{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,17]],"date-time":"2026-03-17T19:44:34Z","timestamp":1773776674002,"version":"3.50.1"},"reference-count":11,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2001,3,1]],"date-time":"2001-03-01T00:00:00Z","timestamp":983404800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2001,3,1]],"date-time":"2001-03-01T00:00:00Z","timestamp":983404800000},"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":[[2001,3]]},"DOI":"10.1023\/a:1016607621405","type":"journal-article","created":{"date-parts":[[2002,12,29]],"date-time":"2002-12-29T18:09:18Z","timestamp":1041185358000},"page":"201-218","source":"Crossref","is-referenced-by-count":6,"title":["On the implementation of ESIRK methods for stiff IVPs"],"prefix":"10.1007","volume":"26","author":[{"given":"J.C.","family":"Butcher","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"D.J.L.","family":"Chen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"317805_CR1","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1007\/BF01932265","volume":"16","author":"J.C. Butcher","year":"1976","unstructured":"J.C. Butcher, On the implementation of implicit Runge\u2013Kutta methods, BIT 16 (1976) 237\u2013240.","journal-title":"BIT"},{"key":"317805_CR2","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1145\/42288.42341","volume":"14","author":"J.C. Butcher","year":"1988","unstructured":"J.C. Butcher, Towards efficient implementation of singly-implicit methods, ACM Trans. Math. Software 14 (1988) 68\u201375.","journal-title":"ACM Trans. Math. Software"},{"key":"317805_CR3","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1016\/S0168-9274(97)00031-7","volume":"24","author":"J.C. Butcher","year":"1997","unstructured":"J.C. Butcher and P. Chartier, A generalization of singly-implicit Runge\u2013Kutta methods, Appl. Numer. Math. 24 (1997) 343\u2013350.","journal-title":"Appl. Numer. Math."},{"key":"317805_CR4","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1023\/A:1019176422613","volume":"20","author":"J.C. Butcher","year":"1999","unstructured":"J.C. Butcher and P. Chartier, The effective order of singly-implicit Runge\u2013Kutta methods, Numer. Algorithms 20 (1999) 269\u2013284.","journal-title":"Numer. Algorithms"},{"key":"317805_CR5","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1016\/S0168-9274(98)00076-2","volume":"28","author":"J.C. Butcher","year":"1998","unstructured":"J.C. Butcher and D.J.L. Chen, ESIRK methods and variable stepsize, Appl. Numer. Math. 28 (1998) 193\u2013207.","journal-title":"Appl. Numer. Math."},{"key":"317805_CR6","unstructured":"D.J.L. Chen, The effective order of singly-implicit methods for stiff differential equations, Ph.D. thesis, The University of Auckland (1998)."},{"key":"317805_CR7","volume-title":"Diagonally extended singly implicit Runge\u2013Kutta methods for stiff initial value problems","author":"M.T. Diamantakis","year":"1995","unstructured":"M.T. Diamantakis, Diagonally extended singly implicit Runge\u2013Kutta methods for stiff initial value problems, Ph.D. thesis, Imperial College, University of London, UK (1995)."},{"key":"317805_CR8","volume-title":"Control of error and convergence in ODE solvers","author":"K. Gustafsson","year":"1993","unstructured":"K. Gustafsson, Control of error and convergence in ODE solvers, Ph.D. thesis, Lund Institute of Technology, Sweden (1993)."},{"key":"317805_CR9","volume-title":"Solving Ordinary Differential Equations II, Stiff and Differential-Algebraic Problems","author":"E. Hairer","year":"1987","unstructured":"E. Hairer and G. Wanner, Solving Ordinary Differential Equations II, Stiff and Differential-Algebraic Problems (Springer, Berlin, 1987)."},{"key":"317805_CR10","volume-title":"A Systematized Collection of ODE Solvers","author":"A. Hindmarsh","year":"1983","unstructured":"A. Hindmarsh, A Systematized Collection of ODE Solvers (North-Holland, Amsterdam, 1983)."},{"key":"317805_CR11","doi-asserted-by":"crossref","first-page":"100","DOI":"10.1007\/BF01939366","volume":"26","author":"S.P. N\u00f8rsett","year":"1986","unstructured":"S.P. N\u00f8rsett and P.G. Thomsen, Local error control in SDIRK-methods, BIT 26 (1986) 100\u201313.","journal-title":"BIT"}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1016607621405.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1023\/A:1016607621405\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1016607621405.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,7]],"date-time":"2025-07-07T07:22:24Z","timestamp":1751872944000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1023\/A:1016607621405"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,3]]},"references-count":11,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2001,3]]}},"alternative-id":["317805"],"URL":"https:\/\/doi.org\/10.1023\/a:1016607621405","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[2001,3]]}}}