Holistic discretisation ensures fidelity to Burger's equation

Roberts, A. J. (2001) Holistic discretisation ensures fidelity to Burger's equation. Applied Numerical Mathematics, 37 (3). pp. 371-396. ISSN 0168-9274


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I analyze a generalized Burgers' equation to introduce a new method of spatial discretization. The analysis is based upon center manifold theory so we are assured that the discretization accurately models the dynamics and may be constructed systematically. The trick to the application of center manifold theory is to divide the physical domain into small elements by introducing insulating internal boundaries which are later removed. Burgers' equation is used as an example to show how the concepts work in practice. The resulting finite difference models are shown to be significantly more accurate than conventional discretizations, particularly for highly nonlinear dynamics. This center manifold approach treats the dynamical equations as a whole, not just as the sum of separate terms—it is holistic. The techniques developed here may be used to accurately model the nonlinear evolution of quite general spatio-temporal dynamical systems.

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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Awaiting Author's and Publ.versions. Deposited in accordance with the copyright policy of the publisher.
Faculty/School / Institute/Centre: Historic - Faculty of Sciences - Department of Maths and Computing (Up to 30 Jun 2013)
Faculty/School / Institute/Centre: Historic - Faculty of Sciences - Department of Maths and Computing (Up to 30 Jun 2013)
Date Deposited: 11 Oct 2007 01:18
Last Modified: 02 Jul 2013 22:48
Uncontrolled Keywords: Burgers' equation; boundary conditions; mathematical models; theorem proving; partial differential equations
Fields of Research (2008): 08 Information and Computing Sciences > 0802 Computation Theory and Mathematics > 080299 Computation Theory and Mathematics not elsewhere classified
01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010301 Numerical Analysis
01 Mathematical Sciences > 0101 Pure Mathematics > 010110 Partial Differential Equations
Socio-Economic Objectives (2008): E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
Identification Number or DOI: https://doi.org/10.1016/S0168-9274(00)00053-2
URI: http://eprints.usq.edu.au/id/eprint/2975

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