{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,11,17]],"date-time":"2023-11-17T08:28:58Z","timestamp":1700209738730},"reference-count":4,"publisher":"Wiley","issue":"9","license":[{"start":{"date-parts":[[2005,6,21]],"date-time":"2005-06-21T00:00:00Z","timestamp":1119312000000},"content-version":"vor","delay-in-days":3946,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Commun. Numer. Meth. Engng."],"published-print":{"date-parts":[[1994,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Semi\u2010discretization methods with iterated corrections are considered for solving the heat equation with boundary conditions containing integrals over the interior of the interval. The given problem is transformed into an ordinary differential system of equations, when we substitute the spatial derivative by finite differences. Such a system is then solved with an implicit integrator together with a quadrature method for the boundary integrals and, for each time step, the numerical scheme \u2010 implicit integrator and quadrature method \u2010 is repeated iteratively in order to achieve a given accuracy. The extra work we need with the iterated corrections enables us to take care of the interrelation of the solution <jats:italic>u<\/jats:italic>(<jats:italic>x, t<\/jats:italic>) at the interior and at the boundary points and also to start the numerical process with rough approximations of <jats:italic>u<\/jats:italic>(0, <jats:italic>t<\/jats:italic>) and <jats:italic>u<\/jats:italic>(1, <jats:italic>t<\/jats:italic>).<\/jats:p><jats:p>An improvement of the results is achieved when we estimate the local spatial truncation error and make the injection of that estimation into the ordinary differential system. Numerical experiments are presented.<\/jats:p>","DOI":"10.1002\/cnm.1640100910","type":"journal-article","created":{"date-parts":[[2005,8,8]],"date-time":"2005-08-08T16:51:14Z","timestamp":1123519874000},"page":"751-758","source":"Crossref","is-referenced-by-count":3,"title":["Semi\u2010discretization method for the heat equation with non\u2010local boundary conditions"],"prefix":"10.1002","volume":"10","author":[{"given":"A. L.","family":"Ara\u00fajo","sequence":"first","affiliation":[]},{"given":"F. Aleixo","family":"Oliveira","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2005,6,21]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1090\/qam\/678203"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1090\/qam\/693879"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01931285"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1090\/qam\/860893"}],"container-title":["Communications in Numerical Methods in Engineering"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fcnm.1640100910","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/cnm.1640100910","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,24]],"date-time":"2023-10-24T12:25:15Z","timestamp":1698150315000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/cnm.1640100910"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1994,9]]},"references-count":4,"journal-issue":{"issue":"9","published-print":{"date-parts":[[1994,9]]}},"alternative-id":["10.1002\/cnm.1640100910"],"URL":"https:\/\/doi.org\/10.1002\/cnm.1640100910","archive":["Portico"],"relation":{},"ISSN":["1069-8299","1099-0887"],"issn-type":[{"value":"1069-8299","type":"print"},{"value":"1099-0887","type":"electronic"}],"subject":[],"published":{"date-parts":[[1994,9]]}}}