Year: 2007
Communications in Computational Physics, Vol. 2 (2007), Iss. 2 : pp. 293–309
Abstract
A numerical algorithm for effective incorporation of parametric uncertainty into mathematical models is presented. The uncertain parameters are modeled as random variables, and the governing equations are treated as stochastic. The solutions, or quantities of interests, are expressed as convergent series of orthogonal polynomial expansions in terms of the input random parameters. A high-order stochastic collocation method is employed to solve the solution statistics, and more importantly, to reconstruct the polynomial expansion. While retaining the high accuracy by polynomial expansion, the resulting “pseudo-spectral” type algorithm is straightforward to implement as it requires only repetitive deterministic simulations. An estimate on error bounded is presented, along with numerical examples for problems with relatively complicated forms of governing equations.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2007-CiCP-7907
Communications in Computational Physics, Vol. 2 (2007), Iss. 2 : pp. 293–309
Published online: 2007-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Collocation methods pseudo-spectral methods stochastic inputs random differential equations uncertainty quantification.