Volume 5, Issue 2-4
Fast Numerical Methods for Stochastic Computations: A Review

Dongbin Xiu

Commun. Comput. Phys., 5 (2009), pp. 242-272.

Published online: 2009-02

Preview Full PDF 332 2177
Export citation
  • 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.

  • Keywords

  • AMS Subject Headings

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{CiCP-5-242, author = {}, title = {Fast Numerical Methods for Stochastic Computations: A Review}, journal = {Communications in Computational Physics}, year = {2009}, volume = {5}, number = {2-4}, pages = {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.

}, issn = {1991-7120}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cicp/7732.html} }
TY - JOUR T1 - Fast Numerical Methods for Stochastic Computations: A Review JO - Communications in Computational Physics VL - 2-4 SP - 242 EP - 272 PY - 2009 DA - 2009/02 SN - 5 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cicp/7732.html KW - AB -

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.

Dongbin Xiu. (2020). Fast Numerical Methods for Stochastic Computations: A Review. Communications in Computational Physics. 5 (2-4). 242-272. doi:
Copy to clipboard
The citation has been copied to your clipboard