{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,20]],"date-time":"2025-09-20T19:03:23Z","timestamp":1758395003152,"version":"3.40.5"},"reference-count":43,"publisher":"Wiley","license":[{"start":{"date-parts":[[2020,7,2]],"date-time":"2020-07-02T00:00:00Z","timestamp":1593648000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2020,7,2]]},"abstract":"<jats:p>In this paper, we present a new family of methods for finding simple roots of nonlinear equations. The convergence analysis shows that the order of convergence of all these methods is three. The originality of this family lies in the fact that these sequences are defined by an explicit expression which depends on a parameter<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mi>p<\/mml:mi><\/mml:math>where<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mi>p<\/mml:mi><\/mml:math>is a nonnegative integer. A first study on the global convergence of these methods is performed. The power of this family is illustrated analytically by justifying that, under certain conditions, the method convergence\u2019s speed increases with the parameter<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mi>p<\/mml:mi><\/mml:math>. This family\u2019s efficiency is tested on a number of numerical examples. It is observed that our new methods take less number of iterations than many other third-order methods. In comparison with the methods of the sixth and eighth order, the new ones behave similarly in the examples considered.<\/jats:p>","DOI":"10.1155\/2020\/3561743","type":"journal-article","created":{"date-parts":[[2020,7,2]],"date-time":"2020-07-02T23:32:35Z","timestamp":1593732755000},"page":"1-13","source":"Crossref","is-referenced-by-count":2,"title":["A New Class of Halley\u2019s Method with Third-Order Convergence for Solving Nonlinear Equations"],"prefix":"10.1155","volume":"2020","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3339-3280","authenticated-orcid":true,"given":"Mohammed","family":"Barrada","sequence":"first","affiliation":[{"name":"Research Team ISIC, High School of Technology, Laboratory of Modelization of Mathematics and Computer Science ENSAM, Moulay Ismail University, Meknes, Morocco"},{"name":"EDPCS, MATA, Faculty of Sciences, Moulay Ismail University of Meknes, Morocco"},{"name":"LERSI, Sidi Mohamed Ben Abdellah University of Fez, 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