Polynomial Chaos for Semiexplicit Differential Algebraic Equations of Index 1

Mathematical modeling of technical applications often yields systems of differential algebraic equations. Uncertainties of physical parameters can be considered by the introduction of random variables. A corresponding uncertainty quantification requires one to solve the stochastic model. We focus on semiexplicit systems of nonlinear differential algebraic equations with index 1. The stochastic model is solved using the expansion of the generalised polynomial chaos. We investigate both the stochastic collocation technique and the stochastic Galerkin method to determine the unknown coefficient functions. In particular, we analyze the index of the larger coupled systems, which result from the stochastic Galerkin method. Numerical simulations of test examples are presented, where the two approaches are compared with respect to their efficiency.