Rechercher


Accueil

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

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

Pour en savoir plus sur cet événement, consultez l'article Séminaires Math-Physique