Year: 2009
Communications in Computational Physics, Vol. 5 (2009), Iss. 2-4 : pp. 242–272
Abstract
This paper presents a review of the current state-of-the-art of numerical methods for stochastic computations. The focus is on efficient high-order methods suitable for practical applications, with a particular emphasis on those based on generalized polynomial chaos (gPC) methodology. The framework of gPC is reviewed, along with its Galerkin and collocation approaches for solving stochastic equations. Properties of these methods are summarized by using results from literature. This paper also attempts to present the gPC based methods in a unified framework based on an extension of the classical spectral methods into multi-dimensional random spaces.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2009-CiCP-7732
Communications in Computational Physics, Vol. 5 (2009), Iss. 2-4 : pp. 242–272
Published online: 2009-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 31