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This method is based on expanding the solution around an iterative initial point. We employ this method to study the unsteady, viscous, and incompressible laminar flow and heat transfer over a shrinking permeable cylinder. More precisely, we solve the unsteady nonlinear Navier\u2013Stokes and energy equations after reducing them to a system of nonlinear boundary\u2010value problems of ordinary differential equations. The present method successfully captures dual solutions for both the flow and heat transfer fields and a unique solution at a specific critical unsteadiness parameter. Comparisons with previous numerical methods and an exact solution verify the validity, accuracy, and efficiency of the present method.<\/jats:p>","DOI":"10.1155\/2018\/8269541","type":"journal-article","created":{"date-parts":[[2018,3,12]],"date-time":"2018-03-12T23:31:53Z","timestamp":1520897513000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":23,"title":["A Numerical Algorithm for Solving Higher\u2010Order Nonlinear BVPs with an Application on Fluid Flow over a Shrinking Permeable Infinite Long Cylinder"],"prefix":"10.1155","volume":"2018","author":[{"given":"Laila Y.","family":"Al Sakkaf","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2853-9337","authenticated-orcid":false,"given":"Qasem M.","family":"Al-Mdallal","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"U.","family":"Al Khawaja","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2018,3,12]]},"reference":[{"key":"e_1_2_10_1_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0096-3003(98)10024-3"},{"key":"e_1_2_10_2_2","doi-asserted-by":"publisher","DOI":"10.1108\/HFF-10-2015-0442"},{"key":"e_1_2_10_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-15374-2"},{"key":"e_1_2_10_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijheatmasstransfer.2017.04.097"},{"key":"e_1_2_10_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.euromechflu.2014.08.008"},{"key":"e_1_2_10_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.compfluid.2012.04.019"},{"key":"e_1_2_10_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijengsci.2006.04.005"},{"key":"e_1_2_10_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijheatmasstransfer.2013.09.047"},{"key":"e_1_2_10_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2011.12.013"},{"key":"e_1_2_10_10_2","doi-asserted-by":"publisher","DOI":"10.1115\/1.4033058"},{"key":"e_1_2_10_11_2","volume-title":"Comput Heat Transfer","author":"Jaluria Y.","year":"2003"},{"key":"e_1_2_10_12_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00042775"},{"key":"e_1_2_10_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijnonlinmec.2007.06.003"},{"key":"e_1_2_10_14_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11242-008-9309-6"},{"key":"e_1_2_10_15_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2010.09.037"},{"key":"e_1_2_10_16_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijheatmasstransfer.2012.12.028"},{"key":"e_1_2_10_17_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2007.06.036"},{"key":"e_1_2_10_18_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijheatmasstransfer.2012.08.051"},{"key":"e_1_2_10_19_2","doi-asserted-by":"publisher","DOI":"10.1080\/00986441003626169"},{"key":"e_1_2_10_20_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.compfluid.2011.01.040"},{"key":"e_1_2_10_21_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijnonlinmec.2007.12.021"},{"key":"e_1_2_10_22_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijheatmasstransfer.2011.12.013"},{"key":"e_1_2_10_23_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijheatmasstransfer.2011.04.024"},{"key":"e_1_2_10_24_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijheatmasstransfer.2010.09.041"},{"key":"e_1_2_10_25_2","doi-asserted-by":"publisher","DOI":"10.1155\/2012\/453457"},{"key":"e_1_2_10_26_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfranklin.2013.07.002"},{"key":"e_1_2_10_27_2","volume-title":"Handbook of Nonlinear Partial Differential Equations","author":"Polyanin A. 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