Work

Wiener chaos vs stochastic collocation methods for linear advection-diffusion equations with multiplicative white noise

Year: 2015

Type: preprint

Abstract: We compare Wiener chaos and stochastic collocation methods for linear advection-reaction-diffusion equations with multiplicative white noise. Both methods are constructed based on a recursive multi-stage algorithm for long-time integration. We derive error estimates for both methods and compare their numerical performance. Numerical results confirm that the recursive multi-stage stochastic collocation method is of order $Δ$ (time step size) in the second-order moments while the recursive multi-stage Wiener chaos method is of order $Δ^{\mathsf{N}}+Δ^2$ ($\mathsf{N}$ is the order of Wiener chaos) for advection-diffusion-reaction equations with commutative noises, in agreement with the theoretical error estimates. However, for non-commutative noises, both methods are of order one in the second-order moments.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1505.03771

Authors: Zhang, Zhongqiang, Tretyakov, Michael V., Rozovskii, Boris, Karniadakis, George E.

Institutions: Worcester Polytechnic Institute, Brown University, University of Nottingham

Language: English

Topic: Numerical methods for differential equations

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, U.S. Department of Energy, Brown University, Leverhulme Trust, Multidisciplinary University Research Initiative, Engineering and Physical Sciences Research Council, Army Research Office

Awards: G1320426082, G2747436919, Robustness-performance optimisation for automated composites manufacture, New evolution equations of the joint response-excitation PDF for stochastic modeling: Theory and numerical methods, G6274897657, RTG: Integrating Dynamics and Stochastics (IDyaS), G7452299184, G8727049869

OpenAlex ID: W2952455547

Cites: 21

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