{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T07:02:43Z","timestamp":1776841363508,"version":"3.51.2"},"reference-count":14,"publisher":"American Mathematical Society (AMS)","issue":"260","license":[{"start":{"date-parts":[[2008,5,9]],"date-time":"2008-05-09T00:00:00Z","timestamp":1210291200000},"content-version":"am","delay-in-days":366,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>Inspired by the theory of modified equations (backward error analysis), a new approach to high-order, structure-preserving numerical integrators for ordinary differential equations is developed. This approach is illustrated with the implicit midpoint rule applied to the full dynamics of the free rigid body. Special attention is paid to methods represented as B-series, for which explicit formulae for the modified differential equation are given. A new composition law on B-series, called substitution law, is presented.<\/p>","DOI":"10.1090\/s0025-5718-07-01967-9","type":"journal-article","created":{"date-parts":[[2007,7,26]],"date-time":"2007-07-26T07:46:03Z","timestamp":1185435963000},"page":"1941-1953","source":"Crossref","is-referenced-by-count":36,"title":["Numerical integrators based on modified differential equations"],"prefix":"10.1090","volume":"76","author":[{"given":"Philippe","family":"Chartier","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ernst","family":"Hairer","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gilles","family":"Vilmart","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2007,5,9]]},"reference":[{"issue":"2","key":"1","doi-asserted-by":"publisher","first-page":"231","DOI":"10.1088\/0951-7715\/3\/2\/001","article-title":"Symplectic integration of Hamiltonian systems","volume":"3","author":"Channell, P. 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Rechnen)","ISSN":"https:\/\/id.crossref.org\/issn\/0010-485X","issn-type":"print"},{"key":"9","series-title":"Cambridge Monographs on Applied and Computational Mathematics","isbn-type":"print","volume-title":"Simulating Hamiltonian dynamics","volume":"14","author":"Leimkuhler, Benedict","year":"2004","ISBN":"https:\/\/id.crossref.org\/isbn\/0521772907"},{"key":"10","unstructured":"R. I. McLachlan. A new implementation of symplectic Runge\u2013Kutta methods. To appear in SIAM J. Sci. Comput."},{"issue":"1","key":"11","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1007\/s10208-004-0118-6","article-title":"The discrete Moser-Veselov algorithm for the free rigid body, revisited","volume":"5","author":"McLachlan, Robert I.","year":"2005","journal-title":"Found. Comput. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/1615-3375","issn-type":"print"},{"key":"12","unstructured":"A. Murua. M\u00e9todos simpl\u00e9cticos desarrollables en P-series. Ph.D. thesis, Univ. 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Private communication, 2005."}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/2007-76-260\/S0025-5718-07-01967-9\/S0025-5718-07-01967-9.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2007-76-260\/S0025-5718-07-01967-9\/S0025-5718-07-01967-9.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T15:03:23Z","timestamp":1776783803000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2007-76-260\/S0025-5718-07-01967-9\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,5,9]]},"references-count":14,"journal-issue":{"issue":"260","published-print":{"date-parts":[[2007,10]]}},"alternative-id":["S0025-5718-07-01967-9"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-07-01967-9","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[2007,5,9]]}}}