{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,3,31]],"date-time":"2023-03-31T22:11:03Z","timestamp":1680300663819},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2014,4,1]]},"abstract":"<jats:title>Abstract.<\/jats:title>\n               <jats:p>\nInitial boundary value problems of the Dirichlet type for quasilinear functional differential equations are considered.\nExplicit difference schemes of the Euler type and implicit difference methods are investigated.\nSufficient conditions for the convergence of approximate solutions\nare given and comparisons of the methods are presented.\nIt is proved that assumptions on the regularity of given functions\nare the same for both classes of the methods. It is shown that conditions on the mesh for explicit\ndifference schemes are more\nrestrictive than suitable assumptions for implicit\nmethods.\nError estimates for both methods are presented.\nInterpolating operators corresponding to functional variables are constructed.\n<\/jats:p>","DOI":"10.1515\/cmam-2013-0025","type":"journal-article","created":{"date-parts":[[2013,11,26]],"date-time":"2013-11-26T20:12:14Z","timestamp":1385496734000},"page":"151-175","source":"Crossref","is-referenced-by-count":0,"title":["Explicit and Implicit Difference Methods for Quasilinear First Order Partial Functional Differential Equations"],"prefix":"10.1515","volume":"14","author":[{"given":"Zdzis\u0142aw","family":"Kamont","sequence":"first","affiliation":[{"name":"Institute of Mathematics, University of Gda\u0144sk, Wit Stwosz Street 57, 80-952 Gda\u0144sk, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Anna","family":"Szafra\u0144ska","sequence":"additional","affiliation":[{"name":"Department of Mathematical and Numerical Analysis, Gda\u0144sk University of Technology, Gabriel Narutowicz Street 11\u201312, 80-233 Gda\u0144sk, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2013,11,27]]},"container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/14\/2\/article-p151.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2013-0025\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2013-0025\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,31]],"date-time":"2023-03-31T21:32:35Z","timestamp":1680298355000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2013-0025\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,11,27]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2014,3,13]]},"published-print":{"date-parts":[[2014,4,1]]}},"alternative-id":["10.1515\/cmam-2013-0025"],"URL":"https:\/\/doi.org\/10.1515\/cmam-2013-0025","relation":{},"ISSN":["1609-4840","1609-9389"],"issn-type":[{"value":"1609-4840","type":"print"},{"value":"1609-9389","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,11,27]]}}}