Integrators for Highly Oscillatory Hamiltonian Systems: A Homogenization<br/><br/>Approach

Monday, July 23, 2007 - 3:30pm - 4:00pm
Frédéric Legoll (École Nationale des Ponts-et-Chaussées)
We introduce a systematic way to construct symplectic schemes for the
numerical integration of a large class of highly oscillatory Hamiltonian
systems. The bottom line of our construction is to consider the Hamilton-Jacobi
form of the Newton equations of motion, and to perform a two-scale
expansion of the solution, for small times and high frequencies.
Several options for the derivation are presented.
The various integrators obtained are tested and compared to several
existing algorithms. The numerical results demonstrate their efficiency.

This is joint work with C. Le Bris (ENPC Paris).