The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
SIAM Journal on Scientific Computing
Adaptive Generalized Polynomial Chaos for Nonlinear Random Oscillators
SIAM Journal on Scientific Computing
High-Order Collocation Methods for Differential Equations with Random Inputs
SIAM Journal on Scientific Computing
Polynomial chaos for multirate partial differential algebraic equations with random parameters
Applied Numerical Mathematics
Polynomial chaos for simulating random volatilities
Mathematics and Computers in Simulation
Uncertainty quantification for integrated circuits: stochastic spectral methods
Proceedings of the International Conference on Computer-Aided Design
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Abstract: We consider periodic problems of autonomous systems of ordinary differential equations or differential algebraic equations. To quantify uncertainties of physical parameters, we introduce random variables in the systems. Phase conditions are required to compute the resulting periodic random process. It follows that the variance of the process depends on the choice of the phase condition. We derive a necessary condition for a random process with a minimal total variance by the calculus of variations. A corresponding numerical method is constructed based on the generalised polynomial chaos. We present numerical simulations of two test examples.