{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,20]],"date-time":"2026-01-20T07:31:18Z","timestamp":1768894278615,"version":"3.49.0"},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2013,10,1]]},"abstract":"<jats:title>Abstract.<\/jats:title><jats:p>\nIn this paper initial boundary value problems, defined using quasilinear diffusion equations of Volterra type, are considered. These equations arise for instance to describe diffusion processes in viscoelastic media whose behavior is represented by a Voigt\u2013Kelvin model or a Maxwell model.\nA finite difference discretization defined on a general non-uniform grid with second order convergence order in space is proposed. The analysis does not follow the usual splitting of the global error using the solution of an elliptic equation induced by the integro-differential equation. The new approach enables us to reduce the smoothness required to the theoretical solution when the usual split technique is used.\nNon-singular and singular kernels are considered.\nNumerical simulations which show the effectiveness of the method are included.\n<\/jats:p>","DOI":"10.1515\/cmam-2013-0017","type":"journal-article","created":{"date-parts":[[2013,10,1]],"date-time":"2013-10-01T02:31:54Z","timestamp":1380594714000},"page":"471-493","source":"Crossref","is-referenced-by-count":13,"title":["A Second Order Approximation for Quasilinear Non-Fickian Diffusion Models"],"prefix":"10.1515","volume":"13","author":[{"given":"Jos\u00e9 A.","family":"Ferreira","sequence":"first","affiliation":[{"name":"1CMUC, Department of Mathematics, University of Coimbra, 3001-454 Coimbra, Portugal"}]},{"given":"Elias","family":"Gudi\u00f1o","sequence":"additional","affiliation":[{"name":"2CMUC, Department of Mathematics, University of Coimbra, 3001-454 Coimbra, Portugal"}]},{"given":"Paula","family":"de Oliveira","sequence":"additional","affiliation":[{"name":"3CMUC, Department of Mathematics, University of Coimbra, 3001-454 Coimbra, Portugal"}]}],"member":"374","container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/13\/4\/article-p471.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/downloadpdf\/journals\/cmam\/13\/4\/article-p471.xml","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,2,28]],"date-time":"2021-02-28T03:03:44Z","timestamp":1614481424000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2013-0017\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,10,1]]},"references-count":0,"journal-issue":{"issue":"4"},"URL":"https:\/\/doi.org\/10.1515\/cmam-2013-0017","relation":{},"ISSN":["1609-4840","1609-9389"],"issn-type":[{"value":"1609-4840","type":"print"},{"value":"1609-9389","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,10,1]]}}}