{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T04:38:53Z","timestamp":1780461533337,"version":"3.54.1"},"reference-count":20,"publisher":"Springer Science and Business Media LLC","issue":"1-4","license":[{"start":{"date-parts":[[2002,12,1]],"date-time":"2002-12-01T00:00:00Z","timestamp":1038700800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2002,12,1]],"date-time":"2002-12-01T00:00:00Z","timestamp":1038700800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numerical Algorithms"],"published-print":{"date-parts":[[2002,12]]},"DOI":"10.1023\/a:1021160023092","type":"journal-article","created":{"date-parts":[[2003,3,21]],"date-time":"2003-03-21T00:40:25Z","timestamp":1048207225000},"page":"281-310","source":"Crossref","is-referenced-by-count":156,"title":["Automatic Control and Adaptive Time-Stepping"],"prefix":"10.1007","volume":"31","author":[{"given":"Gustaf","family":"S\u00f6derlind","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","reference":[{"key":"5092688_CR1","volume-title":"Computer Controlled Systems-Theory and Design","author":"K.J. \u00c5str\u00f6m","year":"1990","unstructured":"K.J. \u00c5str\u00f6m and B. Wittenmark, Computer Controlled Systems-Theory and Design, 2nd ed. (Prentice-Hall, Englewood Cliffs, NJ, 1990).","edition":"2nd ed."},{"key":"5092688_CR2","volume-title":"Numerische Mathematik II: Integration gew\u00f6hnlicher Differentialgleichungen","author":"P. Deuflhard","year":"1994","unstructured":"P. Deuflhard and F. Bornemann, Numerische Mathematik II: Integration gew\u00f6hnlicher Differentialgleichungen (Walter de Gruyter, Berlin, 1994)."},{"key":"5092688_CR3","volume-title":"Numerical Initial Value Problems in Ordinary Differential Equations","author":"C.W. Gear","year":"1971","unstructured":"C.W. Gear, Numerical Initial Value Problems in Ordinary Differential Equations (Prentice-Hall, Englewood Cliffs, NJ, 1971)."},{"key":"5092688_CR4","doi-asserted-by":"crossref","first-page":"270","DOI":"10.1007\/BF01934091","volume":"28","author":"K. Gustafsson","year":"1988","unstructured":"K. Gustafsson, M. Lundh and G. S\u00f6derlind, A PI stepsize control for the numerical solution of ordinary differential equations, BIT 28 (1988) 270\u2013287.","journal-title":"BIT"},{"key":"5092688_CR5","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1145\/210232.210242","volume":"17","author":"K. Gustafsson","year":"1991","unstructured":"K. Gustafsson, Control theoretic techniques for stepsize selection in explicit Runge-Kutta methods, ACM TOMS 17 (1991) 533\u2013554.","journal-title":"ACM TOMS"},{"key":"5092688_CR6","doi-asserted-by":"crossref","first-page":"496","DOI":"10.1145\/198429.198437","volume":"20","author":"K. Gustafsson","year":"1994","unstructured":"K. Gustafsson, Control theoretic techniques for stepsize selection in implicit Runge-Kutta methods, ACM TOMS 20 (1994) 496\u2013517.","journal-title":"ACM TOMS"},{"key":"5092688_CR7","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1137\/S1064827595287109","volume":"18","author":"K. Gustafsson","year":"1997","unstructured":"K. Gustafsson and G. S\u00f6derlind, Control strategies for the iterative solution of nonlinear equations in ODE solvers, SIAM J. Sci. Comput. 18 (1997) 23\u201340.","journal-title":"SIAM J. Sci. Comput."},{"key":"5092688_CR8","volume-title":"Solving Ordinary Differential Equations I: Nonstiff Problems","author":"E. Hairer","year":"1993","unstructured":"E. Hairer, S.P. N\u00b8rsett and G. Wanner, Solving Ordinary Differential Equations I: Nonstiff Problems, 2nd revised ed. (Springer, Berlin, 1993).","edition":"2nd revised ed."},{"key":"5092688_CR9","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-05221-7","volume-title":"Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems","author":"E. Hairer","year":"1996","unstructured":"E. Hairer and G. Wanner, Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems, 2nd revised ed. (Springer, Berlin, 1996).","edition":"2nd revised ed."},{"key":"5092688_CR10","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1145\/214408.214424","volume":"11","author":"G. Hall","year":"1985","unstructured":"G. Hall, Equilibrium states of Runge-Kutta schemes, ACM TOMS 11 (1985) 289\u2013301.","journal-title":"ACM TOMS"},{"key":"5092688_CR11","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1145\/7921.7922","volume":"12","author":"G. Hall","year":"1986","unstructured":"G. Hall, Equilibrium states of Runge-Kutta schemes, part II, ACM TOMS 12 (1986) 183\u2013192.","journal-title":"ACM TOMS"},{"key":"5092688_CR12","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1093\/imanum\/8.3.305","volume":"8","author":"G. Hall","year":"1988","unstructured":"G. Hall and D. Higham, Analysis of stepsize selection schemes for Runge-Kutta codes, IMA J. Num. Anal. 8 (1988) 305\u2013310.","journal-title":"IMA J. Num. Anal."},{"key":"5092688_CR13","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/0377-0427(90)90192-3","volume":"29","author":"D. Higham","year":"1990","unstructured":"D. Higham and G. Hall, Embedded Runge-Kutta formulae with stable equilibrium states, J. Comput. Appl. Math. 29 (1990) 25\u201333.","journal-title":"J. Comput. Appl. Math."},{"key":"5092688_CR14","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1137\/S1064827596306963","volume":"20","author":"H. Olsson","year":"1999","unstructured":"H. Olsson and G. S\u00f6derlind, Stage value predictors and efficient Newton iterations in implicit Runge-Kutta methods, SIAM J. Sci. Comput. 20 (1999) 185\u2013202.","journal-title":"SIAM J. Sci. Comput."},{"key":"5092688_CR15","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1023\/A:1022399225591","volume":"40","author":"H. Olsson","year":"2000","unstructured":"H. Olsson and G. S\u00f6derlind, The approximate Runge-Kutta computational process, BIT 40 (2000) 351\u2013373.","journal-title":"BIT"},{"key":"5092688_CR16","volume-title":"Parallel software for implicit differential equations","author":"J.J.B. de Swart","year":"1997","unstructured":"J.J.B. de Swart, Parallel software for implicit differential equations, Ph.D. thesis, CWI, Amsterdam (1997)."},{"key":"5092688_CR17","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1016\/S0377-0427(97)00166-0","volume":"86","author":"J.J.B. de Swart","year":"1997","unstructured":"J.J.B. de Swart and G. S\u00f6derlind, On the construction of error estimators for implicit Runge-Kutta methods, J. Comput. Appl. Math. 86 (1997) 347\u2013358.","journal-title":"J. Comput. Appl. Math."},{"key":"5092688_CR18","volume-title":"System Identification","author":"T. S\u00f6derstr\u00f6m","year":"1989","unstructured":"T. S\u00f6derstr\u00f6m and P. Stoica, System Identification (Prentice-Hall, Englewood Cliffs, NJ, 1989)."},{"key":"5092688_CR19","first-page":"15","volume":"1","author":"H.A. Watts","year":"1984","unstructured":"H.A. Watts, Step size control in ordinary differential equation solvers, Trans. Soc. Comput. Sim. 1 (1984) 15\u201325.","journal-title":"Trans. Soc. Comput. Sim."},{"key":"5092688_CR20","volume-title":"Automatic numerical integration","author":"J.A. Zonneveld","year":"1964","unstructured":"J.A. Zonneveld, Automatic numerical integration, Ph.D. thesis, Math. Centre Tracts 8, CWI, Amsterdam (1964)."}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1021160023092.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1023\/A:1021160023092\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1021160023092.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,7]],"date-time":"2025-07-07T07:20:59Z","timestamp":1751872859000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1023\/A:1021160023092"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,12]]},"references-count":20,"journal-issue":{"issue":"1-4","published-print":{"date-parts":[[2002,12]]}},"alternative-id":["5092688"],"URL":"https:\/\/doi.org\/10.1023\/a:1021160023092","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,12]]}}}