
Marcio Gameiro, Jean-Philippe Lessard, Yann Ricaud
Added 06 Apr 2016
Updated 06 Apr 2016
Type Journal
Year 2016
Where JCAM
Authors Marcio Gameiro, Jean-Philippe Lessard, Yann Ricaud
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