Geometric Numerical Integration of Differential Equations
Reinout Quispel, La Trobe University, Melbourne Australia

Geometric integration is the numerical integration of a differential equation, while preserving one or more of its geometric/physical properties exactly, i.e. to within round-off error.

Many of these geometric properties are of crucial importance in physical applications: preservation of energy, momentum, angular momentum,  phase-space volume, symmetries, time-reversal symmetry, symplectic structure  and dissipation are examples.

In this talk we present a survey of geometric numerical integration methods for differential equations. We include some very new and exciting results on the exact preservation of energy for ODEs as well as PDEs. These results are related to very classical results obtained by Lax and co-workers in the early eighties.

Our aim is to make the review of use for both the novice and the more experienced practitioner interested in the new developments and directions of the past decade.