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.

DOI: https://doi.org/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

@article{SMAI-JCM_2017__3__205_0, author = {Ernst Hairer and Christian Lubich}, title = {Symmetric multistep methods for charged-particle dynamics}, journal = {The SMAI journal of computational mathematics}, pages = {205--218}, publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles}, volume = {3}, year = {2017}, doi = {10.5802/smai-jcm.25}, mrnumber = {3716756}, zbl = {1416.78037}, language = {en}, url = {https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.25/} }

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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