Applied Maths Seminar: Quispel -- Geometric Numerical Integration of Differential Equations

Reinot Quispel, La Trobe University 

Geometric Numerical Integration of Differential Equations 

Wednesday 21st Oct 14:05-14:55pm, Eastern Avenue Lecture Theatre.  

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.  

In this talk we first present a survey of geometric numerical integration methods for
differential equations, and then exemplify this by discussing symplectic vs
energy-preserving integrators for ODEs as well as for PDEs.  We have tried to make the
review of interest for a broader audience.