Journal
CALCOLO
Volume 57, Issue 3, Pages -Publisher
SPRINGER-VERLAG ITALIA SRL
DOI: 10.1007/s10092-020-00377-3
Keywords
Charged-particle dynamics; Two-step symmetric methods; Backward error analysis; Modulated Fourier expansion
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Funding
- Alexander von Humboldt Foundation
- Natural Science Foundation of Shandong Province (Outstanding Youth Foundation) [ZR2017JL003]
- National Natural Science Foundation of China [11571302, 11671200]
- Foundation of Innovative Science and Technology for youth in universities of Shandong Province [2019KJI001]
- project of Qingtan Scholars of Zaozhuang University
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The study of the long time conservation for numerical methods poses interesting and challenging questions from the point of view of geometric integration. In this paper, we analyze the long time energy and magnetic moment conservations of two-step symmetric methods for charged-particle dynamics. A two-step symmetric method is proposed and its long time behaviour is shown not only in a normal magnetic field but also in a strong magnetic field. The approaches to dealing with these two cases are based on the backward error analysis and modulated Fourier expansion, respectively. It is obtained from the analysis that the method has better long time conservations than the variational method which was researched recently in the literature.
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