{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:40:56Z","timestamp":1740123656073,"version":"3.37.3"},"reference-count":25,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2018,2,19]],"date-time":"2018-02-19T00:00:00Z","timestamp":1518998400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2018,2,19]],"date-time":"2018-02-19T00:00:00Z","timestamp":1518998400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/100006209","name":"Nuclear Physics","doi-asserted-by":"publisher","award":["DE-SC0005823"],"award-info":[{"award-number":["DE-SC0005823"]}],"id":[{"id":"10.13039\/100006209","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2019,2]]},"DOI":"10.1007\/s11075-018-0489-z","type":"journal-article","created":{"date-parts":[[2018,2,19]],"date-time":"2018-02-19T10:22:15Z","timestamp":1519035735000},"page":"377-396","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Picard iteration-based variable-order integrator with dense output employing algorithmic differentiation"],"prefix":"10.1007","volume":"80","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9803-895X","authenticated-orcid":false,"given":"Herman D.","family":"Schaumburg","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Afnan","family":"Al Marzouk","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bela","family":"Erdelyi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2018,2,19]]},"reference":[{"key":"489_CR1","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511535246","volume-title":"Gravitational N-body Simulations: Tools and Algorithms","author":"S Aarseth","year":"2003","unstructured":"Aarseth, S.: Gravitational N-body Simulations: Tools and Algorithms. Cambridge University Press, Cambridge (2003). ISBN: 0-521-43272-3"},{"key":"489_CR2","unstructured":"Abeyratne, S., Erdelyi, B., Schaumburg, H.D.: A novel code with high-order adaptive dynamics to solve the N-body problem. In: Proceedings of 54Th ICFA, pp. 70\u201373. JACoW (2015)"},{"key":"489_CR3","unstructured":"Al Marzouk, A., Erdelyi, B.: Numerical integrator for Coulomb collisions. In: Proceedings of NAPAC, pp. 204\u2013206. JACoW (2013)"},{"key":"489_CR4","volume-title":"Modern map methods in particle beam physics","author":"M Berz","year":"1999","unstructured":"Berz, M.: Modern map methods in particle beam physics. Academic Press, London (1999)"},{"key":"489_CR5","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1007\/978-1-4684-0173-8","volume-title":"Differential Equations and Their Applications, 3rd edn.","author":"M Braun","year":"1983","unstructured":"Braun, M.: Differential Equations and Their Applications, 3rd edn., pp 67\u201380. Springer, New York (1983). ISBN: 0-387-90806-4"},{"key":"489_CR6","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-28438-9","volume-title":"Automatic differentiation: applications, theory, and implementations. Lect. Notes Comput. Sci. Eng","author":"HM B\u00fccker","year":"2006","unstructured":"B\u00fccker, H.M., Corliss, G., Hovland, P., Naumann, U., Norris, B.: Automatic differentiation: applications, theory, and implementations. Lect. Notes Comput. Sci. Eng. Springer, Berlin (2006)"},{"key":"489_CR7","unstructured":"B\u00fccker, M., Hovland, P.: Tools for automatic differentiation. \n                    http:\/\/www.autodiff.org\n                    \n                  . List of selected AD tools"},{"issue":"10\u201312","key":"489_CR8","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1016\/0898-1221(94)00193-6","volume":"28","author":"YF Chang","year":"1994","unstructured":"Chang, Y.F., Corliss, G.: ATOMFT: Solving ODEs and DAEs using Taylor series. Comput. Math. Appl. 28(10\u201312), 209\u2013233 (1994)","journal-title":"Comput. Math. Appl."},{"key":"489_CR9","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1007\/BF01963532","volume":"3","author":"G Dahlquist","year":"1963","unstructured":"Dahlquist, G.: A special stability problem for linear multistep methods. BIT 3, 27\u201343 (1963)","journal-title":"BIT"},{"key":"489_CR10","unstructured":"Fehlberg, E.: Numerical Integration of Differential Equations by Power Series, Illustrated by Physical Examples. Technical Note, no. D-2356. NASA, Washington (1964)"},{"key":"489_CR11","unstructured":"Hairer, E., Norsett, S.P., Wanner, G.: Solving ordinary differential equations i: Nonstiff problems. Springer ser. Comput. Math springer (2013)"},{"key":"489_CR12","first-page":"217","volume":"109","author":"WP Johnson","year":"2002","unstructured":"Johnson, W.P.: The curious history of the Fa\u00e0 di Bruno\u2019s Formula. Amer. Math. Monthly 109, 217\u2013234 (2002)","journal-title":"Amer. Math. Monthly"},{"issue":"1","key":"489_CR13","doi-asserted-by":"publisher","first-page":"99","DOI":"10.1080\/10586458.2005.10128904","volume":"14","author":"\u00c0 Jorba","year":"2005","unstructured":"Jorba, \u00c0., Zou, M.: A software package for the numerical integration of ODEs by means of high-order Taylor methods. Exp. Math. 14(1), 99 (2005)","journal-title":"Exp. Math."},{"key":"489_CR14","doi-asserted-by":"crossref","unstructured":"LeVeque, R.J. 7: Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-Dependent Problems. SIAM, Philadelphia (2007). ISBN: 978-0-898716-29-0","DOI":"10.1137\/1.9780898717839"},{"key":"489_CR15","first-page":"346","volume":"A558","author":"K Makino","year":"2005","unstructured":"Makino, K., Berz, M.: COSY INFINITY version 9. Nucl. Inst. Methods A558, 346\u2013350 (2005)","journal-title":"Nucl. Inst. Methods"},{"issue":"6","key":"489_CR16","doi-asserted-by":"publisher","first-page":"065901","DOI":"10.1088\/0034-4885\/77\/6\/065901","volume":"77","author":"ZE Musielak","year":"2014","unstructured":"Musielak, Z.E., Quarles, B.: The three-body problem. Rep. Progr. Phys. 77(6), 065901 (2014)","journal-title":"Rep. Progr. Phys."},{"key":"489_CR17","first-page":"97","volume":"4","author":"GE Parker","year":"1996","unstructured":"Parker, G.E., Sochacki, J.S.: Implementing the Picard iteration. Neural Parallel Sci. Comput. 4, 97\u2013112 (1996)","journal-title":"Neural Parallel Sci. Comput."},{"key":"489_CR18","doi-asserted-by":"publisher","first-page":"298","DOI":"10.1016\/S0021-9991(03)00101-3","volume":"187","author":"CD Pruett","year":"2003","unstructured":"Pruett, C.D., Rudmin, J.W., Lacy, J.M.: An adaptive n-body algorithm of optimal order. J. Comput. Phys. 187, 298\u2013317 (2003)","journal-title":"J. Comput. Phys."},{"key":"489_CR19","unstructured":"Schaumburg, H.D., Erdelyi, B.: A picard iteration based integrator. In: Proceedings of NAPAC, pp. 210\u2013212. JACoW (2013)"},{"key":"489_CR20","unstructured":"Sim\u00f3, C.: Global dynamics and fast indicators. In: Broer, B.K.H.W., Vegter, G. (eds.) Global analysis of dynamical systems, Chap. 15, pp 373\u2013390. IOP, Bristol and Philadelphia (2001)"},{"key":"489_CR21","doi-asserted-by":"publisher","first-page":"105","DOI":"10.1007\/BF02422379","volume":"36","author":"KF Sundman","year":"1912","unstructured":"Sundman, K.F.: M\u00e8moire sur le probl\u00e8me des trois corps. Acta Math. 36, 105\u2013179 (1912)","journal-title":"Acta Math."},{"key":"489_CR22","doi-asserted-by":"publisher","first-page":"38,40","DOI":"10.1090\/gsm\/140","volume-title":"Ordinary differential equations and dynamical systems, vol. 140","author":"G Teschl","year":"2012","unstructured":"Teschl, G.: Ordinary differential equations and dynamical systems, vol. 140, p 38,40. American Mathematical Society, Providence (2012)"},{"key":"489_CR23","first-page":"350","volume-title":"Introduction to Real Analysis","author":"WF Trench","year":"2003","unstructured":"Trench, W.F.: Introduction to Real Analysis, p 350. Pearson Education, Upper Saddle River (2003). ISBN: 0-13-045786-8"},{"issue":"1","key":"489_CR24","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1007\/BF00048987","volume":"50","author":"Q Wang","year":"1991","unstructured":"Wang, Q.: The global solution of the n-body problem. Celestial Mech. Dyn. Astr. 50(1), 73\u201388 (1991)","journal-title":"Celestial Mech. Dyn. Astr."},{"key":"489_CR25","unstructured":"Zhang, Y., Derbenev, Y., Douglas, D., et al.: Advance in MEIC cooling studies. In: Proceedings of COOL2013, vol. 13 (2013)"}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11075-018-0489-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-018-0489-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-018-0489-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,17]],"date-time":"2020-05-17T15:49:29Z","timestamp":1589730569000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11075-018-0489-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,2,19]]},"references-count":25,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2019,2]]}},"alternative-id":["489"],"URL":"https:\/\/doi.org\/10.1007\/s11075-018-0489-z","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"type":"print","value":"1017-1398"},{"type":"electronic","value":"1572-9265"}],"subject":[],"published":{"date-parts":[[2018,2,19]]},"assertion":[{"value":"24 July 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"31 January 2018","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 February 2018","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}