{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T12:40:08Z","timestamp":1777552808116,"version":"3.51.4"},"reference-count":26,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2017,9,8]],"date-time":"2017-09-08T00:00:00Z","timestamp":1504828800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"Natural Science Foundation of China","doi-asserted-by":"crossref","award":["11401164"],"award-info":[{"award-number":["11401164"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2018,7]]},"DOI":"10.1007\/s11075-017-0395-9","type":"journal-article","created":{"date-parts":[[2017,9,11]],"date-time":"2017-09-11T12:06:17Z","timestamp":1505131577000},"page":"673-700","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Extended explicit pseudo two-step RKN methods for oscillatory systems y\n            \u2033 + M\n            y = f(y)"],"prefix":"10.1007","volume":"78","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9573-989X","authenticated-orcid":false,"given":"Jiyong","family":"Li","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shuo","family":"Deng","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xianfen","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2017,9,8]]},"reference":[{"key":"395_CR1","first-page":"1","volume":"50","author":"EJ Nystr\u00f6m","year":"1925","unstructured":"Nystr\u00f6m, E.J.: Ueber die numerische Integration von Differentialgleichungen. Acta Soc. Sci. Fenn. 50, 1\u201354 (1925)","journal-title":"Acta Soc. Sci. Fenn."},{"key":"395_CR2","volume-title":"Solving ordinary differential equations II: stiff and differential algebraic problems, 2nd edn","author":"E Hairer","year":"2002","unstructured":"Hairer, E., Wanner, G.: Solving ordinary differential equations II: stiff and differential algebraic problems, 2nd edn. Springer, Berlin (2002)"},{"key":"395_CR3","volume-title":"Solving ordinary differential equations I: nonstiff problems, 2nd edn","author":"E Hairer","year":"2002","unstructured":"Hairer, E., N\u00f8rsett, S.P., Wanner, G.: Solving ordinary differential equations I: nonstiff problems, 2nd edn. Springer, Berlin (2002)"},{"key":"395_CR4","volume-title":"Geometric numerical integration, structure-preserving algorithms for ordinary differential equations, 2nd edn","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)"},{"key":"395_CR5","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1007\/BF01386037","volume":"3","author":"W Gautschi","year":"1961","unstructured":"Gautschi, W.: Numerical integration of ordinary differential equation based on trigonometric polynomials. Numer. Math. 3, 381\u2013397 (1961)","journal-title":"Numer. Math."},{"key":"395_CR6","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0010-4655(97)00067-2","volume":"105","author":"LGr Ixaru","year":"1997","unstructured":"Ixaru, L.Gr.: Operations on oscillatory functions. Comput. Phys. Comm. 105, 1\u201319 (1997)","journal-title":"Comput. Phys. Comm."},{"key":"395_CR7","volume-title":"Numerical methods for differential equations and applications","author":"LGr Ixaru","year":"1984","unstructured":"Ixaru, L.Gr.: Numerical methods for differential equations and applications. Reidel, Lancaster, Dordrecht, Boston (1984)"},{"key":"395_CR8","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4020-2100-8","volume-title":"Exponential Fitting","author":"LGr Ixaru","year":"2004","unstructured":"Ixaru, L.Gr.: Exponential Fitting. Kluwer Academic Publishers, Dordrecht, Boston, London (2004)"},{"key":"395_CR9","doi-asserted-by":"crossref","first-page":"2250","DOI":"10.1016\/j.cpc.2009.07.011","volume":"180","author":"X Wu","year":"2009","unstructured":"Wu, X., You, X., Xia, J.: Order conditions for ARKN methods solving oscillatory systems. Comput. Phys. Commun. 180, 2250\u20132257 (2009)","journal-title":"Comput. Phys. Commun."},{"key":"395_CR10","doi-asserted-by":"crossref","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. Commun. 181, 1873\u20131887 (2010)","journal-title":"Comput. Phys. Commun."},{"key":"395_CR11","doi-asserted-by":"crossref","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. Numer. 12, 399\u2013450 (2003)","journal-title":"Acta. Numer."},{"key":"395_CR12","doi-asserted-by":"crossref","first-page":"414","DOI":"10.1137\/S0036142999353594","volume":"38","author":"E Hairer","year":"2001","unstructured":"Hairer, E., Lubich, C.: Long-time energy conservation of numerical methods for oscillatory differential equations. SIAM. J. Numer. Anal. 38, 414\u2013441 (2001)","journal-title":"J. Numer. Anal."},{"key":"395_CR13","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1023\/A:1018930732643","volume":"10","author":"NH Cong","year":"1999","unstructured":"Cong, N.H., Strehmel, K., Weiner, R.: Runge-Kutta-Nystr\u00f6m-type parallel block predictor-corrector methods. Adv. Comput. Math. 10, 115\u2013133 (1999)","journal-title":"Adv. Comput. Math."},{"key":"395_CR14","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1007\/BF01933263","volume":"31","author":"PJ Houwen van der","year":"1991","unstructured":"van der Houwen, P.J., Sommeijer, B.P., Cong, N.H.: Stability of collocation-based Runge-Kutta-Nystr\u00f6m methods. BIT 31, 469\u2013481 (1991)","journal-title":"BIT"},{"key":"395_CR15","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1016\/S0168-9274(01)00031-9","volume":"38","author":"NH Cong","year":"2001","unstructured":"Cong, N.H.: Explicit pseudo two-step RKN methods with stepsize control. Appl. Numer. Math. 38, 135\u2013144 (2001)","journal-title":"Appl. Numer. Math."},{"key":"395_CR16","volume-title":"Handbook of Mathematical Functions","author":"M Abramowitz","year":"1970","unstructured":"Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions. National Bureau of Standards Applied Mathematics Series 55, Dover (1970)"},{"key":"395_CR17","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1016\/S0898-1221(99)00211-4","volume":"38","author":"NH Cong","year":"1999","unstructured":"Cong, N.H., Strehmel, K., Weiner, R.: A general class of explicit pseudo two-step RKN methods on parallel computers. Comput. Math. Appl. 38, 17\u201339 (1999)","journal-title":"Comput. Math. Appl."},{"key":"395_CR18","doi-asserted-by":"crossref","first-page":"465","DOI":"10.1007\/s11075-013-9761-4","volume":"65","author":"JY Li","year":"2014","unstructured":"Li, J.Y., Wu, X.Y.: Error analysis of explicit TSERKN methods for highly oscillatory systems. Numer. Algor. 65, 465\u2013483 (2014)","journal-title":"Numer. Algor."},{"key":"395_CR19","doi-asserted-by":"crossref","first-page":"627","DOI":"10.1137\/0718041","volume":"18","author":"LJ Hayes","year":"1987","unstructured":"Hayes, L.J.: Galerkin alternating-direction methods for nonrectangular regions using patch approximations. SIAM J. Numer. Anal. 18, 627\u2013643 (1987)","journal-title":"SIAM J. Numer. Anal."},{"key":"395_CR20","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1007\/BF01931689","volume":"18","author":"G Dahlquist","year":"1978","unstructured":"Dahlquist, G.: On accuracy and unconditional stability of linear multistep methods for second order differential equations. BIT 18, 133\u2013136 (1978)","journal-title":"BIT"},{"key":"395_CR21","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":"395_CR22","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1093\/imanum\/16.2.179","volume":"16","author":"JP Coleman","year":"1996","unstructured":"Coleman, J.P., Ixaru, L.Gr.: P-stability and exponential-fitting methods for y\n                    \u2033 = f(x,y). IMA J. Numer. Anal. 16, 179\u2013199 (1996)","journal-title":"IMA J. Numer. Anal."},{"key":"395_CR23","doi-asserted-by":"crossref","first-page":"1955","DOI":"10.1016\/j.cpc.2010.09.006","volume":"181","author":"XY Wu","year":"2010","unstructured":"Wu, X.Y., Wang, B.: Multidimensional adapted Runge\u2013Kutta\u2013Nystr\u00f6m methods for oscillatory systems. Comput. Phys. Commun. 181, 1955\u20131962 (2010)","journal-title":"Comput. Phys. Commun."},{"key":"395_CR24","doi-asserted-by":"crossref","first-page":"2486","DOI":"10.1016\/j.cpc.2011.07.007","volume":"182","author":"JY Li","year":"2011","unstructured":"Li, J.Y., Wang, B., You, X., Wu, X.Y.: Two-step extended RKN methods for oscillatory systems. Comput. Phys. Commun. 182, 2486\u20132507 (2011)","journal-title":"Comput. Phys. Commun."},{"key":"395_CR25","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1007\/s11075-012-9583-9","volume":"62","author":"JY Li","year":"2013","unstructured":"Li, J.Y., Wu, X.Y.: Adapted Falkner-type methods solving oscillatory second-order differential equations. Numer. Algorithms 62, 355\u2013381 (2013)","journal-title":"Numer. Algorithms"},{"key":"395_CR26","doi-asserted-by":"crossref","first-page":"1040","DOI":"10.1016\/j.apnum.2005.09.005","volume":"56","author":"JM Franco","year":"2006","unstructured":"Franco, J.M.: New methods for oscillatory systems based on ARKN methods. Appl. Numer. Math. 56, 1040\u20131053 (2006)","journal-title":"Appl. Numer. Math."}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11075-017-0395-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-017-0395-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-017-0395-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2018,6,19]],"date-time":"2018-06-19T06:22:49Z","timestamp":1529389369000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11075-017-0395-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,9,8]]},"references-count":26,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2018,7]]}},"alternative-id":["395"],"URL":"https:\/\/doi.org\/10.1007\/s11075-017-0395-9","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,9,8]]}}}