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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
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: |
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| 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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