Geodesic
Symmetric multistep methods for charged-particle dynamics
Hairer, Ernst1 ; Lubich, Christian2
1Dept. de Mathématiques, Univ. de Genève, CH-1211 Genève 24, Switzerland
2Mathematisches Institut, Univ. Tübingen, D-72076 Tübingen, Germany
The SMAI Journal of computational mathematics, Tome 3 (2017), pp. 205-218
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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.

Publié le :
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

Hairer, Ernst  1   ; Lubich, Christian  2

1 Dept. de Mathématiques, Univ. de Genève, CH-1211 Genève 24, Switzerland
2 Mathematisches Institut, Univ. Tübingen, D-72076 Tübingen, Germany 
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     title = {Symmetric multistep methods for charged-particle dynamics},
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     pages = {205--218},
     year = {2017},
     publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles},
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Hairer, Ernst; Lubich, Christian. Symmetric multistep methods for charged-particle dynamics. The SMAI Journal of computational mathematics, Tome 3 (2017), pp. 205-218. doi: 10.5802/smai-jcm.25

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