BEGIN:VCALENDAR VERSION:2.0 PRODID:-//Talks.cam//talks.cam.ac.uk// X-WR-CALNAME:Talks.cam BEGIN:VEVENT SUMMARY:Numerical treatment of charged particle dynamics in a magnetic fie ld - Ernst Hairer (Université de Genève) DTSTART:20191028T120000Z DTEND:20191028T124500Z UID:TALK134044@talks.cam.ac.uk CONTACT:INI IT DESCRIPTION:Combining the Lorentz force equations with Newton'\;s law g ives a secondorder di \;erential equation in space for the motion of a charged particle in a magnetic \;eld. The most natural and widely used numerical discretization is the Boris algorithm\,which is explicit\, symme tric\, volume-preserving\, and of order 2.In a \;rst part we discuss g eometric properties (long-time behaviour\, and in particularnear energy co nservation) of the Boris algorithm. This is achieved by applying standardb ackward error analysis. Near energy conservation can be obtained also in s ituations\,where the method is not symplectic.In a second part we consider the motion of a charged particle in a strong magnetic \;eld.Backward error analysis can no longer be applied\, and the accuracy (order 2) break sdown. To improve accuracy we modify the Boris algorithm in the spirit of exponentialintegrators. Theoretical estimates are obtained with the help o f modulated Fourierexpansions of the exact and numerical solutions.This ta lk is based on joint work with Christian Lubich\, and Bin Wang.Related pub lications (2017{2019) can be downloaded from LOCATION:Seminar Room 2\, Newton Institute END:VEVENT END:VCALENDAR