{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,1]],"date-time":"2026-03-01T14:23:27Z","timestamp":1772375007409,"version":"3.50.1"},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"1","license":[{"start":{"date-parts":[[2005,1,1]],"date-time":"2005-01-01T00:00:00Z","timestamp":1104537600000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Comput. Methods Appl. Math."],"published-print":{"date-parts":[[2005]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In this paper we study the family of one-leg two-step second-order methods developed by Dahlquist et al., which possess the A-stability and G-stability\nproperties on any grid. These methods are implemented with the local-global step size control derived by Kulikov and Shindin with the aim to obtain automatically the\nnumerical solution with any reasonable accuracy set by the user. We show that the error control is more complicated in one-leg methods, especially when applied to stiffproblems. Thus, we adapt our local-global step size control for the methods indicated\nabove and test these adaptive algorithms in practice.<\/jats:p>","DOI":"10.2478\/cmam-2005-0004","type":"journal-article","created":{"date-parts":[[2013,4,15]],"date-time":"2013-04-15T16:15:03Z","timestamp":1366042503000},"page":"86-96","source":"Crossref","is-referenced-by-count":9,"title":["One-leg Integration of Ordinary Differential Equations with Global Error Control"],"prefix":"10.2478","volume":"5","author":[{"given":"Gennady Yu.","family":"Kulikov","sequence":"first","affiliation":[{"name":"1School of Computational and Applied Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, Johannesburg, South Africa."}]},{"given":"Sergey K.","family":"Shindin","sequence":"additional","affiliation":[{"name":"1School of Computational and Applied Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, Johannesburg, South Africa."}]}],"member":"374","container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/5\/1\/article-p86.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.2478\/cmam-2005-0004\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,22]],"date-time":"2021-04-22T14:20:30Z","timestamp":1619101230000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/5\/1\/article-p86.xml"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005]]},"references-count":0,"journal-issue":{"issue":"1"},"URL":"https:\/\/doi.org\/10.2478\/cmam-2005-0004","relation":{},"ISSN":["1609-9389","1609-4840"],"issn-type":[{"value":"1609-9389","type":"electronic"},{"value":"1609-4840","type":"print"}],"subject":[],"published":{"date-parts":[[2005]]}}}