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Homepage: http://wwwmaths.anu.edu.au/conferences/gni/
Organizers: Reinout Quispel, Robert McLachlan
Description:
Recently a revolution has been taking place in the field of computational differential equations.
Since the time of Poincare,it has been known that qualitative geometric properties of ordinary differential equations play a crucial role in determining their long-time dynamical behaviour.Only in the last decade, however,has a substantial effort started to preserve various geometric properties of ODEs exactly (i.e. up to machine accuracy) in numerical integration algorithms.This has led to a veritable explosion of different methods:
Symplectic integrators for hamiltonian ODEs Lagrangian integrators for Lagrangian ODEs Symmetry-preserving integrators Integrators that preserve first integrals Integrators that preserve volume Integrators that contract volume Integrators that preserve Lyapunov functions Isospectral integrators Lie group integrators Unitary integrators Integrable integrators Lie-Poisson integrators
In this very new and exciting field there are of course many open questions.With the current proliferation of geometric methods,the time is ripe to find some common ground between all these various methods. The main aims of this Symposium are to bring together representatives of as many different subfields of geometric integration as possible (in order to disseminate the rapid developments in each of the subfields),to bring together theorists and people interested in applications (eg to PDE,fluid dynamics,geophysical fluids,molecular dynamics and astrophysics), but also, importantly,we plan to allow plenty of time for informal discussions and cross-fertilization.
Date received: September 21, 2000
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