EDP : Maxime Breden (CMAP, Ecole Polytechnique) : An introduction to computer-assisted proofs for nonlinear equations: how to turn a numerical simulation into a theorem.

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EDP : Maxime Breden (CMAP, Ecole Polytechnique) : An introduction to computer-assisted proofs for nonlinear equations: how to turn a numerical simulation into a theorem.

20 juin / 15:30 - 16:30

Résumé : The goal of a posteriori validation methods is to get a quantitative and rigorous description of some specific solutions of nonlinear ODEs or PDEs, based on numerical simulations. The general strategy consists in combining a priori and a posteriori error estimates, interval arithmetic, and a fixed point theorem applied to a quasi-Newton operator. Starting from a nu- merically computed approximate solution, one can then prove the existence of a true solution in a small and explicit neighborhood of the numerical approximation.
I will first present the main ideas behind these techniques on a simple example, then describe a rather general framework in which they can be applied, and finally, time permitting, discuss some recent applications.

EDP : Maxime Breden (CMAP, Ecole Polytechnique) : An introduction to computer-assisted proofs for nonlinear equations: how to turn a numerical simulation into a theorem.

Détails

Date :
20 juin
Heure :
15:30 - 16:30
Catégorie d’Évènement:

Lieu

Bâtiment Fermat, salle 4205