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International Journal for Uncertainty Quantification
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ISSN Печать: 2152-5080
ISSN Онлайн: 2152-5099

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International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.v1.i3.30
pages 223-240

POLYNOMIAL CHAOS FOR LINEAR DIFFERENTIAL ALGEBRAIC EQUATIONS WITH RANDOM PARAMETERS

Roland Pulch
Institute for Mathematics and Computer Science, University of Greifswald, Walther-Rathenau-Str. 47, D-17489 Greifswald, Germany

Краткое описание

Technical applications are often modeled by systems of differential algebraic equations. The systems may include parameters that involve some uncertainties. We arrange a stochastic model for uncertainty quantification in the case of linear systems of differential algebraic equations. The generalized polynomial chaos yields a larger linear system of differential algebraic equations, whose solution represents an approximation of the corresponding random process. We prove sufficient conditions such that the larger system inherits the index of the original system. Furthermore, the choice of consistent initial values is discussed. Finally, we present numerical simulations of this stochastic model.


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