{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,3]],"date-time":"2022-04-03T01:38:36Z","timestamp":1648949916474},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"1","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>An initial-boundary value problem is considered in an unbounded do-\nmain on the x-axis for a singularly perturbed parabolic reaction-diffusion equation. For small values of the\nparameter \u03b5, a parabolic boundary layer arises in a neighbourhood of the lateral part\nof the boundary. In this problem, the error of a discrete solution in the maximum\nnorm grows without bound even for fixed values of the parameter \u03b5. In\nthe present paper, the proximity of solutions of the initial-boundary value problem\nand of its numerical approximations is considered. Using the method of special grids condensing\nin a neighbourhood of the boundary layer, a special finite difference scheme converging\n\u03b5-uniformly in the weight maximum norm has been constructed.<\/jats:p>","DOI":"10.2478\/cmam-2009-0006","type":"journal-article","created":{"date-parts":[[2013,2,15]],"date-time":"2013-02-15T09:05:50Z","timestamp":1360919150000},"page":"100-110","source":"Crossref","is-referenced-by-count":0,"title":["Numerical Method for Singularly Perturbed Parabolic Equations in Unbounded Domains in the Case of Solutions Growing at Infinity"],"prefix":"10.2478","volume":"9","author":[{"given":"G. I.","family":"Shishkin","sequence":"first","affiliation":[{"name":"1Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, 16 S.Kovalevskaya Str., 620219 Ekaterinburg, Russia."}]}],"member":"374","container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/9\/1\/article-p100.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.2478\/cmam-2009-0006\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,22]],"date-time":"2021-04-22T14:21:22Z","timestamp":1619101282000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/9\/1\/article-p100.xml"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009]]},"references-count":0,"journal-issue":{"issue":"1"},"URL":"https:\/\/doi.org\/10.2478\/cmam-2009-0006","relation":{},"ISSN":["1609-9389","1609-4840"],"issn-type":[{"value":"1609-9389","type":"electronic"},{"value":"1609-4840","type":"print"}],"subject":[],"published":{"date-parts":[[2009]]}}}