Polynomial interpolation and a priori bootstrap for computer-assisted proofs in nonlinear ODEs

DOI10.3934/dcdsb.2018164zbMath1398.65092arXiv1704.03128OpenAlexW2605817388WikidataQ129627692 ScholiaQ129627692MaRDI QIDQ1670296

Maxime Breden, Jean-Philippe Lessard

Publication date: 5 September 2018

Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1704.03128

zbMATH Keywords

computer-assisted proofnonlinear ODEspiecewise polynomial interpolationABC flowsPicard-like operator

Mathematics Subject Classification ID

Periodic orbits of vector fields and flows (37C27) Algorithms with automatic result verification (65G20) Numerical integration (65D30) Approximation methods and numerical treatment of dynamical systems (37M99) Numerical problems in dynamical systems (65P99)

Related Items

A numerical verification method to specify homoclinic orbits as application of local Lyapunov functions ⋮ Validated integration of differential equations with state-dependent delay ⋮ Rigorous numerics for ODEs using Chebyshev series and domain decomposition ⋮ Validated computations for connecting orbits in polynomial vector fields ⋮ A Lorenz-type attractor in a piecewise-smooth system: Rigorous results ⋮ Sliding homoclinic bifurcations in a Lorenz-type system: Analytic proofs

Uses Software

• INTLAB
• dcc
• CAPD
• PolyPaver
• Taylor
• CkAnalytic

Cites Work

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