29 novembre 2017: 1 événement

  • Séminaires Math-Physique

    Mercredi 29 novembre 2017 16:15-17:15 - Katharina Schratz - KIT, Karlsruhe

    Séminaire Math-Physique : Low regularity exponential-type integration schemes for NLS and KdV

    Résumé : The approximation of partial differential equations (PDEs) is nowadays a central task in numerical analysis. In the numerical time integration of PDEs an established remedy is based on the variation-of-constants formula (e.g., Gautschi- and exponential-type methods) or on dividing the full problem into a series of smaller subproblems with the hope that the subproblems can be solved more efficiently (e.g., Splitting methods). In many situations, these classical schemes offer the perfect tool to obtain a suitable approximation in the sense of providing a good resolution of the exact solution in a reasonable amount of time. This, however, drastically changes whenever `non-smooth phenomena’ enter the scene, such as for low-regularity and highly-oscillatory problems. In this talk we introduce a novel integration scheme for the NLS and KdV equation which allows us to approximate solutions under much lower regularity than for instance required for classical splitting or exponential integration schemes. Numerical experiments underline the favorable error behavior for low regularity solutions compared to classical splitting and exponential integration schemes.​

    Lieu : Salle A318

    En savoir plus : Séminaires Math-Physique

29 novembre 2017: 1 événement

  • Séminaire étudiants

    Mercredi 29 novembre 2017 14:15-15:15 - Michaël Mignard - Université de Bourgogne

    Séminaire étudiants : The Yoneda lemma

    Résumé : In the early years of group theory, the best known groups were the permutation groups. Cayley’s theorem (1854) states that in a way, all groups behave like those permutation groups.
    A category that we think we understand well is the category of sets. The Yoneda lemma suggests, in order to study a given category C, to rather study the category of functors from C to the category of sets ; actually, the lemma directly implies that C "embeds" in this category of functors, and this can be seen as a generalization of Cayley’s theorem. The goal of the talk is to prove the lemma, assuming that the audience has no background in category theory. Therefore, we will define categories, functors and natural transformations, and try to give as many examples as necessary in order to understand the concepts.

    Lieu : A318

    En savoir plus : Séminaire étudiants