Computer algebra derives discretisations of the stochastically forced Burgers' partial differential equation

Roberts, A. J. (2006) Computer algebra derives discretisations of the stochastically forced Burgers' partial differential equation. 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 (Unpublished)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 routine documented here empowers you to reproduce and check many of the details described elsewhere. We consider a region of a spatial domain far from any boundaries, and apply stochastic centre manifold techniques to derive a discrete model for the dynamics. The approach automatically parametrises the microscale structures induced by spatially varying stochastic noise within each element. The crucial aspect of this work is that we explore how many noise processes and neighbouring elements 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 00:39
Last Modified: 02 Jul 2013 22:37
Uncontrolled Keywords: computer algebra, Burgers' partial differential equation, stochastic analysis
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/1322

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