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Type: Journal article
Title: A step towards holistic discretisation of stochastic partial differential equations
Author: Roberts, A.
Citation: Australia and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal, 2003; 45(E):C1-C15
Publisher: Australian Mathematical Society
Issue Date: 2003
ISSN: 1446-1811
Statement of
A. J. Roberts
Abstract: 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.
Description: © Austral. Mathematical Soc. 2003.
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Mathematical Sciences publications

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