A step towards holistic discretisation of stochastic partial differential equations

• DOI: 10.48550/arxiv.math/0307290
• Publication Date: 2003-01-01
• Authors: A. J. Roberts
• Keywords: Stochastic Resonance

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