Computer algebra derives the slow manifold of patch or element dynamics on lattices in two dimensions

MacKenzie, Tony and Roberts, A. J. (2014) Computer algebra derives the slow manifold of patch or element dynamics on lattices in two dimensions. Technical Report. University of Adelaide , Adelaide, Australia. [Report]

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Abstract

Developments in dynamical systems theory provides new support for the discretisation of pdes and other microscale systems. Here we explore the methodology applied to the gap-tooth scheme in the equation-free approach of Kevrekidis in two spatial dimensions. The algebraic detail is enormous so we detail computer algebra procedures to handle the enormity. However, modelling the dynamics on 2D spatial patches appears to require a mixed numerical and algebraic approach that is detailed in this report. Being based upon the computation of residuals, the procedures here may be simply adapted to a wide class of reaction-diffusion equations.


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Item Type: Report (Technical Report)
Item Status: Live Archive
Additional Information: This publication is copyright. It may be reproduced in whole or in part for the purposes of study, research, or review, but is subject to the inclusion of an acknowledgment of the source. Accepted 10 Feb 2011, but not published until 2014.
Faculty / Department / School: Current - Faculty of Health, Engineering and Sciences - School of Agricultural, Computational and Environmental Sciences
Date Deposited: 04 Mar 2015 04:22
Last Modified: 11 Dec 2017 06:44
Fields of Research : 01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010301 Numerical Analysis
01 Mathematical Sciences > 0102 Applied Mathematics > 010204 Dynamical Systems in Applications
08 Information and Computing Sciences > 0802 Computation Theory and Mathematics > 080205 Numerical Computation
Socio-Economic Objective: E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
URI: http://eprints.usq.edu.au/id/eprint/21594

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