A step towards holistic discretisation of stochastic partial differential equations

Details A step towards holistic discretisation of stochastic partial differential equations A step towards holistic discretisation of stochastic partial differential equations

2003-07-22

arxiv.org/abs/math/0307290v1

Mathematics

Dynamical Systems

presented at the 5th ICIAM conference

Scientific paper

The long term aim is to use modern dynamical systems theory to derive discretisations of noisy, dissipative partial differential equations. As a first step we here consider a small domain and apply stochastic centre manifold techniques to derive a model. The approach automatically parametrises subgrid scale processes induced by spatially distributed stochastic noise. It is important to discretise stochastic partial differential equations carefully, as we do here, because of the sometimes subtle effects of noise processes. In particular we see how stochastic resonance effectively extracts new noise processes for the model which in this example helps stabilise the zero solution.

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