Spectral Methods for Multiscale Stochastic Differential Equations

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Title: Spectral Methods for Multiscale Stochastic Differential Equations
Author(s): Abdulle, A
Pavliotis, GA
Vaes, U
Item Type: Journal Article
Abstract: This paper presents a new method for the solution of multiscale stochastic differential equations at the diffusive time scale. In contrast to averaging-based methods, e.g., the heterogeneous multiscale method (HMM) or the equation-free method, which rely on Monte Carlo simulations, in this paper we introduce a new numerical methodology that is based on a spectral method. In particular, we use an expansion in Hermite functions to approximate the solution of an appropriate Poisson equation, which is used in order to calculate the coefficients of the homogenized equation. Spectral convergence is proved under suitable assumptions. Numerical experiments corroborate the theory and illustrate the performance of the method. A comparison with the HMM and an application to singularly perturbed stochastic PDEs are also presented.
Publication Date: 8-Aug-2017
Date of Acceptance: 8-Feb-2017
URI: http://hdl.handle.net/10044/1/44400
DOI: https://dx.doi.org/10.1137/16M1094117
ISSN: 2166-2525
Publisher: Society for Industrial and Applied Mathematics
Start Page: 720
End Page: 761
Journal / Book Title: SIAM/ASA Journal on Uncertainty Quantification
Volume: 5
Issue: 1
Copyright Statement: © 2017 SIAM and ASA. Published by SIAM and ASA under the terms of the Creative Commons 4.0 license
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/L025159/1
Publication Status: Published
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences

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