Documents  65L70 | enregistrements trouvés : 5

Research talks;Computer Science

This talk is about verified numerical algorithms in Isabelle/HOL, with a focus on guaranteed enclosures for solutions of ODEs. The enclosures are represented by zonotopes, arising from the use of affine arithmetic. Enclosures for solutions of ODEs are computed by set-based variants of the well-known Runge-Kutta methods.
All of the algorithms are formally verified with respect to a formalization of ODEs in Isabelle/HOL: The correctness proofs are carried out for abstract algorithms, which are specified in terms of real numbers and sets. These abstract algorithms are automatically refined towards executable specifications based on lists, zonotopes, and software floating point numbers. Optimizations for low-dimensional, nonlinear dynamics allow for an application highlight: the computation of an accurate enclosure for the Lorenz attractor. This contributes to an important proof that originally relied on non-verified numerical computations. This talk is about verified numerical algorithms in Isabelle/HOL, with a focus on guaranteed enclosures for solutions of ODEs. The enclosures are represented by zonotopes, arising from the use of affine arithmetic. Enclosures for solutions of ODEs are computed by set-based variants of the well-known Runge-Kutta methods.
All of the algorithms are formally verified with respect to a formalization of ODEs in Isabelle/HOL: The correctness proofs are ...

68T15 ; 34-04 ; 34A12 ; 37D45 ; 65G20 ; 65G30 ; 65G50 ; 65L70 ; 68N15 ; 68Q60 ; 68N30 ; 65Y04

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- xiv; 395 p.
ISBN 978-0-19-967137-3

Numerical mathematics and scientific computation

Localisation : Ouvrage RdC (BELL)

système différentiel avec délai # méthode numérique

65L05 ; 65L06 ; 34K28 ; 34K40 ; 65-02 ; 65L70 ; 65L50 ; 65L20

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- xi; 247 p.
ISBN 978-3-0348-0106-5

International series of numerical mathematics , 0159

Localisation : Ouvrage RdC (EXAC)

équation différentielle # problème de valeures limites # algorithme # estimateur d'erreur à postériori # exemples numériques

65L10 ; 65L12 ; 65L20 ; 65L50 ; 65L70 ; 65-99

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- 85 p.

Kungl. tekniska högskolans handlingar , 0130

Localisation : Ouvrage RdC (DAHL)

borne d'erreur # intégration numérique # limite # stabilité des méthodes numériques # équation différentielle ordinaire

65L20 ; 65L70

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