Validated computation of the local truncation error of Runge–Kutta methods with automatic differentiation

DOI10.1080/10556788.2018.1459620zbMath1397.65068OpenAlexW2802574492WikidataQ129965557 ScholiaQ129965557MaRDI QIDQ4685566

Julien Alexandre dit Sandretto, Alexandre Chapoutot, Olivier Mullier

Publication date: 9 October 2018

Published in: Optimization Methods and Software (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10556788.2018.1459620

zbMATH Keywords

interval analysisautomatic differentiationRunge-Kutta methodsaffine arithmeticvalidated numerical integration

Mathematics Subject Classification ID

General methods in interval analysis (65G40) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Error bounds for numerical methods for ordinary differential equations (65L70) Complexity and performance of numerical algorithms (65Y20) Numerical integration (65D30)

Related Items (9)

Tuning as convex optimisation: a polynomial tuner for multi-parametric combinatorial samplers ⋮ An improved algorithm for the control synthesis of nonlinear sampled switched systems ⋮ Lie symmetries applied to interval integration ⋮ A rigorous implicit \(C^1\) Chebyshev integrator for delay equations ⋮ Verification of machine learning based cyber-physical systems: a comparative study ⋮ Formally-verified round-off error analysis of Runge-Kutta methods ⋮ Phase error analysis of implicit Runge-Kutta methods: new classes of minimal dissipation low dispersion high order schemes ⋮ Parameter synthesis of polynomial dynamical systems ⋮ A theoretical proof of the invalidity of dynamic relaxation arc-length method for snap-back problems

Uses Software

• Cosy
• ODEIntegrator

Cites Work

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• Introduction to Interval Analysis
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