An interval Hermite-Obreschkoff method for computing rigorous bounds on the solution of an initial value problem for an ordinary differential equation

DOI10.1023/A:1009936607335zbMath0947.65081OpenAlexW4252588149MaRDI QIDQ1971082

Kenneth R. Jackson, Nedialko S. Nedialkov

Publication date: 22 March 2000

Published in: Reliable Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1023/a:1009936607335

zbMATH Keywords

stability Taylor series methods interval methods guaranteed bounds Hermite-Obreschkoff method

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) General methods in interval analysis (65G40) Numerical methods for initial value problems involving ordinary differential equations (65L05) Error bounds for numerical methods for ordinary differential equations (65L70)

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Interval arithmetic techniques for the design of controllers for nonlinear dynamical systems with applications in mechatronics ⋮ Error bounds for initial value problems by optimization ⋮ An Hermite-Obreschkoff method for stiff high-index DAE ⋮ Determination of inner and outer bounds of reachable sets through subpavings ⋮ Topological approach to rigorous numerics of chaotic dynamical systems with strong expansion of error bounds ⋮ Interval schemes for singularly perturbed initial value problems ⋮ Period doubling in the Rössler system -- a computer assisted proof ⋮ Improving SAT Modulo ODE for Hybrid Systems Analysis by Combining Different Enclosure Methods ⋮ Solving differential-algebraic equations by Taylor series. I: Computing Taylor coefficients ⋮ Unified framework for the propagation of continuous-time enclosures for parametric nonlinear ODEs

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