{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T03:18:11Z","timestamp":1773803891831,"version":"3.50.1"},"reference-count":13,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2020,2,12]],"date-time":"2020-02-12T00:00:00Z","timestamp":1581465600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2020,2,12]],"date-time":"2020-02-12T00:00:00Z","timestamp":1581465600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100002345","name":"Eberhard Karls Universit\u00e4t T\u00fcbingen","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100002345","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer. Math."],"published-print":{"date-parts":[[2020,4]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A modification of the standard Boris algorithm, called <jats:italic>filtered<\/jats:italic> Boris algorithm, is proposed for the numerical integration of the equations of motion of charged particles in a strong non-uniform magnetic field in the asymptotic scaling known as maximal ordering. With an appropriate choice of filters, second-order error bounds in the position and in the parallel velocity, and first-order error bounds in the normal velocity are obtained with respect to the scaling parameter. This also yields a second-order approximation to the guiding center motion. The proof compares the modulated Fourier expansions of the exact and the numerical solutions. Numerical experiments illustrate the error behaviour of the filtered Boris algorithm.<\/jats:p>","DOI":"10.1007\/s00211-020-01105-3","type":"journal-article","created":{"date-parts":[[2020,2,12]],"date-time":"2020-02-12T03:03:55Z","timestamp":1581476635000},"page":"787-809","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":46,"title":["A filtered Boris algorithm for charged-particle dynamics in a strong magnetic field"],"prefix":"10.1007","volume":"144","author":[{"given":"Ernst","family":"Hairer","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Christian","family":"Lubich","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bin","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,2,12]]},"reference":[{"key":"1105_CR1","unstructured":"Boris, J.P.: Relativistic plasma simulation-optimization of a hybrid code. In: Proceeding of Fourth Conference on Numerical Simulations of Plasmas, pp 3\u201367 (1970)"},{"issue":"2","key":"1105_CR2","doi-asserted-by":"publisher","first-page":"421","DOI":"10.1103\/RevModPhys.79.421","volume":"79","author":"AJ Brizard","year":"2007","unstructured":"Brizard, A.J., Hahm, T.S.: Foundations of nonlinear gyrokinetic Theory. Rev. Modern Phys. 79(2), 421\u2013468 (2007)","journal-title":"Rev. Modern Phys."},{"issue":"2","key":"1105_CR3","doi-asserted-by":"publisher","first-page":"1120","DOI":"10.1137\/15M104952X","volume":"54","author":"F Filbet","year":"2016","unstructured":"Filbet, F., Rodrigues, L.: Asymptotically stable particle-in-cell methods for the vlasov-poisson system with a strong external magnetic field. SIAM J. Numer. Anal. 54(2), 1120\u20131146 (2016)","journal-title":"SIAM J. Numer. Anal."},{"key":"1105_CR4","doi-asserted-by":"publisher","first-page":"930","DOI":"10.1137\/S1064827596313851","volume":"20","author":"B Garc\u00eda-Archilla","year":"1999","unstructured":"Garc\u00eda-Archilla, B., Sanz-Serna, J.M., Skeel, R.D.: Long-time-step methods for oscillatory differential equations. SIAM J. Sci. Comput. 20, 930\u2013963 (1999)","journal-title":"SIAM J. Sci. Comput."},{"key":"1105_CR5","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1007\/s00211-015-0766-x","volume":"34","author":"E Hairer","year":"2016","unstructured":"Hairer, E., Lubich, C.: Long-term analysis of the St\u00f6rmer-Verlet method for Hamiltonian systems with a solution-dependent high frequency. Numer. Math. 34, 119\u2013138 (2016)","journal-title":"Numer. Math."},{"key":"1105_CR6","doi-asserted-by":"publisher","first-page":"969","DOI":"10.1007\/s10543-018-0713-1","volume":"58","author":"E Hairer","year":"2018","unstructured":"Hairer, E., Lubich, C.: Energy behaviour of the Boris method for charged-particle dynamics. BIT 58, 969\u2013979 (2018)","journal-title":"BIT"},{"key":"1105_CR7","doi-asserted-by":"crossref","unstructured":"Hairer, E., Lubich, C.: Long-term analysis of a variational integrator for charged-particle dynamics in a strong magnetic field. Numerische Mathematik (2019, to appear)","DOI":"10.1007\/s00211-019-01093-z"},{"key":"1105_CR8","unstructured":"Hairer, E., Lubich, C., Wanner, G.: Geometric Numerical Integration. Structure-Preserving Algorithms for Ordinary Differential Equations, 2 (ed.) Springer Series in Computational Mathematics 31. Springer, Berlin (2006)"},{"key":"1105_CR9","doi-asserted-by":"publisher","first-page":"403","DOI":"10.1007\/s002110050456","volume":"83","author":"M Hochbruck","year":"1999","unstructured":"Hochbruck, M., Lubich, C.: A Gautschi-type method for oscillatory second-order differential equations. Numer. Math. 83, 403\u2013426 (1999)","journal-title":"Numer. Math."},{"key":"1105_CR10","doi-asserted-by":"crossref","unstructured":"Kruskal, M.: The gyration of a charged particle. Rept. PM-S-33 (NYO-7903), Princeton University, Project Matterhorn (1958)","DOI":"10.2172\/4332926"},{"key":"1105_CR11","series-title":"Interscience Tracts on Physics and Astronomy","doi-asserted-by":"publisher","DOI":"10.1029\/RG001i003p00283","volume-title":"The adiabatic motion of charged particles","author":"TG Northrop","year":"1963","unstructured":"Northrop, T.G.: The adiabatic motion of charged particles. Interscience Tracts on Physics and Astronomy. Interscience Publishers John Wiley & Sons, New York (1963)"},{"issue":"8","key":"1105_CR12","doi-asserted-by":"publisher","first-page":"082702","DOI":"10.1063\/1.5018354","volume":"59","author":"S Possanner","year":"2018","unstructured":"Possanner, S.: Gyrokinetics from variational averaging: existence and error bounds. J. Math. Phys. 59(8), 082702 (2018)","journal-title":"J. Math. Phys."},{"issue":"8","key":"1105_CR13","doi-asserted-by":"publisher","first-page":"084503","DOI":"10.1063\/1.4818428","volume":"20","author":"H Qin","year":"2013","unstructured":"Qin, H., Zhang, S., Xiao, J., Liu, J., Sun, Y., Tang, W.M.: Why is Boris algorithm so good? Phys. Plasm. 20(8), 084503 (2013)","journal-title":"Phys. Plasm."}],"container-title":["Numerische Mathematik"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-020-01105-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00211-020-01105-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-020-01105-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,2,11]],"date-time":"2021-02-11T13:14:35Z","timestamp":1613049275000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00211-020-01105-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,2,12]]},"references-count":13,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2020,4]]}},"alternative-id":["1105"],"URL":"https:\/\/doi.org\/10.1007\/s00211-020-01105-3","relation":{},"ISSN":["0029-599X","0945-3245"],"issn-type":[{"value":"0029-599X","type":"print"},{"value":"0945-3245","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,2,12]]},"assertion":[{"value":"16 July 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 January 2020","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 February 2020","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}