{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,4]],"date-time":"2026-05-04T13:47:29Z","timestamp":1777902449007,"version":"3.51.4"},"reference-count":29,"publisher":"SAGE Publications","issue":"11","license":[{"start":{"date-parts":[[2019,4,8]],"date-time":"2019-04-08T00:00:00Z","timestamp":1554681600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["SIMULATION"],"published-print":{"date-parts":[[2019,11]]},"abstract":"<jats:p>Geometric integrators allow preservation of specific geometric properties of the exact flow of differential equation systems, such as energy, phase-space volume, and time-reversal symmetry, and are particularly reliable for long-run integration. In this study, variable step size composition methods and Gauss methods are implemented in Matlab library integrators, and are tested with several representative problems, including the Kepler problem, the outer solar system and a conservative Lotka\u2013Volterra system. Variable step size integrators often perform better than their fixed step size counterparts and the numerical results show excellent long time preservation of the Hamiltonian in these examples.<\/jats:p>","DOI":"10.1177\/0037549719835026","type":"journal-article","created":{"date-parts":[[2019,4,8]],"date-time":"2019-04-08T04:50:53Z","timestamp":1554699053000},"page":"1055-1067","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":1,"title":["An implementation of geometric integration within Matlab"],"prefix":"10.1177","volume":"95","author":[{"given":"Guillaume","family":"Chauvon","sequence":"first","affiliation":[{"name":"Service de Math\u00e9matique et Recherche op\u00e9rationnelle, Universit\u00e9 de Mons, Belgium"},{"name":"Service d\u2019Automatique, Universit\u00e9 de Mons, Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Philippe","family":"Saucez","sequence":"additional","affiliation":[{"name":"Service de Math\u00e9matique et Recherche op\u00e9rationnelle, Universit\u00e9 de Mons, Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alain","family":"Vande Wouwer","sequence":"additional","affiliation":[{"name":"Service d\u2019Automatique, Universit\u00e9 de Mons, Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2019,4,8]]},"reference":[{"key":"bibr1-0037549719835026","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/39\/19\/S01"},{"key":"bibr2-0037549719835026","volume-title":"Geometric numerical integration. Structure-preserving algorithms for ordinary differential equations","author":"Hairer E","year":"2006","edition":"2"},{"key":"bibr3-0037549719835026","volume-title":"Simulating Hamiltonian dynamics","author":"Leimkuhler B","year":"2004"},{"key":"bibr4-0037549719835026","doi-asserted-by":"publisher","DOI":"10.1007\/BF00048485"},{"key":"bibr5-0037549719835026","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/39\/19\/S03"},{"key":"bibr6-0037549719835026","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.2001.6774"},{"key":"bibr7-0037549719835026","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-55692-0_5"},{"key":"bibr8-0037549719835026","volume-title":"Simulation of dynamic systems with Matlab\u00ae and Simulink","author":"Klee H","year":"2012"},{"key":"bibr9-0037549719835026","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-06790-2"},{"key":"bibr10-0037549719835026","first-page":"1","volume":"18","author":"Shampine LF","year":"1997","journal-title":"J Sci Comput"},{"key":"bibr11-0037549719835026","doi-asserted-by":"publisher","DOI":"10.1021\/ie0302894"},{"key":"bibr12-0037549719835026","doi-asserted-by":"publisher","DOI":"10.1016\/j.cej.2008.05.038"},{"key":"bibr13-0037549719835026","doi-asserted-by":"publisher","DOI":"10.1016\/j.cej.2009.08.017"},{"key":"bibr14-0037549719835026","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4899-3093-4"},{"key":"bibr15-0037549719835026","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRev.159.98"},{"key":"bibr16-0037549719835026","doi-asserted-by":"publisher","DOI":"10.1017\/S0962492902000144"},{"key":"bibr17-0037549719835026","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-9274(97)00061-5"},{"key":"bibr18-0037549719835026","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827595284658"},{"key":"bibr19-0037549719835026","doi-asserted-by":"publisher","DOI":"10.1137\/0914050"},{"key":"bibr20-0037549719835026","doi-asserted-by":"publisher","DOI":"10.1145\/363707.363723"},{"key":"bibr21-0037549719835026","volume-title":"Solving ordinary differential equations. I. Nonstiff problems","author":"Hairer E","year":"1993","edition":"2"},{"key":"bibr22-0037549719835026","first-page":"269","volume":"83","author":"Laburta MP.","year":"1997","journal-title":"J Comput"},{"key":"bibr23-0037549719835026","doi-asserted-by":"publisher","DOI":"10.1086\/115629"},{"key":"bibr24-0037549719835026","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1988-0935077-0"},{"key":"bibr25-0037549719835026","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2013.07.025"},{"key":"bibr26-0037549719835026","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-03-01546-1"},{"key":"bibr27-0037549719835026","doi-asserted-by":"publisher","DOI":"10.1006\/jdeq.1998.3443"},{"key":"bibr28-0037549719835026","volume-title":"The behaviour and attractiveness of the Lotka\u2013Volterra equations","author":"Idema T.","year":"2005"},{"key":"bibr29-0037549719835026","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2003.02.013"}],"container-title":["SIMULATION"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/0037549719835026","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.1177\/0037549719835026","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/0037549719835026","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T11:29:55Z","timestamp":1777634995000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1177\/0037549719835026"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,4,8]]},"references-count":29,"journal-issue":{"issue":"11","published-print":{"date-parts":[[2019,11]]}},"alternative-id":["10.1177\/0037549719835026"],"URL":"https:\/\/doi.org\/10.1177\/0037549719835026","relation":{},"ISSN":["0037-5497","1741-3133"],"issn-type":[{"value":"0037-5497","type":"print"},{"value":"1741-3133","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,4,8]]}}}