Long-time behaviour of numerical integrators for charged particle dynamics (Ernst Hairer, UNIGE)

07.05.2024 14:00 – 15:00

The Boris algorithm is the most popular time integrator for charged particle motion in
electric and magnetic force fields. It is a symmetric one-step method, and it preserves
the phase volume exactly. However, it is not symplectic.
In this talk we prove near-conservation of energy over very long times in the special
cases where either the magnetic field is constant or the electric potential is quadratic.
When none of these assumptions is satisfied, it is illustrated by numerical examples
that the numerical energy can have a linear drift or its error can behave like a random walk.

We thank Martin Gander for drawing our attention to this problem.
The presented results have been obtained in collaboration with Christian Lubich.

Lieu

Conseil Général 7-9, Room 1-05, Séminaire d'analyse numérique

entrée libre