Stochastic finite elements: a spectral approach
Stochastic finite elements: a spectral approach
Applied Numerical Mathematics
High-Order Collocation Methods for Differential Equations with Random Inputs
SIAM Journal on Scientific Computing
Multi time scale differential equations for simulating frequency modulated signals
Applied Numerical Mathematics - Tenth seminar on and differential-algebraic equations (NUMDIFF-10)
Modelling and simulation of autonomous oscillators with random parameters
Mathematics and Computers in Simulation
Polynomial chaos for boundary value problems of dynamical systems
Applied Numerical Mathematics
Uncertainty quantification for integrated circuits: stochastic spectral methods
Proceedings of the International Conference on Computer-Aided Design
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In radio frequency applications, a multivariate model yields an efficient representation of signals with amplitude modulation and/or frequency modulation. Periodic boundary value problems of multirate partial differential algebraic equations (MPDAEs) have to be solved to reproduce the quasiperiodic signals. Typically, technical parameters appear in the system, which may exhibit some uncertainty. Substitution by random variables results in a corresponding stochastic model. We apply the technique of the generalised polynomial chaos to obtain according solutions. A Galerkin approach yields larger coupled systems of MPDAEs. We analyse the properties of the coupled systems with respect to the original formulations. Thereby, we focus on the case of frequency modulation, since the case of amplitude modulation alone is straightforward.