Title: Glimpse of the Infinite – on the Approximation of the Dynamical Behavior for Delay and
Partial Differential Equations
Abstract: Over the last decades so-called set-oriented numerical methods have been developed for the numerical analysis of finite-dimensional dynamical systems. The underlying idea is to approximate the dynamical objects of interest by outer coverings which are created via multilevel subdivision techniques in state space. These schemes have the flexibility to be applied to a variety of problems such as the numerical approximation of invariant manifolds, global attractors or corresponding invariant measures. Since these set-oriented techniques rely on partitions of the (finite-dimensional) state space it is not obvious how to extend them to the situation where the underlying dynamical system is infinite-dimensional. However, in this talk a novel numerical framework for the computation of finite dimensional dynamical objects for infinite dimensional dynamical systems will be presented. Within this framework the classical set-oriented numerical schemes mentioned above are extended to the infinite-dimensional context. The underlying idea is to utilize appropriate embedding techniques for the reconstruction of global attractors in a certain finite dimensional space. This approach will be illustrated by the computation of global attractors both for delay and for partial differential equations such as the Mackey-Glass equation or the Kuramoto-Sivashinsky equation.
Bio: Dr Michael Dellnitz is Chair of Applied Mathematics at Paderborn University, Chairman-Professor at Institut für Industriemathematik, Professor at Paderborn Center for Parallel Computing (PC2) » Vorstand, Professor at Paderborn Institute for Scientific Computation (PaSCo).
More information here.