Polynomial chaos for boundary value problems of dynamical systems

Mathematical modelling of dynamical processes often yields systems of ordinary differential equations (ODEs) or differential algebraic equations (DAEs). We investigate corresponding boundary value problems. Considering uncertainties in physical parameters of the systems, we introduce random variables. This stochastic model is resolved by the strategy of the polynomial chaos. A non-intrusive approach requires the solution of a large number of nonlinear systems with relatively small dimension. An intrusive approach yields just a single nonlinear system with a relatively high dimension. Alternatively, we present a non-intrusive method, which still exhibits a single large nonlinear system. Consequently, the convergence of only one Newton iteration has to be ensured to solve the boundary value problem, while many initial value problems of the original ODEs or DAEs are involved.