An accuracy comparison of polynomial chaos type methods for the propagation of uncertainties

DOI10.1186/2190-5983-3-2zbMath1275.65004OpenAlexW2112758148WikidataQ59302499 ScholiaQ59302499MaRDI QIDQ368157

Albert Gilg, Utz Wever, Manuel Villegas, Florian Augustin, Meinhard Paffrath, Peter Rentrop

Publication date: 18 September 2013

Published in: Journal of Mathematics in Industry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/2190-5983-3-2

zbMATH Keywords

Monte Carlodelay differential equationspolynomial chaos expansionstochastic collocationrandom ordinary differential equationsKalman filter equationnonlinear time-dependent modelspropagation of uncertanties

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Ordinary differential equations and systems with randomness (34F05) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60)

Related Items (1)

A new network approach to Bayesian inference in partial differential equations

Uses Software

• RODAS
• RADAR5

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Uncertainty propagation using Wiener-Haar expansions
• Multi-resolution analysis of Wiener-type uncertainty propagation schemes
• Stochastic Galerkin techniques for random ordinary differential equations
• Hopf bifurcation of a bacteria-immunity system with delayed quorum sensing
• Polynomial chaos for multirate partial differential algebraic equations with random parameters
• An adaptive multi-element generalized polynomial chaos method for stochastic differential equations
• The orthogonal development of non-linear functionals in series of Fourier-Hermite functionals
• On the convergence of generalized polynomial chaos expansions
• Solving Ordinary Differential Equations I
• Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures
• Polynomial chaos for the approximation of uncertainties: Chances and limits
• Performance Evaluation of Generalized Polynomial Chaos
• Spectral Methods for Uncertainty Quantification
• Gaussian Hilbert Spaces
• A new method for the nonlinear transformation of means and covariances in filters and estimators
• Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations
• The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations

This page was built for publication: An accuracy comparison of polynomial chaos type methods for the propagation of uncertainties