{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,5]],"date-time":"2024-09-05T06:06:13Z","timestamp":1725516373626},"publisher-location":"Berlin, Heidelberg","reference-count":14,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540698401"},{"type":"electronic","value":"9783540698487"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"DOI":"10.1007\/978-3-540-69848-7_59","type":"book-chapter","created":{"date-parts":[[2008,8,12]],"date-time":"2008-08-12T12:07:43Z","timestamp":1218542863000},"page":"736-751","source":"Crossref","is-referenced-by-count":2,"title":["Collocation\u2013Based Two Step Runge\u2013Kutta Methods for Ordinary Differential Equations"],"prefix":"10.1007","author":[{"given":"R.","family":"D\u2019Ambrosio","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M.","family":"Ferro","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"B.","family":"Paternoster","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"59_CR1","doi-asserted-by":"crossref","DOI":"10.1002\/0470868279","volume-title":"Numerical methods for Ordinary Differential Equations","author":"J.C. Butcher","year":"2003","unstructured":"Butcher, J.C.: Numerical methods for Ordinary Differential Equations. Wiley, Chichester (2003)"},{"key":"59_CR2","unstructured":"D\u2019Ambrosio, R., Ferro, M., Jackiewicz, Z., Paternoster, B.: Almost two-step collocation methods for Ordinary Differential Equations (in preparation)"},{"key":"59_CR3","first-page":"17","volume":"R-3","author":"A. Guillou","year":"1969","unstructured":"Guillou, A., Soul\u00e9, F.L.: La r\u00e9solution num\u00e9rique des probl\u00e8mes differentiels aux conditions par des m\u00e9thodes de collocation. RAIRO Anal. Num\u00e9r. Ser. Rouge\u00a0R-3, 17\u201344 (1969)","journal-title":"RAIRO Anal. Num\u00e9r. Ser. Rouge"},{"key":"59_CR4","series-title":"Springer Series in Computational Mathematics","volume-title":"Solving Ordinary Differential Equations I \u2013 Nonstiff Problems","author":"E. Hairer","year":"2000","unstructured":"Hairer, E., Norsett, S.P., Wanner, G.: Solving Ordinary Differential Equations I \u2013 Nonstiff Problems. Springer Series in Computational Mathematics, vol.\u00a08. Springer, Berlin (2000)"},{"key":"59_CR5","series-title":"Springer Series in Computational Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-05018-7","volume-title":"Solving Ordinary Differential Equations II \u2013 Stiff and Differential\u2013Algebraic Problems","author":"E. Hairer","year":"2002","unstructured":"Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II \u2013 Stiff and Differential\u2013Algebraic Problems. Springer Series in Computational Mathematics, vol.\u00a014. Springer, Berlin (2002)"},{"key":"59_CR6","unstructured":"Jackiewicz, Z.: General linear methods (in preparation)"},{"issue":"5","key":"59_CR7","doi-asserted-by":"publisher","first-page":"1390","DOI":"10.1137\/0732064","volume":"32","author":"Z. Jackiewicz","year":"1995","unstructured":"Jackiewicz, Z., Tracogna, S.: A general class of two\u2013step Runge\u2013Kutta methods for ordinary differential equations. SIAM J. Numer. Anal.\u00a032(5), 1390\u20131427 (1995)","journal-title":"SIAM J. Numer. Anal."},{"key":"59_CR8","doi-asserted-by":"publisher","first-page":"215","DOI":"10.1007\/BF01933194","volume":"20","author":"L. Kramarz","year":"1980","unstructured":"Kramarz, L.: Stability of collocation methods for the numerical solution of y\n                  \u2033=\u2009f(t,y). BIT\u00a020, 215\u2013222 (1980)","journal-title":"BIT"},{"key":"59_CR9","volume-title":"Numerical methods for ordinary differential systems: The initial value problem","author":"J.D. Lambert","year":"1991","unstructured":"Lambert, J.D.: Numerical methods for ordinary differential systems: The initial value problem. Wiley, Chichester (1991)"},{"issue":"185","key":"59_CR10","doi-asserted-by":"publisher","first-page":"65","DOI":"10.2307\/2008653","volume":"52","author":"I. Lie","year":"1989","unstructured":"Lie, I., Norsett, S.P.: Superconvergence for Multistep Collocation. Mathematics of Computation\u00a052(185), 65\u201379 (1989)","journal-title":"Mathematics of Computation"},{"key":"59_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"418","DOI":"10.1007\/978-3-540-25944-2_55","volume-title":"Computational Science - ICCS 2004","author":"S. Martucci","year":"2004","unstructured":"Martucci, S., Paternoster, B.: Vandermonde\u2013type matrices in two step collocation methods for special second order Ordinary Differential Equations. In: Bubak, M., van Albada, G.D., Sloot, P.M.A., Dongarra, J. (eds.) ICCS 2004. LNCS, vol.\u00a03039, pp. 418\u2013425. Springer, Heidelberg (2004)"},{"issue":"4","key":"59_CR12","first-page":"347","volume":"6","author":"B. Paternoster","year":"2001","unstructured":"Paternoster, B.: General Two-Step Runge-Kutta methods based on algebraic and trigonometric polynomials. Int. J. Appl. Math.\u00a06(4), 347\u2013362 (2001)","journal-title":"Int. J. Appl. Math."},{"key":"59_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"459","DOI":"10.1007\/3-540-47789-6_48","volume-title":"ICCS 2002","author":"B. Paternoster","year":"2002","unstructured":"Paternoster, B.: Two step Runge-Kutta-Nystr\u00f6m methods for y\n                  \u2033=\u2009f(x,y) and P\u2013stability. In: Sloot, P.M.A., Tan, C.J.K., Dongarra, J., Hoekstra, A.G. (eds.) ICCS 2002. LNCS, vol.\u00a02331, pp. 459\u2013466. Springer, Heidelberg (2002)"},{"key":"59_CR14","doi-asserted-by":"crossref","unstructured":"Petzold, L.R., Jay, L.O., Yen, J.: Numerical solution of highly oscillatory ordinary differential equations. Acta Numerica, 437\u2013483 (1997)","DOI":"10.1017\/S0962492900002750"}],"container-title":["Lecture Notes in Computer Science","Computational Science and Its Applications \u2013 ICCSA 2008"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-540-69848-7_59.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,5,3]],"date-time":"2021-05-03T00:09:59Z","timestamp":1620000599000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-540-69848-7_59"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[null]]},"ISBN":["9783540698401","9783540698487"],"references-count":14,"URL":"https:\/\/doi.org\/10.1007\/978-3-540-69848-7_59","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[]}}