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Using modulated Fourier expansions of the exact and numerical solutions, it is analysed to which extent this behaviour is reproduced by the three numerical integrators used with large step sizes that do not resolve the fast gyrorotations.<\/jats:p>","DOI":"10.1007\/s00211-022-01298-9","type":"journal-article","created":{"date-parts":[[2022,6,8]],"date-time":"2022-06-08T18:30:57Z","timestamp":1654713057000},"page":"659-691","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["Large-stepsize integrators for charged-particle dynamics over multiple time scales"],"prefix":"10.1007","volume":"151","author":[{"given":"Ernst","family":"Hairer","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Christian","family":"Lubich","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yanyan","family":"Shi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2022,6,8]]},"reference":[{"issue":"1","key":"1298_CR1","doi-asserted-by":"publisher","first-page":"281","DOI":"10.1088\/0951-7715\/7\/1\/014","volume":"7","author":"G Benettin","year":"1994","unstructured":"Benettin, G., Sempio, P.: Adiabatic invariants and trapping of a point charge in a strong nonuniform magnetic field. 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