{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:59:12Z","timestamp":1760147952896,"version":"build-2065373602"},"reference-count":16,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2023,3,16]],"date-time":"2023-03-16T00:00:00Z","timestamp":1678924800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>In this manuscript, we carry out a study on the generalization of a known family of multipoint scalar iterative processes for approximating the solutions of nonlinear systems. The convergence analysis of the proposed class under various smooth conditions is provided. We also study the stability of this family, analyzing the fixed and critical points of the rational operator resulting from applying the family on low-degree polynomials, as well as the basins of attraction and the orbits (periodic or not) that these points produce. This dynamical study also allows us to observe which members of the family are more stable and which have chaotic behavior. Graphical analyses of dynamical planes, parameter line and bifurcation planes are also studied. Numerical tests are performed on different nonlinear systems for checking the theoretical results and to compare the proposed schemes with other known ones.<\/jats:p>","DOI":"10.3390\/a16030163","type":"journal-article","created":{"date-parts":[[2023,3,17]],"date-time":"2023-03-17T02:29:59Z","timestamp":1679020199000},"page":"163","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Convergence and Stability of a New Parametric Class of Iterative Processes for Nonlinear Systems"],"prefix":"10.3390","volume":"16","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\/0000-0003-4594-071X","authenticated-orcid":false,"given":"Javier","family":"G. Maim\u00f3","sequence":"additional","affiliation":[{"name":"Instituto Tecnol\u00f3gico de Santo Domingo (INTEC), Av. Los Proc\u00e9res 49, Santo Domingo 10602, Dominican Republic"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Antmel","family":"Rodr\u00edguez-Cabral","sequence":"additional","affiliation":[{"name":"Instituto Tecnol\u00f3gico de Santo Domingo (INTEC), Av. Los Proc\u00e9res 49, Santo Domingo 10602, Dominican Republic"},{"name":"Escuela de Matem\u00e1ticas, Universidad Aut\u00f3noma de Santo Domingo (UASD), Ciudad Universitaria, Av. Alma Mater, Santo Domingo 10105, 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":[[2023,3,16]]},"reference":[{"unstructured":"Artidiello, S. (2014). Design, Implementation and Convergence of Iterative Methods for Solving Nonlinear Equations and Systems Using Weight Functions. [Ph.D. Thesis, Universitat Polit\u00e8cnica de Val\u00e8ncia].","key":"ref_1"},{"doi-asserted-by":"crossref","unstructured":"Cordero, A., Moscoso, M.E., and Torregrosa, J.R. (2021). Chaos and Stability of in a New Iterative Family far Solving Nonlinear Equations. Algorithms, 14.","key":"ref_2","DOI":"10.3390\/a14040101"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2369","DOI":"10.1016\/j.aml.2012.07.005","article-title":"Increasing the convergence order of an iterative method for nonlinear systems","volume":"25","author":"Cordero","year":"2012","journal-title":"Appl. Math. Lett."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1007\/s11075-009-9359-z","article-title":"A modified Newton-Jarrat composition","volume":"55","author":"Cordero","year":"2010","journal-title":"Numer. Algorithms"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"110","DOI":"10.1016\/j.cam.2018.06.042","article-title":"Highly efficient family of iterative methods for solving nonlinear models","volume":"346","author":"Behl","year":"2019","journal-title":"J. Comput. Appl. Math."},{"doi-asserted-by":"crossref","unstructured":"Capdevila, R., Cordero, A., and Torregrosa, J. (2019). 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Comput."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/16\/3\/163\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T18:57:01Z","timestamp":1760122621000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/16\/3\/163"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,3,16]]},"references-count":16,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2023,3]]}},"alternative-id":["a16030163"],"URL":"https:\/\/doi.org\/10.3390\/a16030163","relation":{},"ISSN":["1999-4893"],"issn-type":[{"type":"electronic","value":"1999-4893"}],"subject":[],"published":{"date-parts":[[2023,3,16]]}}}