{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,1]],"date-time":"2022-04-01T17:19:22Z","timestamp":1648833562689},"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>In this paper, we introduce a new spectral method based on ultraspherical\npolynomials for solving systems of initial value differential algebraic equations.\nMoreover, the suggested method is applicable for a wide range of differential equations.\nThe method is based on a new investigation of the ultraspherical spectral differentiation\nmatrix to approximate the differential expressions in equations. The produced\nequations lead to algebraic systems and are converted to nonlinear programming. Numerical\nexamples illustrate the robustness, accuracy, and efficiency of the proposed\nmethod.<\/jats:p>","DOI":"10.2478\/cmam-2009-0014","type":"journal-article","created":{"date-parts":[[2013,4,15]],"date-time":"2013-04-15T16:16:52Z","timestamp":1366042612000},"page":"226-237","source":"Crossref","is-referenced-by-count":1,"title":["Ultraspherical Differentiation Method for Solving System of Initial Value Differential Algebraic Equations"],"prefix":"10.2478","volume":"9","author":[{"given":"M.","family":"El-kady","sequence":"first","affiliation":[{"name":"1Department of Mathematics, Faculty of Science, Helwan University, Cairo, Egypt."}]},{"given":"M.A.","family":"Ibrahim","sequence":"additional","affiliation":[{"name":"2Department of Mathematics, Faculty of Science, South Valley University, Qena, Egypt."}]}],"member":"374","container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/9\/3\/article-p226.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.2478\/cmam-2009-0014\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,22]],"date-time":"2021-04-22T14:21:27Z","timestamp":1619101287000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/9\/3\/article-p226.xml"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009]]},"references-count":0,"journal-issue":{"issue":"3"},"URL":"https:\/\/doi.org\/10.2478\/cmam-2009-0014","relation":{},"ISSN":["1609-9389","1609-4840"],"issn-type":[{"value":"1609-9389","type":"electronic"},{"value":"1609-4840","type":"print"}],"subject":[],"published":{"date-parts":[[2009]]}}}