{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,11,9]],"date-time":"2023-11-09T09:00:01Z","timestamp":1699520401326},"reference-count":22,"publisher":"Elsevier BV","issue":"9","license":[{"start":{"date-parts":[[2011,5,1]],"date-time":"2011-05-01T00:00:00Z","timestamp":1304208000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematics and Computers in Simulation"],"published-print":{"date-parts":[[2011,5]]},"DOI":"10.1016\/j.matcom.2011.01.005","type":"journal-article","created":{"date-parts":[[2011,2,2]],"date-time":"2011-02-02T09:45:17Z","timestamp":1296639917000},"page":"1707-1728","source":"Crossref","is-referenced-by-count":26,"title":["Construction and implementation of highly stable two-step continuous methods for stiff differential systems"],"prefix":"10.1016","volume":"81","author":[{"given":"Raffaele","family":"D\u2019Ambrosio","sequence":"first","affiliation":[]},{"given":"Zdzislaw","family":"Jackiewicz","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/j.matcom.2011.01.005_bib0005","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1016\/j.apnum.2004.08.010","article-title":"Nordsieck representation of two-step Runge-Kutta methods for ordinary differential equations","volume":"53","author":"Bartoszewski","year":"2005","journal-title":"Appl. Numer. Math."},{"key":"10.1016\/j.matcom.2011.01.005_bib0015","series-title":"The Numerical Analysis of Ordinary Differential Equations. Runge-Kutta and General Linear Methods","author":"Butcher","year":"1987"},{"key":"10.1016\/j.matcom.2011.01.005_bib0020","series-title":"Numerical Methods for Ordinary Differential Equations","author":"Butcher","year":"2008"},{"issue":"2","key":"10.1016\/j.matcom.2011.01.005_bib0040","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1007\/s10915-010-9378-x","article-title":"Two-step Runge-Kutta methods with quadratic stability functions","volume":"44","author":"Conte","year":"2010","journal-title":"J. Sci. Comput."},{"key":"10.1016\/j.matcom.2011.01.005_bib0045","unstructured":"D. Conte, R. D\u2019Ambrosio, Z. Jackiewicz, B. Paternoster, Algebraically stable two-step collocation methods for ordinary differential equations, submitted for publication."},{"key":"10.1016\/j.matcom.2011.01.005_bib0050","doi-asserted-by":"crossref","first-page":"839","DOI":"10.1016\/j.amc.2008.07.026","article-title":"Two-step almost collocation methods for Volterra integral equations","volume":"204","author":"Conte","year":"2008","journal-title":"Appl. Math. Comput."},{"key":"10.1016\/j.matcom.2011.01.005_bib0055","unstructured":"D. Conte, R. D\u2019Ambrosio, B. Paternoster, Two-step continuous methods with structured coefficient matrices for Volterra integral equations, Appl. Numer. Math., in press."},{"key":"10.1016\/j.matcom.2011.01.005_bib0060","unstructured":"R. D\u2019Ambrosio, Highly Stable Multistage Numerical Methods for Functional Equations, Bi-Nationally Supervised PhD Thesis, University of Salerno - Arizona State University, 2010."},{"issue":"2\u20133","key":"10.1016\/j.matcom.2011.01.005_bib0065","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1007\/s11075-009-9280-5","article-title":"Two-step almost collocation methods for ordinary differential equations","volume":"53","author":"D\u2019Ambrosio","year":"2010","journal-title":"Numer. Algorithms"},{"issue":"2","key":"10.1016\/j.matcom.2011.01.005_bib0070","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1007\/s11075-009-9329-5","article-title":"Continuous two-step Runge-Kutta methods for ordinary differential equations","volume":"54","author":"D\u2019Ambrosio","year":"2010","journal-title":"Numer. Algorithms"},{"key":"10.1016\/j.matcom.2011.01.005_bib0075","unstructured":"R. D\u2019Ambrosio, B. Paternoster, Two-step modified collocation methods with structured coefficient matrices, Appl. Numer. Math., in press."},{"issue":"2","key":"10.1016\/j.matcom.2011.01.005_bib0080","doi-asserted-by":"crossref","first-page":"270","DOI":"10.1007\/BF01934091","article-title":"A PI stepsize control for the numerical solution of ordinary differential equations","volume":"28","author":"Gustafsson","year":"1988","journal-title":"BIT"},{"key":"10.1016\/j.matcom.2011.01.005_bib0085","series-title":"Solving Ordinary Differential Equations. I. Nonstiff Problems, Springer Series in Computational Mathematics 8","author":"Hairer","year":"2000"},{"key":"10.1016\/j.matcom.2011.01.005_bib0090","series-title":"Solving Ordinary Differential Equations. II. Stiff and Differential-Algebraic Problems, Springer Series in Computational Mathematics 14","author":"Hairer","year":"2002"},{"key":"10.1016\/j.matcom.2011.01.005_bib0095","series-title":"General Linear Methods for Ordinary Differential Equations","author":"Jackiewicz","year":"2009"},{"key":"10.1016\/j.matcom.2011.01.005_bib0100","doi-asserted-by":"crossref","first-page":"1390","DOI":"10.1137\/0732064","article-title":"A general class of two-step Runge-Kutta methods for ordinary differential equations","volume":"32","author":"Jackiewicz","year":"1995","journal-title":"SIAM J. Numer. Anal."},{"key":"10.1016\/j.matcom.2011.01.005_bib0105","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1007\/BF02142812","article-title":"Variable stepsize continuous two-step Runge-Kutta methods for ordinary differential equations","volume":"12","author":"Jackiewicz","year":"1996","journal-title":"Numer. Algorithms"},{"key":"10.1016\/j.matcom.2011.01.005_bib0110","series-title":"Computational Methods in Ordinary Differential Equations","author":"Lambert","year":"1973"},{"issue":"2","key":"10.1016\/j.matcom.2011.01.005_bib0120","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1016\/0377-0427(84)90020-7","article-title":"Error estimators for stiff differential equations","volume":"11","author":"Shampine","year":"1984","journal-title":"J. Comput. Appl. Math."},{"key":"10.1016\/j.matcom.2011.01.005_bib0125","first-page":"205","article-title":"\u00dcber Potenzreihen die im Innern des Einheitskreises beschr\u00e4nkt sind","volume":"147","author":"Schur","year":"1916","journal-title":"J. Reine Angew. Math."},{"issue":"1\u20134","key":"10.1016\/j.matcom.2011.01.005_bib0130","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1023\/A:1021160023092","article-title":"Automatic control and adaptive time-stepping","volume":"31","author":"S\u00f6derlind","year":"2002","journal-title":"Numer. Algorithms"},{"issue":"1","key":"10.1016\/j.matcom.2011.01.005_bib0135","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/641876.641877","article-title":"Digital filters in adaptive time-stepping","volume":"29","author":"S\u00f6derlind","year":"2003","journal-title":"ACM Trans. Math. Software"}],"container-title":["Mathematics and Computers in Simulation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0378475411000334?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0378475411000334?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2018,12,5]],"date-time":"2018-12-05T03:54:02Z","timestamp":1543982042000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0378475411000334"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,5]]},"references-count":22,"journal-issue":{"issue":"9","published-print":{"date-parts":[[2011,5]]}},"alternative-id":["S0378475411000334"],"URL":"https:\/\/doi.org\/10.1016\/j.matcom.2011.01.005","relation":{},"ISSN":["0378-4754"],"issn-type":[{"value":"0378-4754","type":"print"}],"subject":[],"published":{"date-parts":[[2011,5]]}}}