{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T12:26:17Z","timestamp":1774355177873,"version":"3.50.1"},"reference-count":25,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2018,3,23]],"date-time":"2018-03-23T00:00:00Z","timestamp":1521763200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Adv Comput Math"],"published-print":{"date-parts":[[2019,2]]},"DOI":"10.1007\/s10444-018-9603-y","type":"journal-article","created":{"date-parts":[[2018,3,23]],"date-time":"2018-03-23T01:35:45Z","timestamp":1521768945000},"page":"1-21","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["Variational integrators for orbital problems using frequency estimation"],"prefix":"10.1007","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7047-9438","authenticated-orcid":false,"given":"Odysseas","family":"Kosmas","sequence":"first","affiliation":[]},{"given":"Sigrid","family":"Leyendecker","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2018,3,23]]},"reference":[{"key":"9603_CR1","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139107136","volume-title":"Highly Oscillatory Problems","author":"B Engquist","year":"2009","unstructured":"Engquist, B., Fokas, A., Hairer, E., Iserles, A.: Highly Oscillatory Problems. Cambridge University Press, Cambridge (2009)"},{"key":"9603_CR2","doi-asserted-by":"publisher","first-page":"223","DOI":"10.1016\/S0167-2789(97)00051-1","volume":"106","author":"J Wendlandt","year":"1997","unstructured":"Wendlandt, J., Marsden, J.: Mechanical integrators derived from a discrete variational principle. Phys. D 106, 223\u2013246 (1997)","journal-title":"Phys. D"},{"key":"9603_CR3","doi-asserted-by":"publisher","first-page":"3353","DOI":"10.1063\/1.532892","volume":"40","author":"C Kane","year":"2001","unstructured":"Kane, C., Marsden, J., Ortiz, M.: Symplectic-energy-momentum preserving variational integrators. J. Math. Phys. 40, 3353\u20133371 (2001)","journal-title":"J. Math. Phys."},{"key":"9603_CR4","doi-asserted-by":"publisher","first-page":"357","DOI":"10.1017\/S096249290100006X","volume":"10","author":"J Marsden","year":"2001","unstructured":"Marsden, J., West, M.: Discrete mechanics and variational integrators. Acta Numerica 10, 357\u2013514 (2001)","journal-title":"Acta Numerica"},{"key":"9603_CR5","doi-asserted-by":"publisher","first-page":"399","DOI":"10.1017\/S0962492902000144","volume":"12","author":"E Hairer","year":"2003","unstructured":"Hairer, E., Lubich, C., Wanner, G.: Geometric numerical integration illustrated by the st\u00f6rmer-verlet method. Acta Numerica 12, 399\u2013450 (2003)","journal-title":"Acta Numerica"},{"key":"9603_CR6","volume-title":"Simulating Hamiltonian Dynamics","author":"B Leimkuhler","year":"2004","unstructured":"Leimkuhler, B., Reich, S.: Simulating Hamiltonian Dynamics. Cambridge Monographs on Applied and Computational Mathematics, Cambridge (2004)"},{"key":"9603_CR7","doi-asserted-by":"publisher","first-page":"955","DOI":"10.1007\/s10444-014-9394-8","volume":"41","author":"S Ober-Bl\u00f6baum","year":"2015","unstructured":"Ober-Bl\u00f6baum, S., Saake, N.: Construction and analysis of higher order Galerkin variational integrators. Adv. Comput. Math. 41, 955\u2013986 (2015)","journal-title":"Adv. Comput. Math."},{"key":"9603_CR8","doi-asserted-by":"publisher","first-page":"4193","DOI":"10.3934\/dcds.2015.35.4193","volume":"35","author":"CM Campos","year":"2015","unstructured":"Campos, C.M., Ober-Bl\u00f6baum, S., Tr\u00e9lat, E.: High order variational integrators in the optimal control of mechanical systems. Discrete Contin. Dyn. Syst. A 35, 4193\u20134223 (2015)","journal-title":"Discrete Contin. Dyn. Syst. A"},{"key":"9603_CR9","doi-asserted-by":"publisher","first-page":"375","DOI":"10.1093\/imanum\/drv062","volume":"37","author":"S Ober-Bl\u00f6baum","year":"2017","unstructured":"Ober-Bl\u00f6baum, S.: Galerkin variational integrators and modified symplectic Runge-Kutta methods. IMA J. Numer. Anal. 37, 375\u2013406 (2017)","journal-title":"IMA J. Numer. Anal."},{"key":"9603_CR10","doi-asserted-by":"publisher","first-page":"685","DOI":"10.1002\/nme.1620150506","volume":"15","author":"L Brusca","year":"1980","unstructured":"Brusca, L., Nigro, L.: A one-step method for direct integration of structural dynamic equations. Internat. J. Numer. Methods Engnr. 15, 685\u2013699 (1980)","journal-title":"Internat. J. Numer. Methods Engnr."},{"key":"9603_CR11","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1016\/j.cpc.2005.10.007","volume":"174","author":"H de Vyver Van","year":"2006","unstructured":"Van de Vyver, H.: A fourth-order symplectic exponentially fitted integrator. Comput. Phys. Commun. 174, 255\u2013262 (2006)","journal-title":"Comput. Phys. Commun."},{"key":"9603_CR12","doi-asserted-by":"publisher","first-page":"381","DOI":"10.1007\/BF01386037","volume":"3","author":"W Gautschi","year":"1961","unstructured":"Gautschi, W.: Numerical integration of ordinary differential equations based on trigonometric polynomials. Numer. Math. 3, 381\u2013397 (1961)","journal-title":"Numer. Math."},{"key":"9603_CR13","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1007\/BF01395931","volume":"19","author":"T Lyche","year":"1972","unstructured":"Lyche, T.: Chebyshevian multistep methods for ordinary differential equations. Num. Math. 19, 65\u201375 (1972)","journal-title":"Num. Math."},{"key":"9603_CR14","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4020-2100-8","volume-title":"Exponential Fitting","author":"LGr Ixaru","year":"2004","unstructured":"Ixaru, L.Gr., Vanden Berghe, G.: Exponential Fitting. Kluwer Academic Publishers, Dordrecht (2004)"},{"key":"9603_CR15","doi-asserted-by":"publisher","first-page":"1266","DOI":"10.1016\/j.aim.2011.10.018","volume":"229","author":"M Cappiello","year":"2012","unstructured":"Cappiello, M., Nicola, F.: Regularity and decay of solutions of nonlinear harmonic oscillators. Adv. Math. 229, 1266\u20131299 (2012)","journal-title":"Adv. Math."},{"key":"9603_CR16","doi-asserted-by":"publisher","first-page":"562","DOI":"10.1016\/j.cpc.2009.11.005","volume":"181","author":"OT Kosmas","year":"2010","unstructured":"Kosmas, O.T., Vlachos, D.S.: Phase-fitted discrete Lagrangian integrators. Comput. Phys. Commun. 181, 562\u2013568 (2010)","journal-title":"Comput. Phys. Commun."},{"key":"9603_CR17","doi-asserted-by":"publisher","first-page":"677","DOI":"10.1002\/pamm.201210327","volume":"12","author":"OT Kosmas","year":"2012","unstructured":"Kosmas, O.T., Leyendecker, S.: Phase lag analysis of variational integrators using interpolation techniques. PAMM Proc. Appl. Math. Mech. 12, 677\u2013678 (2012)","journal-title":"PAMM Proc. Appl. Math. Mech."},{"key":"9603_CR18","doi-asserted-by":"publisher","first-page":"1779","DOI":"10.1137\/080732936","volume":"7","author":"A Stern","year":"2009","unstructured":"Stern, A., Grinspun, E.: Implicit-explicit integration of highly oscillatory problems. SIAM Multiscale Model. Simul. 7, 1779\u20131794 (2009)","journal-title":"SIAM Multiscale Model. Simul."},{"key":"9603_CR19","doi-asserted-by":"publisher","first-page":"1497","DOI":"10.1093\/imanum\/drq027","volume":"31","author":"M Leok","year":"2011","unstructured":"Leok, M., Zhang, J.: Discrete Hamiltonian variational integrators. IMA J. Numer. Anal. 31, 1497\u20131532 (2011)","journal-title":"IMA J. Numer. Anal."},{"key":"9603_CR20","doi-asserted-by":"publisher","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. IMA J. Appl. Math. 18, 189\u2013202 (1976)","journal-title":"IMA J. Appl. Math."},{"key":"9603_CR21","volume-title":"Numerical Recipes in C: the Art of Scientific Computing","author":"WH Press","year":"1992","unstructured":"Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P.: Numerical Recipes in C: the Art of Scientific Computing. Cambridge University Press, Cambridge (1992)"},{"key":"9603_CR22","doi-asserted-by":"publisher","first-page":"2632","DOI":"10.1016\/j.cam.2011.12.021","volume":"33","author":"OT Kosmas","year":"2012","unstructured":"Kosmas, O.T., Vlachos, D.S.: Local path fitting: a new approach to variational integrators. J. Comput. Appl. Math. 33, 2632\u20132642 (2012)","journal-title":"J. Comput. Appl. Math."},{"key":"9603_CR23","first-page":"1927","volume":"1389","author":"OT Kosmas","year":"2011","unstructured":"Kosmas, O.T.: Charged particle in an electromagnetic field using variational integrators. ICNAAM Numer. Anal. Appl. Math. 1389, 1927\u20131931 (2011)","journal-title":"ICNAAM Numer. Anal. Appl. Math."},{"key":"9603_CR24","doi-asserted-by":"publisher","first-page":"605","DOI":"10.1007\/s10444-015-9436-x","volume":"42","author":"OT Kosmas","year":"2016","unstructured":"Kosmas, O.T., Leyendecker, S.: Analysis of higher order phase fitted variational integrators. Adv. Comput. Math. 42, 605\u2013619 (2016)","journal-title":"Adv. Comput. Math."},{"key":"9603_CR25","unstructured":"Kosmas, O.T., Leyendecker, S.: Stability analysis of high order phase fitted variational integrators. In: Proceedings of WCCM XI - ECCM V - ECFD VI, vol. 1389, pp. 548\u2013556 (2014)"}],"container-title":["Advances in Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10444-018-9603-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-018-9603-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-018-9603-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,3,22]],"date-time":"2019-03-22T20:31:38Z","timestamp":1553286698000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10444-018-9603-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,3,23]]},"references-count":25,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2019,2]]}},"alternative-id":["9603"],"URL":"https:\/\/doi.org\/10.1007\/s10444-018-9603-y","relation":{},"ISSN":["1019-7168","1572-9044"],"issn-type":[{"value":"1019-7168","type":"print"},{"value":"1572-9044","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,3,23]]},"assertion":[{"value":"22 June 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 March 2018","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 March 2018","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}