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Type: Journal article
Title: Derive boundary conditions for holistic discretisations of Burgers' equation
Author: Roberts, A.
Citation: Australia and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal, 2003; 44(E):C664-C686
Publisher: Australian Mathematical Society
Issue Date: 2003
ISSN: 1446-1811
Statement of
A. J. Roberts
Abstract: I previously used Burgers' equation to introduce a new method of numerical discretisation of \pde{}s. The analysis is based upon centre manifold theory so we are assured that the discretisation accurately models all the processes and their subgrid scale interactions. Here I show how boundaries to the physical domain may be naturally incorporated into the numerical modelling of Burgers' equation. We investigate Neumann and Dirichlet boundary conditions. As well as modelling the nonlinear advection, the method naturally derives symmetric matrices with constant bandwidth to correspond to the self-adjoint diffusion operator. The techniques developed here may be used to accurately model the nonlinear evolution of quite general spatio-temporal dynamical systems on bounded domains.
Description: © Austral. Mathematical Soc. 2003.
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Mathematical Sciences publications

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