{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T03:32:57Z","timestamp":1648524777099},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"3","license":[{"start":{"date-parts":[[2009,1,1]],"date-time":"2009-01-01T00:00:00Z","timestamp":1230768000000},"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":[[2009]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A convection-dominated singularly perturbed two-point boundary problem\nis considered. For the numerical analysis of such problems, it is necessary to prove\ncertain a priori bounds on the derivatives of its solution. This paper provides a survey\nof the ways in which such bounds can be proved, while assessing the feasibility of\nextending such proofs to convection-dominated partial differential equations, and also\nintroduces a new proof based on a classical finite-difference argument of Brandt.<\/jats:p>","DOI":"10.2478\/cmam-2009-0017","type":"journal-article","created":{"date-parts":[[2013,4,15]],"date-time":"2013-04-15T16:13:17Z","timestamp":1366042397000},"page":"281-291","source":"Crossref","is-referenced-by-count":0,"title":["Singularly Perturbed Convection \u2014 Diffusion Problems in One Dimension: Bounds on Derivatives"],"prefix":"10.2478","volume":"9","author":[{"given":"A.","family":"Naughton","sequence":"first","affiliation":[{"name":"1School of Mathematics and Statistics, University of St. Andrews, North Haugh, St. Andrews, Fife KY16 9SS, Scotland."}]},{"given":"M.","family":"Stynes","sequence":"additional","affiliation":[{"name":"2Department of Mathematics, National University of Ireland, Cork, Ireland."}]}],"member":"374","container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/9\/3\/article-p281.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.2478\/cmam-2009-0017\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,22]],"date-time":"2021-04-22T14:21:28Z","timestamp":1619101288000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/9\/3\/article-p281.xml"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009]]},"references-count":0,"journal-issue":{"issue":"3"},"URL":"https:\/\/doi.org\/10.2478\/cmam-2009-0017","relation":{},"ISSN":["1609-9389","1609-4840"],"issn-type":[{"value":"1609-9389","type":"electronic"},{"value":"1609-4840","type":"print"}],"subject":[],"published":{"date-parts":[[2009]]}}}