Stochastic Galerkin techniques for random ordinary differential equations
type: Item
instance of: scholarly article
title: Stochastic Galerkin techniques for random ordinary differential equations
zbMATH Open document ID: 1268.65006
published in: Numerische Mathematik
publication date: 2013-02-04T00:00:00Z
review text: The stochastic Galerkin method is introduced for solving systems of random ordinary differential equations. The idea is to develop a generalized Wiener expansion of the solution and coefficients in the truncated expansion solved by a weak Galerkin approach. The convergence is studied along with the behaviour of certain classes of Runge-Kutta methods applied to random ordinary differential equations. Some simple numerical tests are performed.
Mathematics Subject Classification ID: 65C30
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 60H35
Mathematics Subject Classification ID: 34F05
Mathematics Subject Classification ID: 65L20
zbMATH DE Number: 6134323
zbMATH Keywords: random ordinary differential equations
zbMATH Keywords: stochastic Galerkin method
zbMATH Keywords: convergence
zbMATH Keywords: numerical examples
zbMATH Keywords: generalized Wiener expansion
zbMATH Keywords: Runge-Kutta method
author: F. Augustin
author: Peter Rentrop
reviewed by: Kevin Burrage
MaRDI profile type: Publication
full work available at URL: s00211-012-0466-8
OpenAlex ID: W2169128073
cites work: Polynomial chaos for the approximation of uncertainties: Chances and limits
cites work: Q3205177
cites work: Estimation of Linear Functionals on Sobolev Spaces with Application to Fourier Transforms and Spline Interpolation
cites work: A fictitious domain approach to the numerical solution of PDEs in stochastic domains
cites work: Q4551183
cites work: Stochastic projectional schemes for random linear operator equations of the first and second kinds
cites work: On the convergence of generalized polynomial chaos expansions
cites work: Weak convergence of approximate solutions of random equations
cites work: Q4869639
cites work: Polynomial Chaos in Stochastic Finite Elements
cites work: Q3997987
cites work: Solving Ordinary Differential Equations I
cites work: Gaussian Hilbert Spaces
cites work: Pathwise Taylor schemes for random ordinary differential equations
cites work: Numerical solution of SDE through computer experiments. Including floppy disk
cites work: Q4004325
cites work: Pathwise convergent higher order numerical schemes for random ordinary differential equations
cites work: Uncertainty propagation using Wiener-Haar expansions
cites work: Multi-resolution analysis of Wiener-type uncertainty propagation schemes
cites work: Spectral Methods for Uncertainty Quantification
cites work: On Latin hypercube sampling
cites work: Finite elements for stochastic media problems
cites work: Adapted polynomial chaos expansion for failure detection
cites work: Polynomial chaos for multirate partial differential algebraic equations with random parameters
cites work: Runge–Kutta Methods for the Strong Approximation of Solutions of Stochastic Differential Equations
cites work: Thirteen ways to estimate global error
cites work: Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures
cites work: The Homogeneous Chaos
cites work: The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
DOI: 10.1007/S00211-012-0466-8
description: scientific article; zbMATH DE number 6134323