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

被引：7

作者：

Gameiro, Marcio ^{[1
]}

Lessard, Jean-Philippe ^{[2
]}

Ricaud, Yann ^{[2
]}

机构：

[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

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2016年 / 292卷

基金：

加拿大自然科学与工程研究理事会; 巴西圣保罗研究基金会;

关键词：

Rigorous numerics; Piecewise smooth systems; Periodic orbits; Contraction mapping theorem; Chebyshev series; Filippov; PARAMETERIZATION METHOD; CONNECTING ORBITS; (UN)STABLE MANIFOLDS; CHUAS CIRCUIT; PROOF;

D O I：

10.1016/j.cam.2015.05.016

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：654 / 673

页数：20

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