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Polynomial Chaos for Analysing Periodic Processes of Differential Algebraic Equations with Random Parameters
Author(s) -
Pulch Roland
Publication year - 2008
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200810069
Subject(s) - polynomial chaos , polynomial , mathematics , stochastic differential equation , dynamical systems theory , algebraic number , differential equation , algebraic equation , stochastic process , boundary value problem , differential algebraic equation , deterministic system (philosophy) , deterministic simulation , statistical physics , mathematical analysis , monte carlo method , ordinary differential equation , physics , nonlinear system , quantum mechanics , statistics
Mathematical models of dynamical systems typically include technical parameters. Assuming an uncertainty, some parameters are replaced by random variables and the solution of the time–dependent system becomes a stochastic process. We consider forced oscillators, which are modelled by systems of differential algebraic equations. Consequently, periodic boundary conditions are imposed on the system. We apply the technique of the generalised polynomial chaos to resolve the stochastic model. Numerical simulations based on the electric circuit of a transistor amplifier are presented. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)