Title: Geometric Numerical Integration of Differential Equations

Abstract:

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. The field has tantalizing connections to dynamical systems, as well as to Lie groups. This talk starts by presenting a survey of geometric numerical integration methods for differential equations. If time permits, this will be followed by a discussion of some recent developments.