{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,30]],"date-time":"2022-03-30T23:24:27Z","timestamp":1648682667097},"reference-count":5,"publisher":"Hindawi Limited","license":[{"start":{"date-parts":[[2015,1,1]],"date-time":"2015-01-01T00:00:00Z","timestamp":1420070400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2015]]},"abstract":"<jats:p>The aim of this work is to study a semidiscrete Crank-Nicolson type scheme in order to approximate numerically the Dirichlet-to-Neumann semigroup. We construct an approximating family of operators for the Dirichlet-to-Neumann semigroup, which satisfies the assumptions of Chernoff\u2019s product formula, and consequently the Crank-Nicolson scheme converges to the exact solution. Finally, we write a<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:msub><mml:mrow><mml:mi>P<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn mathvariant=\"normal\">1<\/mml:mn><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:math>finite element scheme for the problem, and we illustrate this convergence by means of a FreeFem++ implementation.<\/jats:p>","DOI":"10.1155\/2015\/429641","type":"journal-article","created":{"date-parts":[[2015,7,9]],"date-time":"2015-07-09T21:01:29Z","timestamp":1436475689000},"page":"1-5","source":"Crossref","is-referenced-by-count":0,"title":["A Crank-Nicolson Scheme for the Dirichlet-to-Neumann Semigroup"],"prefix":"10.1155","volume":"2015","author":[{"given":"Rola","family":"Ali Ahmad","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Beirut Arab University, P.O. Box 11-5020, Beirut, Lebanon"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Toufic","family":"El Arwadi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Beirut Arab University, P.O. Box 11-5020, Beirut, Lebanon"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Houssam","family":"Chrayteh","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Beirut Arab University, P.O. Box 11-5020, Beirut, Lebanon"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jean-Marc","family":"Sac-Ep\u00e9e","sequence":"additional","affiliation":[{"name":"Institut \u00c9lie Cartan de Lorraine, UMR 7502, Universit\u00e9 de Lorraine, 57 045 Metz, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"98","reference":[{"key":"10","year":"2012"},{"issue":"3","key":"4","first-page":"241","volume":"11","year":"2006","journal-title":"Advances in Differential Equations"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1007\/s00233-012-9380-8"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1007\/s00233-014-9572-5"},{"key":"11","series-title":"Graduate Texts in Mathematics","volume":"194","year":"2000"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2015\/429641.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2015\/429641.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2015\/429641.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2016,8,18]],"date-time":"2016-08-18T19:50:17Z","timestamp":1471549817000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2015\/429641\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015]]},"references-count":5,"alternative-id":["429641","429641"],"URL":"https:\/\/doi.org\/10.1155\/2015\/429641","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"value":"1110-757X","type":"print"},{"value":"1687-0042","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015]]}}}