Laboratoire de Mathématiques de Besançon - UMR 6623 CNRS

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19 novembre 2020: 1 événement

  • Séminaire d’Analyse Numérique et Calcul Scientifique

    Jeudi 19 novembre 11:00-12:00 - Maxime Breden - CMAP, Ecole Polytechnique

    Séminaire d’Analyse Numérique et Calcul Scientifique

    Résumé : An introduction to computer-assisted proofs for nonlinear equations : how to turn a numerical simulation into a theorem
    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 numerically computed approximate solution, one can then prove the existence of a true solution in a small and explicit neighborhood of the numerical approximation.
    In this talk I will discuss the main ideas behind these techniques, describe a rather general framework in which they can be applied, and showcase their interest by presenting examples of application in population dynamics and fluid dynamics.

    Lieu : En ligne

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