{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,12]],"date-time":"2026-03-12T20:59:29Z","timestamp":1773349169923,"version":"3.50.1"},"reference-count":12,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2013,2,15]],"date-time":"2013-02-15T00:00:00Z","timestamp":1360886400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numer. Math."],"published-print":{"date-parts":[[2013,7]]},"DOI":"10.1007\/s00211-013-0522-z","type":"journal-article","created":{"date-parts":[[2013,2,14]],"date-time":"2013-02-14T06:42:21Z","timestamp":1360824141000},"page":"517-539","source":"Crossref","is-referenced-by-count":8,"title":["Symmetric multistep methods for constrained Hamiltonian systems"],"prefix":"10.1007","volume":"124","author":[{"given":"Paola","family":"Console","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ernst","family":"Hairer","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Christian","family":"Lubich","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2013,2,15]]},"reference":[{"key":"522_CR1","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1016\/0021-9991(83)90014-1","volume":"52","author":"HC Andersen","year":"1983","unstructured":"Andersen, H.C.: Rattle: a \u201cvelocity\u201d version of the shake algorithm for molecular dynamics calculations. J. Comput. Phys. 52, 24\u201334 (1983)","journal-title":"J. Comput. Phys."},{"issue":"8","key":"522_CR2","doi-asserted-by":"crossref","first-page":"609","DOI":"10.1002\/zamm.19970770813","volume":"77","author":"C Ar\u00e9valo","year":"1997","unstructured":"Ar\u00e9valo, C., F\u00fchrer, C., S\u00f6derlind, G.: $\\beta $-Blocked multistep methods for Euler\u2013Lagrange DAEs: linear analysis. Z. Angew. Math. Mech. 77(8), 609\u2013617 (1997)","journal-title":"Z. Angew. Math. Mech."},{"key":"522_CR3","doi-asserted-by":"crossref","unstructured":"Console, P., Hairer, E.: Long-term stability of symmetric partitioned linear multistep methods. In: Current Challenges in Stability Issues for Numerical Differential Equations, C.I.M.E. Summer Sch., pp. 1\u201336. Springer, Berlin (2013)","DOI":"10.1007\/978-3-319-01300-8_1"},{"key":"522_CR4","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1007\/s002110050469","volume":"84","author":"E Hairer","year":"1999","unstructured":"Hairer, E.: Backward error analysis for multistep methods. Numer. Math. 84, 199\u2013232 (1999)","journal-title":"Numer. Math."},{"key":"522_CR5","doi-asserted-by":"crossref","unstructured":"Hairer, E., Hairer, M.: GniCodes\u2014Matlab programs for geometric numerical integration. In: Frontiers in Numerical Analysis (Durham 2002), pp. 199\u2013240. Springer, Berlin (2003)","DOI":"10.1007\/978-3-642-55692-0_5"},{"key":"522_CR6","doi-asserted-by":"crossref","first-page":"699","DOI":"10.1007\/s00211-004-0520-2","volume":"97","author":"E Hairer","year":"2004","unstructured":"Hairer, E., Lubich, C.: Symmetric multistep methods over long times. Numer. Math. 97, 699\u2013723 (2004)","journal-title":"Numer. Math."},{"key":"522_CR7","unstructured":"Hairer, E., Lubich, C., Wanner, G.: Geometric numerical integration. Structure-Preserving Algorithms for Ordinary Differential Equations. Springer Series in Computational Mathematics, vol. 31, 2nd edn. Springer, Berlin (2006)"},{"key":"522_CR8","doi-asserted-by":"crossref","first-page":"368","DOI":"10.1137\/0733019","volume":"33","author":"L Jay","year":"1996","unstructured":"Jay, L.: Symplectic partitioned Runge\u2013Kutta methods for constrained Hamiltonian systems. SIAM J. Numer. Anal. 33, 368\u2013387 (1996)","journal-title":"SIAM J. Numer. Anal."},{"key":"522_CR9","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1093\/imamat\/18.2.189","volume":"18","author":"JD Lambert","year":"1976","unstructured":"Lambert, J.D., Watson, I.A.: Symmetric multistep methods for periodic initial value problems. J. Inst. Math. Appl. 18, 189\u2013202 (1976)","journal-title":"J. Inst. Math. Appl."},{"key":"522_CR10","unstructured":"Quinlan, G.D., Tremaine, S.: Symmetric multistep methods for the numerical integration of planetary orbits. Astron. J. 100, 1694\u20131700 (1990)"},{"key":"522_CR11","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1137\/0733025","volume":"33","author":"S Reich","year":"1996","unstructured":"Reich, S.: Symplectic integration of constrained Hamiltonian systems by composition methods. SIAM J. Numer. Anal. 33, 475\u2013491 (1996)","journal-title":"SIAM J. Numer. Anal."},{"key":"522_CR12","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1016\/0021-9991(77)90098-5","volume":"23","author":"J-P Ryckaert","year":"1977","unstructured":"Ryckaert, J.-P., Ciccotti, G., Berendsen, H.J.C.: Numerical integration of the cartesian equations of motion of a system with constraints: molecular dynamics of $n$-alkanes. J. Comput. Phys. 23, 327\u2013341 (1977)","journal-title":"J. Comput. Phys."}],"container-title":["Numerische Mathematik"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-013-0522-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00211-013-0522-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-013-0522-z","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,7,9]],"date-time":"2019-07-09T14:54:58Z","timestamp":1562684098000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00211-013-0522-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,2,15]]},"references-count":12,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2013,7]]}},"alternative-id":["522"],"URL":"https:\/\/doi.org\/10.1007\/s00211-013-0522-z","relation":{},"ISSN":["0029-599X","0945-3245"],"issn-type":[{"value":"0029-599X","type":"print"},{"value":"0945-3245","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,2,15]]}}}