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Journal of Nonlinear Science

, Volume 21, Issue 6, pp 897–920 | Cite as

Approximations to the Stochastic Burgers Equation

  • Martin Hairer
  • Jochen Voss
Article

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.

Keywords

Stochastic Burgers equation Correction term Numerical approximation 

Mathematics Subject Classification (2000)

60H35 60H15 35K55 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.University of WarwickCoventryUK
  2. 2.University of LeedsLeedsUK

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