The Wiener-Askey Polynomial Chaos for Stochastic Differential Equations

Abstract

We present a new method for solving stochastic differential equations based on Galerking 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.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2003
Accession Number
ADA460654

Entities

People

  • Dongbin Xiu
  • George Karniadakis

Organizations

  • Brown University

Tags

DTIC Thesaurus Topics

  • Applied Mathematics
  • Computational Science
  • Difference Equations
  • Differential Equations
  • Equations
  • Fluid Dynamics
  • Gaussian Distributions
  • Gaussian Processes
  • Mathematics
  • Monte Carlo Method
  • Partial Differential Equations
  • Polynomials
  • Probability
  • Probability Density Functions
  • Random Variables
  • Stochastic Processes
  • Weighting Functions

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Statistical inference.