POLYNOMIAL CHAOS FOR LINEAR DIFFERENTIAL ALGEBRAIC EQUATIONS WITH RANDOM PARAMETERS

Abstract

Technical applications are often modeled by systems of differential algebraic equations. The systems may include parameters that involve some uncertainties. We arrange a stochastic model for uncertainty quantification in the case of linear systems of differential algebraic equations. The generalized polynomial chaos yields a larger linear system of differential algebraic equations, whose solution represents an approximation of the corresponding random process. We prove sufficient conditions such that the larger system inherits the index of the original system. Furthermore, the choice of consistent initial values is discussed. Finally, we present numerical simulations of this stochastic model.