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Ernst Hairer; Christian Lubich
Symmetric multistep methods for charged-particle dynamics
SMAI-Journal of computational mathematics, 3 (2017), p. 205-218, doi: 10.5802/smai-jcm.25
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Class. Math.: 65L06, 65P10, 78A35, 78M25
Keywords: linear multistep method, charged particle, magnetic field, energy conservation, backward error analysis, modified differential equation, modulated Fourier expansion


A class of explicit symmetric multistep methods is proposed for integrating the equations of motion of charged particles in an electro-magnetic field. The magnetic forces are built into these methods in a special way that respects the Lagrangian structure of the problem. It is shown that such methods approximately preserve energy and momentum over very long times, proportional to a high power of the inverse stepsize. We explain this behaviour by studying the modified differential equation of the methods and by analysing the remarkably stable propagation of parasitic solution components.


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