Polynomial Chaos for Analysing Periodic Processes of Differential Algebraic Equations with Random Parameters

Abstract

Mathematical models of dynamical systems typically include technical parameters. Assuming an uncertainty, some parameters are replaced by random variables and the solution of the time–dependent system becomes a stochastic process. We consider forced oscillators, which are modelled by systems of differential algebraic equations. Consequently, periodic boundary conditions are imposed on the system. We apply the technique of the generalised polynomial chaos to resolve the stochastic model. Numerical simulations based on the electric circuit of a transistor amplifier are presented. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)