Applicability of the interval Taylor model to the computational proof of existence of periodic trajectories in systems of ordinary differential equations

DOI10.1134/S0012266118040092zbMath1415.65152OpenAlexW2803730510WikidataQ129825294 ScholiaQ129825294MaRDI QIDQ721909

N. M. Evstigneev, O. I. Ryabkov

Publication date: 20 July 2018

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

Full work available at URL: https://doi.org/10.1134/s0012266118040092

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Interval and finite arithmetic (65G30) Numerical methods for initial value problems involving ordinary differential equations (65L05)

Related Items (3)

Analysis and optimization of an adaptive interpolation algorithm for the numerical solution of a system of ordinary differential equations with interval parameters ⋮ 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 ⋮ Algorithms for constructing isolating sets of phase flows and computer-assisted proofs with the use of interval Taylor models

Uses Software

• Cosy

Cites Work

• 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
• Validated solutions of initial value problems for ordinary differential equations
• A computer-assisted proof on the stability of the Kolmogorov flows of incompressible viscous fluid
• Algorithm for the numerical proof of the existence of periodic trajectories in two-dimensional nonautonomous systems of ordinary differential equations
• A computer-assisted proof for the Kolmogorov flows of incompressible viscous fluid
• Validated solutions of initial value problems for parametric ODEs
• Introduction to Interval Analysis
• On optimization of weight quadrature formulas
• Existence of Globally Attracting Solutions for One-Dimensional Viscous Burgers Equation with Nonautonomous Forcing---A Computer Assisted Proof
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