{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T18:00:35Z","timestamp":1773856835474,"version":"3.50.1"},"reference-count":18,"publisher":"Springer Science and Business Media LLC","issue":"3-4","license":[{"start":{"date-parts":[[1999,2,1]],"date-time":"1999-02-01T00:00:00Z","timestamp":917827200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[1999,2,1]],"date-time":"1999-02-01T00:00:00Z","timestamp":917827200000},"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":[[1999,2]]},"DOI":"10.1023\/a:1019135630307","type":"journal-article","created":{"date-parts":[[2003,2,19]],"date-time":"2003-02-19T23:30:27Z","timestamp":1045697427000},"page":"237-261","source":"Crossref","is-referenced-by-count":30,"title":["Experiments with a variable-order type 1 DIMSIM code"],"prefix":"10.1007","volume":"22","author":[{"given":"J.C.","family":"Butcher","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"P.","family":"Chartier","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Z.","family":"Jackiewicz","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"329365_CR1","volume-title":"The Numerical Analysis of Ordinary Differential Equations","author":"J.C. Butcher","year":"1987","unstructured":"J.C. Butcher, The Numerical Analysis of Ordinary Differential Equations (Wiley, Chichester\/New York, 1987)."},{"key":"329365_CR2","doi-asserted-by":"publisher","first-page":"347","DOI":"10.1016\/0168-9274(93)90059-Z","volume":"11","author":"J.C. Butcher","year":"1993","unstructured":"J.C. Butcher, Diagonally-implicit multi-stage integration methods, Appl. Numer. Math. 11 (1993) 347\u2013363.","journal-title":"Appl. Numer. Math."},{"key":"329365_CR3","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1007\/BF01935014","volume":"34","author":"J.C. Butcher","year":"1994","unstructured":"J.C. Butcher, A transformation for the analysis of DIMSIMs, BIT 34 (1994) 25\u201332.","journal-title":"BIT"},{"key":"329365_CR4","series-title":"Report Series","volume-title":"The construction of DIMSIMs for stiff ODEs and DAEs","author":"J.C. Butcher","year":"1994","unstructured":"J.C. Butcher and P. Chartier, The construction of DIMSIMs for stiff ODEs and DAEs, Report Series No. 308, The University of Auckland, New Zealand (July 1994)."},{"key":"329365_CR5","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1023\/A:1019195215402","volume":"16","author":"J.C. Butcher","year":"1997","unstructured":"J.C. Butcher, P. Chartier and Z. Jackiewicz, Nordsieck representation of DIMSIMs, Numer. Algorithms 16 (1997) 209\u2013230.","journal-title":"Numer. Algorithms"},{"key":"329365_CR6","doi-asserted-by":"publisher","first-page":"452","DOI":"10.1007\/BF01990528","volume":"33","author":"J.C. Butcher","year":"1993","unstructured":"J.C. Butcher and Z. Jackiewicz, Diagonally implicit general linear methods for ordinary differential equations, BIT 33 (1993) 452\u2013472.","journal-title":"BIT"},{"key":"329365_CR7","doi-asserted-by":"publisher","first-page":"385","DOI":"10.1016\/S0168-9274(96)00043-8","volume":"21","author":"J.C. Butcher","year":"1996","unstructured":"J.C. Butcher and Z. Jackiewicz, Construction of diagonally implicit general linear methods of type 1 and 2 for ordinary differential equations, Appl. Numer. Math. 21 (1996) 385\u2013415.","journal-title":"Appl. Numer. Math."},{"key":"329365_CR8","doi-asserted-by":"publisher","first-page":"2119","DOI":"10.1137\/S0036142995282509","volume":"34","author":"J.C. Butcher","year":"1997","unstructured":"J.C. Butcher and Z. Jackiewicz, Implementation of diagonally implicit multistage integration methods for ordinary differential equations, SIAM J. Numer. Anal. 34 (1997) 2119\u20132141.","journal-title":"SIAM J. Numer. Anal."},{"key":"329365_CR9","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/S0168-9274(97)00109-8","volume":"27","author":"J.C. Butcher","year":"1998","unstructured":"J.C. Butcher and Z. Jackiewicz, Construction of high order diagonally implicit multistage integration methods for ordinary differential equations, Appl. Numer. Math. 27 (1998) 1\u201312.","journal-title":"Appl. Numer. Math."},{"key":"329365_CR10","doi-asserted-by":"publisher","first-page":"181","DOI":"10.1016\/S0377-0427(97)00039-3","volume":"81","author":"J.C. Butcher","year":"1997","unstructured":"J.C. Butcher, Z. Jackiewicz and H.D. Mittelmann, Nonlinear optimization approach to construction of general linear methods of high order, J. Comput. Appl. Math. 81 (1997) 181\u2013196.","journal-title":"J. Comput. Appl. Math."},{"key":"329365_CR11","first-page":"7","volume":"11","author":"P. Chartier","year":"1998","unstructured":"P. Chartier, The potential of parallel multi-value methods for the simulation of large real-life problems, CWI Quarterly 11 (1998) 7\u201332.","journal-title":"CWI Quarterly"},{"key":"329365_CR12","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1016\/0771-050X(80)90013-3","volume":"6","author":"J.R. Dormand","year":"1980","unstructured":"J.R. Dormand and P.J. Prince, A family of embedded Runge\u2013Kutta formulae, J. Comput. Appl. Math. 6 (1980) 19\u201326.","journal-title":"J. Comput. Appl. Math."},{"key":"329365_CR13","doi-asserted-by":"publisher","first-page":"175","DOI":"10.1016\/0377-0427(87)90015-X","volume":"18","author":"I. Gladwell","year":"1987","unstructured":"I. Gladwell, L.F. Shampine and R.W. Brankin, Automatic selection of the initial step size for an ODE solver, J. Comput. Appl. Math. 18 (1987) 175\u2013192.","journal-title":"J. Comput. Appl. Math."},{"key":"329365_CR14","volume-title":"Solving Ordinary Differential Equations I. Nonstiff Problems","author":"E. Hairer","year":"1993","unstructured":"E. Hairer, S.P. N\u00f8rsett and G. Wanner, Solving Ordinary Differential Equations I. Nonstiff Problems (Springer, Berlin, 1993)."},{"key":"329365_CR15","volume-title":"Numerical Solution of Ordinary Differential Equations","author":"L.F. Shampine","year":"1994","unstructured":"L.F. Shampine, Numerical Solution of Ordinary Differential Equations (Chapman Hall, New York\/London, 1994)."},{"key":"329365_CR16","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1137\/S1064827594276424","volume":"18","author":"L.F. Shampine","year":"1977","unstructured":"L.F. Shampine and M.W. Reichelt, The Matlab ODE suite, SIAM J. Sci. Comput. 18 (1977) 1\u201322.","journal-title":"SIAM J. Sci. Comput."},{"key":"329365_CR17","unstructured":"W.M. Wright, The construction of order 4 DIMSIM for ordinary differential equations, submitted."},{"key":"329365_CR18","volume-title":"Theoretical and practical investigation","author":"W.M. Wright","year":"1999","unstructured":"W.M. Wright, General linear methods for ordinary differential equations. Theoretical and practical investigation, M.Sc. thesis, The University of Auckland, New Zealand (1999)."}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1019135630307.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1023\/A:1019135630307\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1019135630307.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,7]],"date-time":"2025-07-07T07:17:15Z","timestamp":1751872635000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1023\/A:1019135630307"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999,2]]},"references-count":18,"journal-issue":{"issue":"3-4","published-print":{"date-parts":[[1999,2]]}},"alternative-id":["329365"],"URL":"https:\/\/doi.org\/10.1023\/a:1019135630307","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[1999,2]]}}}