{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,10]],"date-time":"2026-06-10T15:44:05Z","timestamp":1781106245061,"version":"3.54.1"},"reference-count":24,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2021,10,21]],"date-time":"2021-10-21T00:00:00Z","timestamp":1634774400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,10,21]],"date-time":"2021-10-21T00:00:00Z","timestamp":1634774400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J. Appl. Math. Comput."],"published-print":{"date-parts":[[2022,10]]},"DOI":"10.1007\/s12190-021-01647-1","type":"journal-article","created":{"date-parts":[[2021,10,21]],"date-time":"2021-10-21T10:05:04Z","timestamp":1634810704000},"page":"2877-2886","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":20,"title":["A new fifth-order iterative method free from second derivative for solving nonlinear equations"],"prefix":"10.1007","volume":"68","author":[{"given":"Noori Yasir","family":"Abdul-Hassan","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ali Hasan","family":"Ali","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6329-8228","authenticated-orcid":false,"given":"Choonkil","family":"Park","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2021,10,21]]},"reference":[{"key":"1647_CR1","doi-asserted-by":"publisher","first-page":"568","DOI":"10.31197\/atnaa.890281","volume":"5","author":"M Abdullahi","year":"2021","unstructured":"Abdullahi, M., Halilu, A., Awwal, A.: On efficient matrix-free method via quasi-Newton approach for solving system of nonlinear equations. ATNAA 5, 568\u2013579 (2021)","journal-title":"ATNAA"},{"key":"1647_CR2","doi-asserted-by":"publisher","first-page":"67","DOI":"10.31197\/atnaa.624777","volume":"4","author":"IK Argyros","year":"2020","unstructured":"Argyros, I.K., George, S.: On an iterative method without inverses of derivatives for solving equations. ATNAA 4, 67\u201376 (2020)","journal-title":"ATNAA"},{"key":"1647_CR3","unstructured":"Burden, R.L., Faires, J. D., Reynolds, A. C: Numerical Analysis. PWS Publishing Company, Bostan (2001)"},{"key":"1647_CR4","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1016\/j.cam.2007.07.004","volume":"219","author":"C Chun","year":"2008","unstructured":"Chun, C.: A simply constructed third-order modifications of Newtons method. J. Comput. Appl. Math. 219, 81\u201389 (2008)","journal-title":"J. Comput. Appl. Math."},{"key":"1647_CR5","first-page":"654","volume":"197","author":"C Chun","year":"2008","unstructured":"Chun, C., Ham, Y.: Some fourth-order modifications of Newtons method. Appl. Math. Comput. 197, 654\u2013658 (2008)","journal-title":"Appl. Math. Comput."},{"key":"1647_CR6","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1590\/S0101-82052008000300003","volume":"27","author":"L Fang","year":"2008","unstructured":"Fang, L., Sun, L., He, G.: An efficient Newton-type method with fifth-order convergence for solving nonlinear equations. Comput. Appl. Math. 27, 269\u2013274 (2008)","journal-title":"Comput. Appl. Math."},{"key":"1647_CR7","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1007\/s12190-020-01426-4","volume":"66","author":"F Haddouchi","year":"2021","unstructured":"Haddouchi, F., Houari, N.: Monotone positive solution of fourth order boundary value problem with mixed integral and multi-point boundary conditions. J. Appl. Math. Comput. 66, 87\u2013109 (2021)","journal-title":"J. Appl. Math. Comput."},{"key":"1647_CR8","doi-asserted-by":"publisher","first-page":"136","DOI":"10.1098\/rstl.1694.0029","volume":"18","author":"E Halley","year":"1964","unstructured":"Halley, E.: A new exact and easy method for finding the roots of equations generally and without any previous reduction. Phil. Roy. Soc. London 18, 136\u2013147 (1964)","journal-title":"Phil. Roy. Soc. London"},{"key":"1647_CR9","first-page":"287","volume":"194","author":"Y Ham","year":"2007","unstructured":"Ham, Y., Chun, C.: A fifth-order iterative method for solving nonlinear equations. Appl. Math. Comput. 194, 287\u2013290 (2007)","journal-title":"Appl. Math. Comput."},{"key":"1647_CR10","volume-title":"The Numerical Treatment of a Single Nonlinear Equation","author":"AS Householder","year":"1970","unstructured":"Householder, A.S.: The Numerical Treatment of a Single Nonlinear Equation. McGraw-Hill, New York (1970)"},{"key":"1647_CR11","doi-asserted-by":"publisher","first-page":"561","DOI":"10.1007\/s12190-020-01449-x","volume":"66","author":"J Huang","year":"2021","unstructured":"Huang, J., Qiao, Z., Zhang, J., Arshad, S., Tang, Y.: Two linearized schemes for time fractional nonlinear wave equations with four-order derivative. J. Appl. Math. Comput. 66, 561\u2013579 (2021)","journal-title":"J. Appl. Math. Comput."},{"key":"1647_CR12","doi-asserted-by":"crossref","unstructured":"Ivanov, I. G., Mateva, T.: Interval methods with fifth order of convergence for solving nonlinear scalar equations, Axioms 8 (2019), Paper No. 15","DOI":"10.3390\/axioms8010015"},{"key":"1647_CR13","first-page":"704","volume":"183","author":"J Kou","year":"2006","unstructured":"Kou, J., Li, Y., Wang, X.: Modified Halleys method free from second derivative. Appl. Math. Comput. 183, 704\u2013708 (2006)","journal-title":"Appl. Math. Comput."},{"key":"1647_CR14","first-page":"471","volume":"184","author":"J Kou","year":"2007","unstructured":"Kou, J., Li, Y., Wang, X.: A composite fourth-order iterative method for solving non-linear equations. Appl. Math. Comput. 184, 471\u2013475 (2007)","journal-title":"Appl. Math. Comput."},{"key":"1647_CR15","doi-asserted-by":"crossref","unstructured":"Li, S., Li, H., Cheng, L.: Some second-derivative-free variants of Halley\u2019s method for multiple roots. Appl. Math. Comput. 215, 2192\u20132198 (2009)","DOI":"10.1016\/j.amc.2009.08.010"},{"key":"1647_CR16","first-page":"383","volume":"211","author":"AK Maheshwari","year":"2009","unstructured":"Maheshwari, A.K.: A fourth order iterative method for solving nonlinear equations. Appl. Math. Comput. 211, 383\u2013391 (2009)","journal-title":"Appl. Math. Comput."},{"key":"1647_CR17","first-page":"95","volume":"4","author":"MA Noor","year":"2018","unstructured":"Noor, M.A.: Fifth-order convergent iterative method for solving nonlinear equations using quadrature formula. J. Math. Control Sci. Appl. 4, 95\u2013104 (2018)","journal-title":"J. Math. Control Sci. Appl."},{"issue":"93","key":"1647_CR18","first-page":"4617","volume":"6","author":"MA Noor","year":"2012","unstructured":"Noor, M.A., Khan, W.A.: Fourth-order iterative method free from second derivative for solving nonlinear equations. Appl. Math. Sci. 6(93), 4617\u20134625 (2012)","journal-title":"Appl. Math. Sci."},{"key":"1647_CR19","first-page":"297","volume":"14","author":"M Rafiullah","year":"2011","unstructured":"Rafiullah, M.: A fifth-order iterative method for solving nonlinear equations. Numer. Anal. Appl. 14, 297\u2013302 (2011)","journal-title":"Numer. Anal. Appl."},{"key":"1647_CR20","doi-asserted-by":"publisher","first-page":"101","DOI":"10.1080\/00207160500113306","volume":"83","author":"JR Sharma","year":"2006","unstructured":"Sharma, J.R., Goyal, R.K.: Fourth-order derivative-free methods for solving nonlinear equations. Int. J. Comput. Math. 83, 101\u2013106 (2006)","journal-title":"Int. J. Comput. Math."},{"key":"1647_CR21","doi-asserted-by":"publisher","first-page":"701","DOI":"10.1016\/j.jksus.2018.03.021","volume":"31","author":"OS Solaiman","year":"2019","unstructured":"Solaiman, O.S., Hashim, I.: Two new efficient sixth order iterative methods for solving nonlinear equations. J. King Saud Univ. Sci. 31, 701\u2013705 (2019)","journal-title":"J. King Saud Univ. Sci."},{"key":"1647_CR22","doi-asserted-by":"publisher","first-page":"159","DOI":"10.53006\/rna.950067","volume":"4","author":"R Suparatulatorn","year":"2021","unstructured":"Suparatulatorn, R., Suantai, S.: Stability and convergence analysis of hybrid algorithms for Berinde contraction mappings and its applications. RNA 4, 159\u2013168 (2021)","journal-title":"RNA"},{"key":"1647_CR23","doi-asserted-by":"publisher","first-page":"110107","DOI":"10.1016\/j.chaos.2020.110107","volume":"140","author":"NH Tuan","year":"2020","unstructured":"Tuan, N.H., Mohammadi, H.S.: Rezapour A mathematical model for COVID-19 transmission by using the Caputo fractional derivative. Chaos, Solitons Fract 140, 110107 (2020)","journal-title":"Chaos, Solitons Fract"},{"key":"1647_CR24","doi-asserted-by":"publisher","first-page":"112811","DOI":"10.1016\/j.cam.2020.112811","volume":"375","author":"NH Tuan","year":"2020","unstructured":"Tuan, N.H., Zhou, Y.: Well-posedness of an initial value problem for fractional diffusion equation with Caputo-Fabrizio derivative. J. Comput. Appl. Math. 375, 112811 (2020)","journal-title":"J. Comput. Appl. Math."}],"container-title":["Journal of Applied Mathematics and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-021-01647-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s12190-021-01647-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-021-01647-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,11]],"date-time":"2023-11-11T13:50:49Z","timestamp":1699710649000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s12190-021-01647-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,10,21]]},"references-count":24,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2022,10]]}},"alternative-id":["1647"],"URL":"https:\/\/doi.org\/10.1007\/s12190-021-01647-1","relation":{},"ISSN":["1598-5865","1865-2085"],"issn-type":[{"value":"1598-5865","type":"print"},{"value":"1865-2085","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,10,21]]},"assertion":[{"value":"31 May 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 October 2021","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 October 2021","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 October 2021","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"Not applicable.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Availablity of data and materials"}},{"value":"The authors declare that they have no competing interests.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"Not applicable.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Fundings"}}]}}