{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:54:17Z","timestamp":1760234057229,"version":"build-2065373602"},"reference-count":14,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2021,3,24]],"date-time":"2021-03-24T00:00:00Z","timestamp":1616544000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100014440","name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades","doi-asserted-by":"publisher","award":["PGC2018-095896-B-C22"],"award-info":[{"award-number":["PGC2018-095896-B-C22"]}],"id":[{"id":"10.13039\/100014440","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>In this paper, we present a new parametric family of three-step iterative for solving nonlinear equations. First, we design a fourth-order triparametric family that, by holding only one of its parameters, we get to accelerate its convergence and finally obtain a sixth-order uniparametric family. With this last family, we study its convergence, its complex dynamics (stability), and its numerical behavior. The parameter spaces and dynamical planes are presented showing the complexity of the family. From the parameter spaces, we have been able to determine different members of the family that have bad convergence properties, as attracting periodic orbits and attracting strange fixed points appear in their dynamical planes. Moreover, this same study has allowed us to detect family members with especially stable behavior and suitable for solving practical problems. Several numerical tests are performed to illustrate the efficiency and stability of the presented family.<\/jats:p>","DOI":"10.3390\/a14040101","type":"journal-article","created":{"date-parts":[[2021,3,24]],"date-time":"2021-03-24T15:42:19Z","timestamp":1616600539000},"page":"101","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Chaos and Stability in a New Iterative Family for Solving Nonlinear Equations"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7462-9173","authenticated-orcid":false,"given":"Alicia","family":"Cordero","sequence":"first","affiliation":[{"name":"Institute for Multidisciplinary Mathematics, Universitat Polit\u00e8cnica de Val\u00e8ncia, Camino de Vera s\/n, 46022 Val\u00e8ncia, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5182-3099","authenticated-orcid":false,"given":"Marlon","family":"Moscoso-Mart\u00ednez","sequence":"additional","affiliation":[{"name":"Institute for Multidisciplinary Mathematics, Universitat Polit\u00e8cnica de Val\u00e8ncia, Camino de Vera s\/n, 46022 Val\u00e8ncia, Spain"}],"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":"Institute for Multidisciplinary Mathematics, Universitat Polit\u00e8cnica de Val\u00e8ncia, Camino de Vera s\/n, 46022 Val\u00e8ncia, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,3,24]]},"reference":[{"key":"ref_1","unstructured":"Neta, B. (1983). Numerical Methods for the Solution of Equations, Net-A-Sof."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Petkovi\u0107, M., Neta, B., Petkovi\u0107, L., and D\u017euni\u0107, J. (2013). Multipoint Methods for Solving Nonlinear Equations, Academic Press. [1st ed.].","DOI":"10.1016\/B978-0-12-397013-8.00002-9"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Amat, S., and Busquier, S. (2017). Advances in Iterative Methods for Nonlinear Equations, Springer.","DOI":"10.1007\/978-3-319-39228-8"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"194","DOI":"10.1016\/j.amc.2016.08.034","article-title":"Design and multidimensional extension of iterative methods for solving nonlinear problems","volume":"293","author":"Artidiello","year":"2017","journal-title":"Appl. Math. Comput."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Hunt, B.R., and Ott, E. (2015). Defining chaos. Chaos Interdiscip. J. 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