Computer algebra resolves a multitude of microscale interactions to model stochastic partial differential equations

Roberts, A. J. (2005) Computer algebra resolves a multitude of microscale interactions to model stochastic partial differential equations. Technical Report. University of Southern Queensland, Faculty of Sciences, Department of Maths and Computing, Toowoomba, Australia. (Unpublished)

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Abstract

[Abstract]: The computer algebra routines documented here empower you to reproduce and check many of the details described by Roberts (2006). We consider a small spatial domain, representing a finite element, and apply stochastic centre manifold techniques to derive a one degree of freedom model for the dynamics in the element. 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 many noise processes may interact in nonlinear dynamics.


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Item Type: Report (Technical Report)
Item Status: Live Archive
Additional Information: USQ publication.
Depositing User: Prof Tony Roberts
Faculty / Department / School: Historic - Faculty of Sciences - Department of Maths and Computing
Date Deposited: 11 Oct 2007 00:37
Last Modified: 02 Jul 2013 22:36
Uncontrolled Keywords: computer algebra, stochastic partial differential equations
Fields of Research (FOR2008): 01 Mathematical Sciences > 0101 Pure Mathematics > 010109 Ordinary Differential Equations, Difference Equations and Dynamical Systems
01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010301 Numerical Analysis
01 Mathematical Sciences > 0104 Statistics > 010406 Stochastic Analysis and Modelling
URI: http://eprints.usq.edu.au/id/eprint/1242

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