BIRS Workshop Lecture Videos

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BIRS Workshop Lecture Videos

Large Long-time behaviour of numerical integrators for charged particle dynamics Hairer, Ernst


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. Nevertheless, numerical experiments confirm an excellent long-time near energy preservation of the system. In this talk we present a multistep extension of the Boris algorithm, which is explicit, symmetric, and has arbitrarily high order. Near preservation of energy and momentum for the underlying one-step method, and the boundedness of parasitic solution components are proved. A rigorous proof for the excellent near energy preservation of the Boris algorithm is still missing. (We thank Martin Gander for drawing our attention to this problem.)

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