9 research outputs found
Mini-Workshop: Dynamics of Stochastic Systems and their Approximation
The aim of this workshop was to bring together specialists in the area of stochastic dynamical systems and stochastic numerical analysis to exchange their ideas about the state of the art of approximations of stochastic dynamics. Here approximations are considered in the analytical sense in terms of deriving reduced dynamical systems, which are less complex, as well as in the numerical sense via appropriate simulation methods. The main theme is concerned with the efficient treatment of stochastic dynamical systems via both approaches assuming that ideas and methods from one ansatz may prove beneficial for the other. A particular goal was to systematically identify open problems and challenges in this area
Random Attractors for Stochastic Partly Dissipative Systems
We prove the existence of a global random attractor for a certain class of
stochastic partly dissipative systems. These systems consist of a partial (PDE)
and an ordinary differential equation (ODE), where both equations are coupled
and perturbed by additive white noise. The deterministic counterpart of such
systems and their long-time behaviour have already been considered but there is
no theory that deals with the stochastic version of partly dissipative systems
in their full generality. We also provide several examples for the application
of the theory.Comment: 29 page
MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications
Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described
Generalized averaged Gaussian quadrature and applications
A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal