Roberts, A. J. (2006) Resolving the multitude of microscale interactions accurately models stochastic partial differential equations. LMS Journal of Computation and Mathematics, 9. pp. 193-221.
Constructing numerical models of noisy partial differential equations is very delicate. Our long term aim is to use modern dynamical systems theory to derive discretisations of dissipative stochastic partial differential equations. As a second step we consider here a small domain, representing a finite element, and derive a one degree of freedom model for the dynamics in the element; stochastic centre manifold theory supports the model. The approach automatically parametrises the microscale structures induced by spatially varying stochastic noise within the element. The crucial aspect of this work is that we explore how a multitude of microscale noise processes may interact in nonlinear dynamical systems. The analysis finds that noise processes with coarse structure across a finite element are the significant noises for the modelling. Further, the nonlinear dynamics abstracts effectively new noise sources over the macroscale time scales resolved by the model.
|Item Type:||Article (Commonwealth Reporting Category C)|
|Uncontrolled Keywords:||differential equations; numerical modelling; manifold theory|
|Subjects:||230000 Mathematical Sciences > 230200 Statistics > 230202 Stochastic Analysis and Modelling
230000 Mathematical Sciences > 230100 Mathematics > 230116 Numerical Analysis
230000 Mathematical Sciences > 230100 Mathematics > 230113 Dynamical Systems
|Depositing User:||Prof Tony Roberts|
|Date Deposited:||11 Oct 2007 00:37|
|Last Modified:||02 Jul 2013 22:36|
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