{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,17]],"date-time":"2026-01-17T07:46:04Z","timestamp":1768635964902,"version":"3.49.0"},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"3","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>This paper presents a new technique for numerical treatments of Volterra\ndelay integro-differential equations that have many applications in biological and physical\nsciences. The technique is based on the mono-implicit Runge \u2014 Kutta method for treating the differential part and the collocation method (using\nBoole\u2019s quadrature rule) for treating the integral part. The efficiency and stability\nproperties of this technique have been studied. Numerical results are presented to\ndemonstrate the effectiveness of the methodology.<\/jats:p>","DOI":"10.2478\/cmam-2009-0018","type":"journal-article","created":{"date-parts":[[2013,4,15]],"date-time":"2013-04-15T15:48:24Z","timestamp":1366040904000},"page":"292-318","source":"Crossref","is-referenced-by-count":28,"title":["Numerical Treatments for Volterra Delay Integro-differential Equations"],"prefix":"10.2478","volume":"9","author":[{"given":"F. A.","family":"Rihan","sequence":"first","affiliation":[{"name":"1Department of Mathematics, Helwan University, Cairo, Egypt."}]},{"given":"E. H.","family":"Doha","sequence":"additional","affiliation":[{"name":"2Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt."}]},{"given":"M. I.","family":"Hassan","sequence":"additional","affiliation":[{"name":"3Department of Mathematics, Faculty of Engineering, Ain Shams University, Cairo, Egypt."}]},{"given":"N. M.","family":"Kamel","sequence":"additional","affiliation":[{"name":"3Department of Mathematics, Faculty of Engineering, Ain Shams University, Cairo, Egypt."}]}],"member":"374","container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/9\/3\/article-p292.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.2478\/cmam-2009-0018\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,22]],"date-time":"2021-04-22T14:21:28Z","timestamp":1619101288000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/9\/3\/article-p292.xml"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009]]},"references-count":0,"journal-issue":{"issue":"3"},"URL":"https:\/\/doi.org\/10.2478\/cmam-2009-0018","relation":{},"ISSN":["1609-9389","1609-4840"],"issn-type":[{"value":"1609-9389","type":"electronic"},{"value":"1609-4840","type":"print"}],"subject":[],"published":{"date-parts":[[2009]]}}}