TY - JOUR
T1 - Fast Numerical Methods for Stochastic Computations: A Review
AU - Dongbin Xiu
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 - <p style="text-align: justify;">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.</p>