Polynomial Chaos for the Computation of Failure Probabilities in Periodic Problems

Numerical simulation of electric circuits uses systems of differential algebraic equations (DAEs) in general. We examine forced oscillators, where the DAE models involve periodic solutions. Uncertainties in physical parameters can be described by random variables. We apply the strategy of the generalised polynomial chaos (gPC) to resolve the stochastic model. In particular, failure probabilities are determined using the approximation from gPC. We present results of numerical simulations for a system of DAEs modelling a Schmitt trigger.