Fast NumericalMethods for Stochastic Computations: A Review

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. AMS subject classifications: 41A10, 60H35, 65C30, 65C50

8 Figures and Tables

020402008200920102011201220132014201520162017
Citations per Year

202 Citations

Semantic Scholar estimates that this publication has 202 citations based on the available data.

See our FAQ for additional information.

Cite this paper

@inproceedings{Xiu2008FastNF, title={Fast NumericalMethods for Stochastic Computations: A Review}, author={Dongbin Xiu}, year={2008} }