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Computational Techniques and Applications Conference and Workshops - CTAC99
September 20-24, 1999
The Australian National University
Canberra, ACT, Australia

Organizers
Mike Osborne, Bob Gingold, Steve Roberts, David Harrar II, Thanh Tran, Bob Anderssen, Henry Gardner, Markus Hegland, Lutz Grosz

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Holistic finite differences accurately model the dynamics of the Kuramoto-Sivashinsky equation
by
Tony MacKenzie
University of Southern Queensland
Coauthors: Tony Roberts (University of Southern Queensland)

We analyse the fourth order nonlinear Kuramoto-Sivashinsky equation to develop an accurate finite difference approximation to its dynamics. The analysis is based upon centre manifold theory so we are assured that the finite difference model accurately models the dynamics and may be constructed systematically. The theory is applied after dividing the physical domain into small elements by introducing insulating internal boundaries which are later removed. The Kuramoto-Sivashinsky equation is used as an example to show how holistic finite differences may be applied to fourth order nonlinear spatio-temporal dynamical systems. This novel centre manifold approach is holistic in the sense that it treats the dynamical equations as a whole, not just as the sum of separate terms.

Date received: September 1, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cadr-29.