{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:46:32Z","timestamp":1760150792689,"version":"build-2065373602"},"reference-count":31,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2023,12,31]],"date-time":"2023-12-31T00:00:00Z","timestamp":1703980800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, a new parametric class of optimal fourth-order iterative methods to estimate the solutions of nonlinear equations is presented. After the convergence analysis, a study of the stability of this class is made using the tools of complex discrete dynamics, allowing those elements of the class with lower dependence on initial estimations to be selected in order to find a very stable subfamily. Numerical tests indicate that the stable members perform better on quadratic polynomials than the unstable ones when applied to other non-polynomial functions. Moreover, the performance of the best elements of the family are compared with known methods, showing robust and stable behaviour.<\/jats:p>","DOI":"10.3390\/axioms13010034","type":"journal-article","created":{"date-parts":[[2023,12,31]],"date-time":"2023-12-31T10:01:06Z","timestamp":1704016866000},"page":"34","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Stability Analysis of a New Fourth-Order Optimal Iterative Scheme for Nonlinear Equations"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7462-9173","authenticated-orcid":false,"given":"Alicia","family":"Cordero","sequence":"first","affiliation":[{"name":"Multidisciplinary Mathematics Institute, Universitat Polit\u00e8cnica de Val\u00e8ncia (UPV), 46022 Valencia, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9397-7571","authenticated-orcid":false,"given":"Jos\u00e9 A.","family":"Reyes","sequence":"additional","affiliation":[{"name":"Departamento de Ciencias B\u00e1sicas, Instituto Tecnol\u00f3gico de Santo Domingo (INTEC), Santo Domingo 10801, Dominican Republic"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9893-0761","authenticated-orcid":false,"given":"Juan R.","family":"Torregrosa","sequence":"additional","affiliation":[{"name":"Multidisciplinary Mathematics Institute, Universitat Polit\u00e8cnica de Val\u00e8ncia (UPV), 46022 Valencia, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7755-5635","authenticated-orcid":false,"given":"Mar\u00eda P.","family":"Vassileva","sequence":"additional","affiliation":[{"name":"Departamento de Ciencias B\u00e1sicas, Instituto Tecnol\u00f3gico de Santo Domingo (INTEC), Santo Domingo 10801, Dominican Republic"}]}],"member":"1968","published-online":{"date-parts":[[2023,12,31]]},"reference":[{"key":"ref_1","unstructured":"Danby, J.M.A. (1992). 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