{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,23]],"date-time":"2026-02-23T18:47:52Z","timestamp":1771872472767,"version":"3.50.1"},"reference-count":56,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2018,6,2]],"date-time":"2018-06-02T00:00:00Z","timestamp":1527897600000},"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":["Numer Algor"],"published-print":{"date-parts":[[2019,5]]},"DOI":"10.1007\/s11075-018-0552-9","type":"journal-article","created":{"date-parts":[[2018,6,2]],"date-time":"2018-06-02T04:11:50Z","timestamp":1527912710000},"page":"345-376","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":40,"title":["On the effectiveness of spectral methods for the numerical solution of multi-frequency highly oscillatory Hamiltonian problems"],"prefix":"10.1007","volume":"81","author":[{"given":"Luigi","family":"Brugnano","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6120-4427","authenticated-orcid":false,"given":"Juan I.","family":"Montijano","sequence":"additional","affiliation":[]},{"given":"Luis","family":"R\u00e1ndez","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2018,6,2]]},"reference":[{"key":"552_CR1","doi-asserted-by":"publisher","first-page":"881","DOI":"10.1007\/s10444-014-9390-z","volume":"41","author":"P Amodio","year":"2015","unstructured":"Amodio, P., Brugnano, L., Iavernaro, F.: Energy-conserving methods for Hamiltonian boundary value problems and applications in astrodynamics. Adv. Comput. Math. 41, 881\u2013905 (2015)","journal-title":"Adv. Comput. Math."},{"key":"552_CR2","doi-asserted-by":"publisher","first-page":"247","DOI":"10.1007\/s10915-012-9656-x","volume":"54","author":"G Ariel","year":"2013","unstructured":"Ariel, G., Engquist, B., Kim, S., Lee, Y., Tsai, R.: A multiscale method for highly oscillatory dynamical systems using a Poincar\u00e9 map type technique. J. Sci. Comput. 54, 247\u2013268 (2013)","journal-title":"J. Sci. Comput."},{"key":"552_CR3","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/j.amc.2017.04.018","volume":"318","author":"L Barletti","year":"2018","unstructured":"Barletti, L., Brugnano, L., Frasca Caccia, G., Iavernaro, F.: Energy-conserving methods for the nonlinear Schr\u00f6dinger equation. Appl. Math.Comput. 318, 3\u201318 (2018)","journal-title":"Appl. Math.Comput."},{"key":"552_CR4","doi-asserted-by":"publisher","first-page":"88","DOI":"10.1006\/jcph.2000.6427","volume":"160","author":"P Betsch","year":"2000","unstructured":"Betsch, P., Steinmann, P.: Inherently energy conserving time finite elements for classical mechanics. J. Comp. Phys. 160, 88\u2013116 (2000)","journal-title":"J. Comp. Phys."},{"key":"552_CR5","doi-asserted-by":"publisher","first-page":"355","DOI":"10.1016\/S0168-9274(97)00072-X","volume":"25","author":"CL Bottasso","year":"1997","unstructured":"Bottasso, C.L.: A new look at finite elements in time: a variational interpretation of Runge\u2013Kutta methods. Appl. Numer. Math. 25, 355\u2013368 (1997)","journal-title":"Appl. Numer. Math."},{"key":"552_CR6","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1016\/S0377-0427(99)00280-0","volume":"116","author":"L Brugnano","year":"2000","unstructured":"Brugnano, L.: Blended block BVMs (B3VMs): A family of economical implicit methods for ODEs. J. Comput. Appl. Math. 116, 41\u201362 (2000)","journal-title":"J. Comput. Appl. Math."},{"key":"552_CR7","doi-asserted-by":"publisher","first-page":"3890","DOI":"10.1016\/j.cam.2012.02.033","volume":"236","author":"L Brugnano","year":"2012","unstructured":"Brugnano, L., Calvo, M., Montijano, J.I., R\u00e0ndez, L.: Energy preserving methods for Poisson systems. J. Comput. Appl. Math. 236, 3890\u20133904 (2012)","journal-title":"J. Comput. Appl. Math."},{"key":"552_CR8","doi-asserted-by":"publisher","first-page":"020003","DOI":"10.1063\/1.4992149","volume":"1863","author":"L Brugnano","year":"2017","unstructured":"Brugnano, L., Calvo, M., Montijano, J.I., R\u00e1ndez, L.: Fourier methods for oscillatory differential problems with a constant high frequency. AIP Conf. Proc. 1863, 020003 (2017)","journal-title":"AIP Conf. Proc."},{"key":"552_CR9","doi-asserted-by":"publisher","first-page":"633","DOI":"10.1007\/s11075-014-9825-0","volume":"65","author":"L Brugnano","year":"2014","unstructured":"Brugnano, L., Frasca Caccia, G., Iavernaro, F.: Efficient implementation of Gauss collocation and Hamiltonian boundary value methods. Numer. Algorithms 65, 633\u2013650 (2014)","journal-title":"Numer. Algorithms"},{"key":"552_CR10","doi-asserted-by":"crossref","first-page":"842","DOI":"10.1016\/j.amc.2015.08.078","volume":"270","author":"L Brugnano","year":"2015","unstructured":"Brugnano, L., Frasca Caccia, G., Iavernaro, F.: Energy conservation issues in the numerical solution of the semilinear wave equation. Appl. Math.Comput. 270, 842\u2013870 (2015)","journal-title":"Appl. Math.Comput."},{"key":"552_CR11","doi-asserted-by":"publisher","DOI":"10.1201\/b19319","volume-title":"Line integral methods for conservative problems","author":"L Brugnano","year":"2016","unstructured":"Brugnano, L., Iavernaro, F.: Line integral methods for conservative problems. Chapman and Hall\/CRC, Boca Raton (2016)"},{"issue":"1-2","key":"552_CR12","first-page":"17","volume":"5","author":"L Brugnano","year":"2010","unstructured":"Brugnano, L., Iavernaro, F., Trigiante, D.: Hamiltonian boundary value methods (energy preserving discrete line integral methods). JNAIAM J. Numer. Anal. Ind. Appl. Math. 5(1-2), 17\u201337 (2010)","journal-title":"JNAIAM J. Numer. Anal. Ind. Appl. Math."},{"key":"552_CR13","doi-asserted-by":"publisher","first-page":"375","DOI":"10.1016\/j.cam.2011.07.022","volume":"236","author":"L Brugnano","year":"2011","unstructured":"Brugnano, L., Iavernaro, F., Trigiante, D.: A note on the efficient implementation of Hamiltonian BVMs. J. Comput. Appl. Math. 236, 375\u2013383 (2011)","journal-title":"J. Comput. Appl. Math."},{"key":"552_CR14","first-page":"8053","volume":"218","author":"L Brugnano","year":"2012","unstructured":"Brugnano, L., Iavernaro, F., Trigiante, D.: The lack of continuity and the role of infinite and infinitesimal in numerical methods for ODEs: the case of symplecticity. Appl. Math.Comput. 218, 8053\u20138063 (2012)","journal-title":"Appl. Math.Comput."},{"key":"552_CR15","doi-asserted-by":"crossref","first-page":"8475","DOI":"10.1016\/j.amc.2012.01.074","volume":"218","author":"L Brugnano","year":"2012","unstructured":"Brugnano, L., Iavernaro, F., Trigiante, D.: A simple framework for the derivation and analysis of effective one-step methods for ODEs. Appl. Math.Comput. 218, 8475\u20138485 (2012)","journal-title":"Appl. Math.Comput."},{"key":"552_CR16","doi-asserted-by":"publisher","first-page":"650","DOI":"10.1016\/j.cnsns.2014.05.030","volume":"20","author":"L Brugnano","year":"2015","unstructured":"Brugnano, L., Iavernaro, F., Trigiante, D.: Analysis of Hamiltonian boundary value methods (HBVMs): a class of energy-preserving Runge-Kutta methods for the numerical solution of polynomial Hamiltonian systems. Commun. Nonlinear Sci. Numer. Simul. 20, 650\u2013667 (2015)","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"552_CR17","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1016\/S0168-9274(01)00140-4","volume":"42","author":"L Brugnano","year":"2002","unstructured":"Brugnano, L., Magherini, C.: Blended implementation of block implicit methods for ODEs. Appl. Numer. Math. 42, 29\u201345 (2002)","journal-title":"Appl. Numer. Math."},{"key":"552_CR18","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1016\/j.cam.2003.09.004","volume":"164\u2013165","author":"L Brugnano","year":"2004","unstructured":"Brugnano, L., Magherini, C.: The BiM code for the numerical solution of ODEs. J. Comput. Appl. Math. 164\u2013165, 145\u2013158 (2004)","journal-title":"J. Comput. Appl. Math."},{"key":"552_CR19","doi-asserted-by":"publisher","first-page":"777","DOI":"10.1016\/j.cam.2006.02.057","volume":"205","author":"L Brugnano","year":"2007","unstructured":"Brugnano, L., Magherini, C.: Blended implicit methods for solving ODE and DAE problems, and their extension for second order problems. J. Comput. Appl. Math. 205, 777\u2013790 (2007)","journal-title":"J. Comput. Appl. Math."},{"key":"552_CR20","doi-asserted-by":"publisher","first-page":"542","DOI":"10.1016\/j.apnum.2008.03.008","volume":"59","author":"L Brugnano","year":"2009","unstructured":"Brugnano, L., Magherini, C.: Recent advances in linear analysis of convergence for splittings for solving ODE problems. Appl. Numer. Math. 59, 542\u2013557 (2009)","journal-title":"Appl. Numer. Math."},{"key":"552_CR21","doi-asserted-by":"publisher","first-page":"34","DOI":"10.1016\/j.cam.2005.05.005","volume":"189","author":"L Brugnano","year":"2006","unstructured":"Brugnano, L., Magherini, C., Mugnai, F.: Blended implicit methods for the numerical solution of DAE problems. J. Comput. Appl. Math. 189, 34\u201350 (2006)","journal-title":"J. Comput. Appl. Math."},{"issue":"10","key":"552_CR22","doi-asserted-by":"publisher","first-page":"1077","DOI":"10.1016\/j.apnum.2011.06.007","volume":"61","author":"MP Calvo","year":"2011","unstructured":"Calvo, M.P., Chartier, P., Murua, A., Sanz-Serna, J.M.: Numerical stroboscopic averaging for ODEs and DAEs. Appl. Numer. Math. 61(10), 1077\u20131095 (2011)","journal-title":"Appl. Numer. Math."},{"key":"552_CR23","doi-asserted-by":"publisher","first-page":"635","DOI":"10.1007\/s00211-004-0518-9","volume":"4","author":"M Calvo","year":"2004","unstructured":"Calvo, M., Jay, L.O., Montijano, J.I., R\u00e1ndez, L.: Approximate compositions of a near identity map by multi-revolution Runge-Kutta methods. Numer. Math. 4, 635\u2013666 (2004)","journal-title":"Numer. Math."},{"key":"552_CR24","doi-asserted-by":"publisher","first-page":"26","DOI":"10.1016\/j.apnum.2015.01.001","volume":"91","author":"B Cano","year":"2015","unstructured":"Cano, B., Gonz\u00e1lez-Pach\u00f3n, A.: Exponential time integration of solitary waves of cubic Schr\u00f6dinger equation. Appl. Numer. Math. 91, 26\u201345 (2015)","journal-title":"Appl. Numer. Math."},{"key":"552_CR25","doi-asserted-by":"publisher","first-page":"30","DOI":"10.1016\/j.apnum.2012.11.005","volume":"66","author":"B Cano","year":"2013","unstructured":"Cano, B., Moreta, M.J.: High-order symmetric multistep cosine methods. Appl. Numer. Math. 66, 30\u201344 (2013)","journal-title":"Appl. Numer. Math."},{"issue":"4","key":"552_CR26","doi-asserted-by":"publisher","first-page":"2808","DOI":"10.1137\/080715974","volume":"47","author":"F Castella","year":"2009","unstructured":"Castella, F., Chartier, P., Fao, E.: An averaging technique for highly oscillatory Hamiltonian problems. SIAM J. Numer. Math. 47(4), 2808\u20132837 (2009)","journal-title":"SIAM J. Numer. Math."},{"key":"552_CR27","doi-asserted-by":"crossref","unstructured":"Cohen, D., Jahnke, T., Lorenz, K., Lubich, C.: Numerical integrators for highly oscillatory hamiltonian systems: a review. In: Mielke, A. (ed.) Analysis, modeling and simulation of multiscale problems, pp 553\u2013576. Springer, Berlin (2006)","DOI":"10.1007\/3-540-35657-6_20"},{"key":"552_CR28","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1007\/BF01601932","volume":"30","author":"P Deuflhard","year":"1979","unstructured":"Deuflhard, P.: A study of extrapolation methods based on multistep schemes without parasitic solutions. Z. Angew. Math. Phys. 30, 177\u2013189 (1979)","journal-title":"Z. Angew. Math. Phys."},{"key":"552_CR29","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1016\/S0377-0427(99)00213-7","volume":"112","author":"GA Evans","year":"1999","unstructured":"Evans, G.A., Webster, J.R.: A comparison of some methods for the evaluation of highly oscillatory integrals. J. Comput. Appl. Math. 112, 55\u201369 (1999)","journal-title":"J. Comput. Appl. Math."},{"key":"552_CR30","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."},{"issue":"3","key":"552_CR31","doi-asserted-by":"publisher","first-page":"930","DOI":"10.1137\/S1064827596313851","volume":"20","author":"B Garc\u00eda-Archilla","year":"1998","unstructured":"Garc\u00eda-Archilla, B., Sanz-Serna, J.M., Skeel, R.D.: Long-time steps methods for oscillatory differential equations. SIAM J. Sci. Comput. 20(3), 930\u2013963 (1998)","journal-title":"SIAM J. Sci. Comput."},{"issue":"1-2","key":"552_CR32","first-page":"73","volume":"5","author":"E Hairer","year":"2010","unstructured":"Hairer, E.: Energy-preserving variant of collocation methods. JNAIAM J. Numer. Anal. Ind. Appl. Math. 5(1-2), 73\u201384 (2010)","journal-title":"JNAIAM J. Numer. Anal. Ind. Appl. Math."},{"key":"552_CR33","volume-title":"Geometric numerical integration. Structure-preserving algorithms for ordinary differential equations","author":"E Hairer","year":"2006","unstructured":"Hairer, E., Lubich, C., Wanner, G.: Geometric numerical integration. Structure-preserving algorithms for ordinary differential equations, 2nd edn. Springer, Berlin (2006)","edition":"2"},{"key":"552_CR34","doi-asserted-by":"publisher","first-page":"1069","DOI":"10.1137\/040611434","volume":"43","author":"M Hochbruck","year":"2005","unstructured":"Hochbruck, M., Ostermann, A.: Explicit exponential Runge-Kutta methods for semilinear parabolic problems. SIAM J. Numer. Anal. 43, 1069\u20131090 (2005)","journal-title":"SIAM J. Numer. Anal."},{"key":"552_CR35","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1017\/S0962492910000048","volume":"19","author":"M Hochbruck","year":"2010","unstructured":"Hochbruck, M., Ostermann, A.: Exponential integrators. Acta Numer. 19, 209\u2013286 (2010)","journal-title":"Acta Numer."},{"key":"552_CR36","doi-asserted-by":"publisher","first-page":"415","DOI":"10.1090\/S0025-5718-1972-0321301-2","volume":"26","author":"BL Hulme","year":"1972","unstructured":"Hulme, B.L.: One-step piecewise polynomial Galerkin methods for initial value problems. Math. Comp. 26, 415\u2013426 (1972)","journal-title":"Math. Comp."},{"key":"552_CR37","doi-asserted-by":"publisher","first-page":"881","DOI":"10.1090\/S0025-5718-1972-0315899-8","volume":"26","author":"BL Hulme","year":"1972","unstructured":"Hulme, B.L.: Discrete Galerkin and related one-step methods for ordinary differential equations. Math. Comp. 26, 881\u2013891 (1972)","journal-title":"Math. Comp."},{"key":"552_CR38","unstructured":"Jansing, G.: EXPODE \u2014 advanced exponential time integration toolbox for MATLAB. arXiv: 1404.4580v1 [math.NA] (2014)"},{"issue":"4","key":"552_CR39","doi-asserted-by":"publisher","first-page":"2036","DOI":"10.1137\/15M1032752","volume":"54","author":"Y-w Li","year":"2016","unstructured":"Li, Y.-w., Wu, X.: Functionally fitted energy\u2013preserving methods for solving oscillatory nonlinear Hamiltonian systems. SIAM J. Numer. Anal. 54(4), 2036\u20132059 (2016)","journal-title":"SIAM J. Numer. Anal."},{"key":"552_CR40","doi-asserted-by":"publisher","first-page":"437","DOI":"10.1017\/S0962492900002750","volume":"6","author":"LR Petzold","year":"1997","unstructured":"Petzold, L.R., Jay, L.O., Yen, J.: Numerical solution of highly oscillatory ordinary differential equations. Acta Numer. 6, 437\u2013483 (1997)","journal-title":"Acta Numer."},{"key":"552_CR41","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4899-3093-4","volume-title":"Numerical hamiltonian problems","author":"JM Sanz-Serna","year":"1994","unstructured":"Sanz-Serna, J.M., Calvo, M.P.: Numerical hamiltonian problems. Chapman & Hall, London (1994)"},{"issue":"3","key":"552_CR42","doi-asserted-by":"publisher","first-page":"253","DOI":"10.1081\/SME-200027930","volume":"32","author":"SS Shome","year":"2004","unstructured":"Shome, S.S., Haug, E.J., Jay, L.O.: Dual-rate integration using partitioned Runge-Kutta methods for mechanical systems with interacting subsystems. Mech. Based Des. Struct. Mach. 32(3), 253\u2013282 (2004)","journal-title":"Mech. Based Des. Struct. Mach."},{"key":"552_CR43","doi-asserted-by":"crossref","unstructured":"Solcia, T., Masarati, P.: Multirate simulation of complex multibody systems. In: ECCOMAS Thematic Conference (2011)","DOI":"10.1115\/DETC2011-47306"},{"key":"552_CR44","doi-asserted-by":"publisher","first-page":"2158","DOI":"10.1016\/j.amc.2012.08.062","volume":"219","author":"W Tang","year":"2012","unstructured":"Tang, W., Sun, Y.: Time finite element methods: a unified framework for numerical discretizations of ODEs. Appl. Math. Comp. 219, 2158\u20132179 (2012)","journal-title":"Appl. Math. Comp."},{"issue":"11","key":"552_CR45","doi-asserted-by":"publisher","first-page":"8362","DOI":"10.1063\/1.461263","volume":"95","author":"ME Tuckerman","year":"1991","unstructured":"Tuckerman, M.E., Berne, B.J.: Molecular dynamics in systems with multiple time scales: systems with stiff and soft degrees of freedom and with short and long range forces. J. Chem. Phys. 95(11), 8362\u20138364 (1991)","journal-title":"J. Chem. Phys."},{"key":"552_CR46","doi-asserted-by":"publisher","first-page":"1873","DOI":"10.1016\/j.cpc.2010.07.046","volume":"181","author":"X Wu","year":"2010","unstructured":"Wu, X., You, X., Shi, W., Wang, B.: ERKN integrators for systems of oscillatory second-order differential equations. Comput. Phys. Comm. 181, 1873\u20131887 (2010)","journal-title":"Comput. Phys. Comm."},{"key":"552_CR47","doi-asserted-by":"publisher","first-page":"587","DOI":"10.1016\/j.jcp.2012.10.015","volume":"235","author":"X Wu","year":"2013","unstructured":"Wu, X., Wang, B., Shi, W.: Efficient energy-preserving integrators for oscillatory Hamiltonian systems. J. Comput. Phys. 235, 587\u2013605 (2013)","journal-title":"J. Comput. Phys."},{"key":"552_CR48","doi-asserted-by":"publisher","first-page":"1876","DOI":"10.1137\/15M1023257","volume":"38","author":"YW Li","year":"2016","unstructured":"Li, Y.W., Wu, X.: Exponential integrators preserving first integrals or Lyapunov functions for conservative or dissipative systems. SIAM J. Sci. Comput. 38, 1876\u20131895 (2016)","journal-title":"SIAM J. Sci. Comput."},{"key":"552_CR49","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-35338-3","volume-title":"Structure-preserving algorithms for oscillatory differential equations","author":"X Wu","year":"2013","unstructured":"Wu, X., You, X., Wang, B.: Structure-preserving algorithms for oscillatory differential equations. Springer-Verlag, Berlin (2013)"},{"key":"552_CR50","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-48156-1","volume-title":"Structure-preserving algorithms for oscillatory differential equations, vol. II","author":"X Wu","year":"2015","unstructured":"Wu, X., Liu, K., Shi, W.: Structure-preserving algorithms for oscillatory differential equations, vol. II. Springer-Verlag, Heidelberg (2015)"},{"key":"552_CR51","doi-asserted-by":"publisher","first-page":"151","DOI":"10.1007\/s10208-014-9241-9","volume":"16","author":"B Wang","year":"2016","unstructured":"Wang, B., Iserles, A., Wu, X.: Arbitrary-order trigonometric Fourier collocation methods for multi-frequency oscillatory systems. Found. Comput. Math. 16, 151\u2013181 (2016)","journal-title":"Found. Comput. Math."},{"key":"552_CR52","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1016\/j.cam.2016.09.017","volume":"313","author":"B Wang","year":"2017","unstructured":"Wang, B., Wu, X., Meng, F.: Trigonometric collocation methods based on Lagrange basis polynomials for multi-frequency oscillatory second-order differential equations. J. Comput. Appl. Math. 313, 185\u2013201 (2017)","journal-title":"J. Comput. Appl. Math."},{"key":"552_CR53","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1007\/s10092-016-0179-y","volume":"54","author":"B Wang","year":"2017","unstructured":"Wang, B., Yang, H., Meng, F.: Sixth order symplectic and symmetric explicit ERKN schemes for solving multi-frequency oscillatory nonlinear Hamiltonian equations. Calcolo 54, 117\u2013140 (2017)","journal-title":"Calcolo"},{"key":"552_CR54","doi-asserted-by":"publisher","first-page":"909","DOI":"10.1007\/s11075-016-0225-5","volume":"75","author":"X Zeng","year":"2017","unstructured":"Zeng, X., Yang, H., Wu, X.: An improved tri-colored rooted-tree theory and order conditions for ERKN methods for general multi-frequency oscillatory systems. Numer. Algorithms 75, 909\u2013935 (2017)","journal-title":"Numer. Algorithms"},{"key":"552_CR55","doi-asserted-by":"publisher","first-page":"164","DOI":"10.1016\/j.apnum.2017.04.008","volume":"119","author":"B Wang","year":"2017","unstructured":"Wang, B., Meng, F., Fang, Y.: Efficient implementation of RKN-type Fourier collocation methods for second-order differential equations. Appl. Numer. Math. 119, 164\u2013178 (2017)","journal-title":"Appl. Numer. Math."},{"key":"552_CR56","doi-asserted-by":"publisher","first-page":"1185","DOI":"10.1016\/j.physleta.2012.02.040","volume":"376","author":"B Wang","year":"2012","unstructured":"Wang, B., Wu, X.: A new high precision energy-preserving integrator for system of oscillatory second-order differential equations. Phys. Lett. A 376, 1185\u20131190 (2012)","journal-title":"Phys. Lett. A"}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-018-0552-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11075-018-0552-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-018-0552-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,11,3]],"date-time":"2020-11-03T01:42:30Z","timestamp":1604367750000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11075-018-0552-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,6,2]]},"references-count":56,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2019,5]]}},"alternative-id":["552"],"URL":"https:\/\/doi.org\/10.1007\/s11075-018-0552-9","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,6,2]]},"assertion":[{"value":"23 November 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 May 2018","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 June 2018","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}