Use of shrink wrapping for interval Taylor models in algorithms of computer-assisted proof of the existence of periodic trajectories in systems of ordinary differential equations

DOI10.1134/S0012266121030113zbMath1471.34073OpenAlexW3155068562MaRDI QIDQ2019639

N. M. Evstigneev, O. I. Ryabkov, D. A. Shul'min

Publication date: 21 April 2021

Published in: Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0012266121030113

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Interval and finite arithmetic (65G30)

Uses Software

• RODES

Cites Work

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• Applicability of the interval Taylor model to the computational proof of existence of periodic trajectories in systems of ordinary differential equations
• Verified integration of ODEs and flows using differential algebraic methods on high-order Taylor models
• Topological-numerical approach to the existence of periodic trajectories in ODE's
• A rigorous ODE solver and Smale's 14th problem
• Algorithms for constructing isolating sets of phase flows and computer-assisted proofs with the use of interval Taylor models
• Validated solutions of initial value problems for parametric ODEs
• Introduction to Interval Analysis
• On Taylor Model Based Integration of ODEs
• Verified high-order inversion of functional dependencies and interval Newton methods

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