{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,25]],"date-time":"2025-12-25T07:20:52Z","timestamp":1766647252098,"version":"build-2065373602"},"reference-count":19,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2022,10,21]],"date-time":"2022-10-21T00:00:00Z","timestamp":1666310400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004837","name":"ERDF: A way to making Europe","doi-asserted-by":"publisher","award":["PGC2018-095896-B-C22","MCIN\/AEI\/10.13039\/5011000113033"],"award-info":[{"award-number":["PGC2018-095896-B-C22","MCIN\/AEI\/10.13039\/5011000113033"]}],"id":[{"id":"10.13039\/501100004837","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>In this manuscript, we propose a parametric family of iterative methods of fourth-order convergence, and the stability of the class is studied through the use of tools of complex dynamics. We obtain the fixed and critical points of the rational operator associated with the family. A stability analysis of the fixed points allows us to find sets of values of the parameter for which the behavior of the corresponding method is stable or unstable; therefore, we can select the regions of the parameter in which the methods behave more efficiently when they are applied for solving nonlinear equations or the regions in which the schemes have chaotic behavior.<\/jats:p>","DOI":"10.3390\/a15100387","type":"journal-article","created":{"date-parts":[[2022,10,23]],"date-time":"2022-10-23T20:43:50Z","timestamp":1666557830000},"page":"387","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Dynamics and Stability on a Family of Optimal Fourth-Order Iterative Methods"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7462-9173","authenticated-orcid":false,"given":"Alicia","family":"Cordero","sequence":"first","affiliation":[{"name":"Instituto de Matem\u00e1tica Multidisciplinar, Universitat Polit\u00e8cnica de Val\u00e8ncia, Camino de Vera, s\/n, 46022 Valencia, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4199-6484","authenticated-orcid":false,"given":"Miguel A.","family":"Leonardo Sep\u00falveda","sequence":"additional","affiliation":[{"name":"Ciencias B\u00e1sicas y Ambientales (CBA), Instituto Tecnol\u00f3gico de Santo Domingo (INTEC), Area de Ciencia B\u00e1sica y Ambiental, Av. Los Pr\u00f3ceres, Gala, Apartado Postal 342-9 and 249-2, Santo Domingo 10602, Dominican Republic"},{"name":"Departamento de Matem\u00e1tica, Instituto Superior de Formaci\u00f3n Docente Salom\u00e9 Ure\u00f1a, Recinto F\u00e9lix Evaristo Mej\u00eda (ISFODOSU), Av. Caonabo con esq. Leonardo da Vinci, Urb. Renacimiento, Sector Mirador Sur, Santo Domingo 10114, Dominican Republic"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9893-0761","authenticated-orcid":false,"given":"Juan R.","family":"Torregrosa","sequence":"additional","affiliation":[{"name":"Instituto de Matem\u00e1tica Multidisciplinar, Universitat Polit\u00e8cnica de Val\u00e8ncia, Camino de Vera, s\/n, 46022 Valencia, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,21]]},"reference":[{"key":"ref_1","unstructured":"Traub, I.F. (1964). Iterative Methods for the Solution of Equations, Prentice-Hall."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Petkovi\u0107, M.S., Neta, B., Petkovi\u0107, L.D., and D\u017euni\u0107, J. (2013). Multipoint Methods for Solving Nonlinear Equations, Academic Press.","DOI":"10.1016\/B978-0-12-397013-8.00002-9"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Amat, S., and Busquier, S. (2016). Advances in Iterative Methods for Nonlinear Equations, Springer.","DOI":"10.1007\/978-3-319-39228-8"},{"key":"ref_4","unstructured":"Ostrowski, A.M. (1960). 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Comput."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/15\/10\/387\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:58:43Z","timestamp":1760144323000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/15\/10\/387"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,10,21]]},"references-count":19,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2022,10]]}},"alternative-id":["a15100387"],"URL":"https:\/\/doi.org\/10.3390\/a15100387","relation":{},"ISSN":["1999-4893"],"issn-type":[{"type":"electronic","value":"1999-4893"}],"subject":[],"published":{"date-parts":[[2022,10,21]]}}}