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Journal of Computational Mathematics

Symmetric multistep methods for charged-particle dynamics
Ernst Hairer1; Christian Lubich2
1 Dept. de Mathématiques, Univ. de Genève, CH-1211 Genève 24, Switzerland
2 Mathematisches Institut, Univ. Tübingen, D-72076 Tübingen, Germany
The SMAI Journal of computational mathematics, Volume 3 (2017), pp. 205-218.

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.

Published online:
DOI: 10.5802/smai-jcm.25
Classification: 65L06, 65P10, 78A35, 78M25
Keywords: linear multistep method, charged particle, magnetic field, energy conservation, backward error analysis, modified differential equation, modulated Fourier expansion
Ernst Hairer 1; Christian Lubich 2

1 Dept. de Mathématiques, Univ. de Genève, CH-1211 Genève 24, Switzerland
2 Mathematisches Institut, Univ. Tübingen, D-72076 Tübingen, Germany
License: CC-BY-NC-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Ernst Hairer; Christian Lubich. Symmetric multistep methods for charged-particle dynamics. The SMAI Journal of computational mathematics, Volume 3 (2017), pp. 205-218. doi : 10.5802/smai-jcm.25. https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.25/

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