| Full text | |
| Author(s): |
Total Authors: 3
|
| Affiliation: | [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
Total Affiliations: 2
|
| Document type: | Journal article |
| Source: | Journal of Computational and Applied Mathematics; v. 292, p. 654-673, JAN 15 2016. |
| Web of Science Citations: | 3 |
| 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. (C) 2015 Published by Elsevier B.V. (AU) | |
| FAPESP's process: | 13/50382-7 - Rigorous computations for nonlinear partial differential equations |
| Grantee: | Marcio Fuzeto Gameiro |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 10/00875-9 - Topological methods and rigorous numerics for bifurcations of dynamical systems |
| Grantee: | Marcio Fuzeto Gameiro |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 13/07460-7 - Rigorous computations for PDEs |
| Grantee: | Marcio Fuzeto Gameiro |
| Support Opportunities: | Regular Research Grants |