POLYNOMIAL CHAOS FOR LINEAR DIFFERENTIAL ALGEBRAIC EQUATIONS WITH RANDOM PARAMETERS

Roland Pulch

32 citations0/0 files storedInternational Journal for Uncertainty Quantification

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Probabilistic and Robust Engineering Design Numerical methods for differential equations Fuzzy Systems and Optimization

Abstract

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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References

1991Stochastic Finite Elements: A Spectral Approach 2002The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations 2005High-Order Collocation Methods for Differential Equations with Random Inputs 2009Fast Numerical Methods for Stochastic Computations: A Review 2008Polynomial chaos for the approximation of uncertainties: Chances and limits

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2015Sensitivity analysis and model order reduction for random linear dynamical systems 2011Generalised Polynomial Chaos for a Class of Linear Conservation Laws 2013Uncertainty quantification for integrated circuits: Stochastic spectral methods 2011POLYNOMIAL CHAOS FOR SEMIEXPLICIT DIFFERENTIAL ALGEBRAIC EQUATIONS OF INDEX 1 2019Stability Preservation in Stochastic Galerkin Projections of Dynamical Systems

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