|Date:||Wed, November 9, 2011|
|Place:||Research I Seminar room|
Abstract: Symplectic time integration schemes for differential equations are observed to preserve invariants of mechanical systems, such as the energy, extremely well over long times. For ordinary differential equations, this is a well-understood phenomenon; the main tool of proof is backward error analysis, which I will explain.
For partial differential equations, backward error analysis suffers from serious analytical difficulties. I will briefly survey what has been done so far, and then turn to a new variational approach which, at the current time, does not yet provide a complete proof, but may point a way out of the analytical difficulties.