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Approximations to the stochastic Burgers equation

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Hairer, Martin and Voss, Jochen (2011) Approximations to the stochastic Burgers equation. Journal of Nonlinear Science, Vol.21 (No.6). pp. 897-920. doi:10.1007/s00332-011-9104-3

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Official URL: http://dx.doi.org/10.1007/s00332-011-9104-3

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Abstract

This article is devoted to the numerical study of various finite-difference approximations to the stochastic Burgers equation. Of particular interest in the one-dimensional case is the situation where the driving noise is white both in space and in time. We demonstrate that in this case, different finite-difference schemes converge to different limiting processes as the mesh size tends to zero. A theoretical explanation of this phenomenon is given and we formulate a number of conjectures for more general classes of equations, supported by numerical evidence.

Item Type: Journal Article
Divisions: Faculty of Science, Engineering and Medicine > Science > Mathematics
Journal or Publication Title: Journal of Nonlinear Science
Publisher: Springer
ISSN: 0938-8974
Official Date: 2011
Dates:
DateEvent
2011Published
Volume: Vol.21
Number: No.6
Page Range: pp. 897-920
DOI: 10.1007/s00332-011-9104-3
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Funder: Engineering and Physical Sciences Research Council (EPSRC) , Royal Society
Grant number: EP/E002269/1 EP/D071593/1 (EPSRC)

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