{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T00:00:20Z","timestamp":1773792020227,"version":"3.50.1"},"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> The paper deals with difference schemes for the heat-conduction equa-\ntion with nonlocal boundary conditions containing two real parameters. Such\nschemes have been investigated for some special parameter values, but the general case\nwas not considered previously. The eigenvalue problem arises as a result of variable\ndivision and is solved here explicitly. The so-called reality domains were selected on\nthe plane for which all eigenvalues and eigenfunctions are real. It was demon-\nstrated that the difference schemes in question are symmetrizable in reality domains,\nthat is their transition operators are similar to self-adjoint ones. The necessary and\nsufficient stability conditions for difference schemes under consideration are obtained\nwith respect to the initial data in the specially constructed norm. The equivalence of\nthe above-mentioned norm to the grid L2-norm has been proved.<\/jats:p>","DOI":"10.2478\/cmam-2009-0005","type":"journal-article","created":{"date-parts":[[2013,2,15]],"date-time":"2013-02-15T09:05:50Z","timestamp":1360919150000},"page":"79-99","source":"Crossref","is-referenced-by-count":7,"title":["Stability of the Two-parameter Set of Nonlocal Difference Schemes"],"prefix":"10.2478","volume":"9","author":[{"given":"A.","family":"GULIN","sequence":"first","affiliation":[{"name":"1Faculty of Computational Mathematics and Cybernetics, Moscow State University, Leninskii Gory, Moscow, 119 992, Russia."}]},{"given":"V.","family":"MOROZOVA","sequence":"additional","affiliation":[{"name":"2Faculty of Computational Mathematics and Cybernetics, Moscow State University, Leninskii Gory, Moscow, 119 992, Russia."}]}],"member":"374","container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/9\/1\/article-p79.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.2478\/cmam-2009-0005\/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-p79.xml"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009]]},"references-count":0,"journal-issue":{"issue":"1"},"URL":"https:\/\/doi.org\/10.2478\/cmam-2009-0005","relation":{},"ISSN":["1609-9389","1609-4840"],"issn-type":[{"value":"1609-9389","type":"electronic"},{"value":"1609-4840","type":"print"}],"subject":[],"published":{"date-parts":[[2009]]}}}