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Two singular points are both boundary values points of the differential equation. The numerical solutions are developed by modified differential transform method (DTM) for expanded point. Linear and nonlinear models are solved by this method to get more reliable and efficient numerical results. It can also solve ordinary differential equations where the traditional one fails. Besides, we give the convergence of this new method.<\/jats:p>","DOI":"10.1155\/2014\/138087","type":"journal-article","created":{"date-parts":[[2014,1,5]],"date-time":"2014-01-05T21:00:55Z","timestamp":1388955655000},"page":"1-6","source":"Crossref","is-referenced-by-count":3,"title":["Modified Differential Transform Method for Two Singular Boundary Values Problems"],"prefix":"10.1155","volume":"2014","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8854-8027","authenticated-orcid":true,"given":"Yinwei","family":"Lin","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering, National Cheng Kung University, Tainan 70101, Taiwan"}]},{"given":"Hsiang-Wen","family":"Tang","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, National Cheng Kung University, Tainan 70101, Taiwan"}]},{"given":"Cha\u2019o-Kuang","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, National Cheng Kung University, Tainan 70101, Taiwan"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1002\/mma.887"},{"issue":"5","key":"2","first-page":"763\u2013770","volume":"55","year":"1969","journal-title":"Acad\u00e9mie Royale de Belgique Bulletin de la Classe des Sciences"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2009.08.016"},{"issue":"3","key":"4","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1515\/zna-2010-0301","volume":"65","year":"2010","journal-title":"Zeitschrift fur Naturforschung"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2011.09.037"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1016\/S0096-3003(01)00021-2"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1016\/j.nonrwa.2007.08.017"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2003.12.048"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1016\/S0096-3003(99)00223-4"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-9274(02)00252-0"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1016\/S0096-3003(02)00656-2"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfranklin.2010.10.005"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2010.09.007"},{"issue":"128","key":"14","first-page":"18","volume":"11","year":"1976","journal-title":"Elektronikai Modelirovanie Vyp"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1080\/00207160512331329050"},{"issue":"70","key":"16","first-page":"3465","volume":"5","year":"2011","journal-title":"Applied Mathematical Sciences"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1016\/S0096-3003(98)10115-7"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1016\/S0096-3003(99)00293-3"},{"issue":"1","key":"19","first-page":"39","volume":"6","year":"2011","journal-title":"International Mathematical Forum"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2006.05.173"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1016\/S0096-3003(03)00581-2"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.1016\/j.physleta.2009.09.036"},{"key":"23","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2006.01.022"},{"key":"24","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2011.03.007"},{"key":"25","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2010.01.053"},{"key":"26","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2011.01.111"},{"issue":"1","key":"27","first-page":"128","volume":"5","year":"2010","journal-title":"Applications and Applied Mathematics"},{"key":"28","doi-asserted-by":"publisher","DOI":"10.1080\/00207160802562572"},{"key":"29","doi-asserted-by":"publisher","DOI":"10.1088\/0253-6102\/60\/2\/03"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/138087.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/138087.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/138087.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,8,13]],"date-time":"2020-08-13T11:21:27Z","timestamp":1597317687000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2014\/138087\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"references-count":29,"alternative-id":["138087","138087"],"URL":"https:\/\/doi.org\/10.1155\/2014\/138087","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2014]]}}}