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

Autor(es)

Gameiro, Marcio ^[1] ; Lessard, Jean-Philippe ^[2] ; Ricaud, Yann ^[2]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, ICMC, Dept Matemat Aplicada & Estat, BR-13560970 Sao Carlos, SP - Brazil

^[2] Univ Laval, Dept Math & Stat, Quebec City, PQ G1V 0A6 - Canada

• Tipo de documento: Artigo Científico
• Fonte: Journal of Computational and Applied Mathematics; v. 292, p. 654-673, JAN 15 2016.
• Citações Web of Science: 3

Resumo

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. (C) 2015 Published by Elsevier B.V. (AU)

• Processo FAPESP: 13/50382-7 - Rigorous computations for nonlinear partial differential equations. (fapesp-caldo)
• Beneficiário: Marcio Fuzeto Gameiro
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 10/00875-9 - Métodos topológicos e numéricos rigorosos para bifurcações em sistemas dinâmicos
• Beneficiário: Marcio Fuzeto Gameiro
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 13/07460-7 - Computações rigorosas para EDPs
• Beneficiário: Marcio Fuzeto Gameiro
• Modalidade de apoio: Auxílio à Pesquisa - Regular