Scientific Computing Group Seminars - Detail View

Speaker: R. Pulch

Affiliation: Bergische Universität Wuppertal, Germany

Talk Title: Polynomial Chaos for Analyzing Oscillators with Random Parameters

Invited by: Jan S Hesthaven

Time: Feb. 20 2009 11 a.m.

Location: 182 George Street, Room 110

Abstract:

Mathematical modeling of dynamical systems often leads to systems of ordinary differential equations (ODEs) or differential algebraic equations (DAEs). Typically, the systems include physical or technical parameters, which may exhibit some uncertainties. If the parameters are replaced by random variables, then a stochastic system has to be resolved for uncertainty quantification. We consider systems of ODEs and DAEs with periodic solutions, where systems with time-dependent input signals as well as autonomous oscillators are investigated. The generalized polynomial chaos yields a larger coupled system to achieve the desired information. We analyze the stability properties for periodic solutions of the coupled system in connection to the solutions of the original system. Furthermore, numerical methods are constructed to solve periodic boundary value problems of the coupled systems. We present corresponding simulation results.