{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,30]],"date-time":"2025-10-30T07:04:09Z","timestamp":1761807849488,"version":"3.37.3"},"reference-count":27,"publisher":"Wiley","license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"name":"Deanship of Scientific Research, King Abdulaziz University, Jeddah","award":["130-014-D1434"],"award-info":[{"award-number":["130-014-D1434"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2013]]},"abstract":"<jats:p>In this research paper, we present higher-order quasilinearization methods for the boundary value problems as well as coupled boundary value problems. The construction of higher-order convergent methods depends on a decomposition method which is different from Adomain decomposition method (Motsa and Sibanda, 2013). The reported method is very general and can be extended to desired order of convergence for highly nonlinear differential equations and also computationally superior to proposed iterative method based on Adomain decomposition because our proposed iterative scheme avoids the calculations of Adomain polynomials and achieves the same computational order of convergence as authors have claimed in Motsa and Sibanda, 2013. In order to check the validity and computational performance, the constructed iterative schemes are also successfully applied to bifurcation problems to calculate the values of critical parameters. The numerical performance is also tested for one-dimension Bratu and Frank-Kamenetzkii equations.<\/jats:p>","DOI":"10.1155\/2013\/259371","type":"journal-article","created":{"date-parts":[[2013,11,28]],"date-time":"2013-11-28T16:01:28Z","timestamp":1385654488000},"page":"1-11","source":"Crossref","is-referenced-by-count":20,"title":["An Efficient Higher-Order Quasilinearization Method for Solving Nonlinear BVPs"],"prefix":"10.1155","volume":"2013","author":[{"given":"Eman S.","family":"Alaidarous","sequence":"first","affiliation":[{"name":"Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2944-0352","authenticated-orcid":true,"given":"Malik Zaka","family":"Ullah","sequence":"additional","affiliation":[{"name":"Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2634-5130","authenticated-orcid":true,"given":"Fayyaz","family":"Ahmad","sequence":"additional","affiliation":[{"name":"Departamento de F\u00edsica i Enginyeria Nuclear, Universitat Polit\u00e8cnica de Catalunya, Compte d\u2019Urgell 187, 08036 Barcelona, Spain"}]},{"given":"A.S.","family":"Al-Fhaid","sequence":"additional","affiliation":[{"name":"Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1145\/321850.321860"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2011.02.009"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1137\/0710072"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1007\/s11075-011-9467-4"},{"year":"1976","key":"5"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2009.10.030"},{"year":"1960","key":"7"},{"issue":"1","key":"9","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1016\/S0010-4655(01)00191-6","volume":"138","journal-title":"Computer Physics Communications"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1063\/1.533092"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1016\/S0010-4655(01)00415-5"},{"issue":"7","key":"12","doi-asserted-by":"crossref","first-page":"1227","DOI":"10.1134\/1.1992578","volume":"68","year":"2005","journal-title":"Physics of Atomic Nuclei"},{"year":"1965","key":"8"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1007\/s11075-012-9629-z"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1016\/0895-7177(90)90125-7"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2005.05.009"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1016\/S0096-3003(02)00345-4"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2010.12.029"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1137\/0903012"},{"issue":"30","key":"20","first-page":"1493","volume":"2","year":"2007","journal-title":"International Journal of Contemporary Mathematical"},{"volume":"50","journal-title":"Romanian Journal of Physics","key":"21"},{"key":"22","first-page":"621","volume":"50","year":"2005","journal-title":"Romanian Journal of Physics"},{"key":"23","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2004.06.059"},{"year":"1969","key":"24"},{"issue":"4","key":"25","doi-asserted-by":"crossref","first-page":"613","DOI":"10.3390\/mca15040613","volume":"15","year":"2010","journal-title":"Mathematical & Computational Applications"},{"year":"1983","key":"26"},{"key":"27","doi-asserted-by":"publisher","DOI":"10.1007\/s00521-012-1261-2"},{"key":"28","doi-asserted-by":"publisher","DOI":"10.1016\/S0893-9659(00)00100-2"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/259371.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/259371.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/259371.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,4]],"date-time":"2019-08-04T02:35:52Z","timestamp":1564886152000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2013\/259371\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"references-count":27,"alternative-id":["259371","259371"],"URL":"https:\/\/doi.org\/10.1155\/2013\/259371","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2013]]}}}