Imperial College London
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Professor Grigorios A. Pavliotis

Faculty of Natural Sciences, Department of Mathematics

Professor of Applied Mathematics
 
 
 
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Contact

 

+44 (0)20 7594 8564g.pavliotis Website

 
 
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Location

 

736aHuxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Abdulle:2017:10.1137/16M1094117,
author = {Abdulle, A and Pavliotis, GA and Vaes, U},
doi = {10.1137/16M1094117},
journal = {SIAM/ASA Journal on Uncertainty Quantification},
pages = {720--761},
title = {Spectral Methods for Multiscale Stochastic Differential Equations},
url = {http://dx.doi.org/10.1137/16M1094117},
volume = {5},
year = {2017}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - This paper presents a new method for the solution of multiscale stochastic differential equations atthe diffusive time scale. In contrast to averaging-based methods, e.g., the heterogeneous multiscalemethod (HMM) or the equation-free method, which rely on Monte Carlo simulations, in this paperwe introduce a new numerical methodology that is based on a spectral method. In particular, we usean 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 convergenceis proved under suitable assumptions. Numerical experiments corroborate the theory and illustratethe performance of the method.  A comparison with the HMM and an application to singularlyperturbed stochastic PDEs are also presented.
AU  - Abdulle,A
AU  - Pavliotis,GA
AU  - Vaes,U
DO  - 10.1137/16M1094117
EP  - 761
PY  - 2017///
SN  - 2166-2525
SP  - 720
TI  - Spectral Methods for Multiscale Stochastic Differential Equations
T2  - SIAM/ASA Journal on Uncertainty Quantification
UR  - http://dx.doi.org/10.1137/16M1094117
UR  - http://hdl.handle.net/10044/1/44400
VL  - 5
ER  -
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