The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations

Authors:
Dongbin Xiu;George Em Karniadakis
Affiliations:
-;-
Venue:
SIAM Journal on Scientific Computing
Year:
2002

Citing 0
Cited 163

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Abstract

We present a new method for solving stochastic differential equations based on Galerkin projections and extensions of Wiener's polynomial chaos. Specifically, we represent the stochastic processes with an optimum trial basis from the Askey family of orthogonal polynomials that reduces the dimensionality of the system and leads to exponential convergence of the error. Several continuous and discrete processes are treated, and numerical examples show substantial speed-up compared to Monte Carlo simulations for low dimensional stochastic inputs.