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Stochastic collocation and stochastic Galerkin methods for linear differential algebraic equations.

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Název: Stochastic collocation and stochastic Galerkin methods for linear differential algebraic equations.
Autoři: Pulch, Roland1 pulchr@uni-greifswald.de
Zdroj: Journal of Computational & Applied Mathematics. May2014, Vol. 262, p281-291. 11p.
Témata: *STOCHASTIC processes, *COLLOCATION methods, *GALERKIN methods, *LINEAR differential equations, *ALGEBRAIC equations, *PARAMETER estimation
Abstrakt: Abstract: We consider time-invariant linear systems of differential algebraic equations, which include physical parameters or other parameters. Uncertainties of the parameters are modelled by random variables. We expand the corresponding random-dependent solutions in the polynomial chaos. Approximations of unknown coefficient functions can be obtained by quadrature or sampling schemes. Alternatively, stochastic collocation methods or the stochastic Galerkin approach yield larger coupled systems of differential algebraic equations. We show the equivalence of these types of numerical methods under certain assumptions. The index of the coupled systems is analysed in comparison to the original systems. Sufficient conditions for an identical index are derived. Furthermore, we present results of numerical simulations for an example. [Copyright &y& Elsevier]
Databáze: Academic Search Index
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Abstrakt:Abstract: We consider time-invariant linear systems of differential algebraic equations, which include physical parameters or other parameters. Uncertainties of the parameters are modelled by random variables. We expand the corresponding random-dependent solutions in the polynomial chaos. Approximations of unknown coefficient functions can be obtained by quadrature or sampling schemes. Alternatively, stochastic collocation methods or the stochastic Galerkin approach yield larger coupled systems of differential algebraic equations. We show the equivalence of these types of numerical methods under certain assumptions. The index of the coupled systems is analysed in comparison to the original systems. Sufficient conditions for an identical index are derived. Furthermore, we present results of numerical simulations for an example. [Copyright &y& Elsevier]
ISSN:03770427
DOI:10.1016/j.cam.2013.10.046