Stochastic collocation and stochastic Galerkin methods for linear differential algebraic equations

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摘要

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.

论文关键词:Differential algebraic equations,Index,Polynomial chaos,Stochastic collocation method,Stochastic Galerkin method,Uncertainty quantification

论文评审过程:Received 9 November 2012, Revised 18 October 2013, Available online 4 November 2013.

论文官网地址:https://doi.org/10.1016/j.cam.2013.10.046