{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,13]],"date-time":"2026-01-13T02:56:17Z","timestamp":1768272977522,"version":"3.49.0"},"reference-count":34,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2024,5,21]],"date-time":"2024-05-21T00:00:00Z","timestamp":1716249600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004233","name":"Ayuda a Primeros Proyectos de Investigaci\u00f3n (PAID-06-23), Vicerrectorado de Investigaci\u00f3n de la Universitat Polit\u00e8cnica de Val\u00e8ncia (UPV)","doi-asserted-by":"publisher","award":["PAID-06-23"],"award-info":[{"award-number":["PAID-06-23"]}],"id":[{"id":"10.13039\/501100004233","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This paper introduces an iterative method with a remarkable level of accuracy, namely fourth-order convergence. The method is specifically tailored to meet the optimality condition under the Kung\u2013Traub conjecture by linear combination. This method, with an efficiency index of approximately 1.5874, employs a blend of localized and semi-localized analysis to improve both efficiency and convergence. This study aims to investigate semi-local convergence, dynamical analysis to assess stability and convergence rate, and the use of the proposed solver for systems of nonlinear equations. The results underscore the potential of the proposed method for several applications in polynomiography and other areas of mathematical research. The improved performance of the proposed optimal method is demonstrated with mathematical models taken from many domains, such as physics, mechanics, chemistry, and combustion, to name a few.<\/jats:p>","DOI":"10.3390\/axioms13060341","type":"journal-article","created":{"date-parts":[[2024,5,22]],"date-time":"2024-05-22T07:56:11Z","timestamp":1716364571000},"page":"341","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["A New Optimal Numerical Root-Solver for Solving Systems of Nonlinear Equations Using Local, Semi-Local, and Stability Analysis"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7225-2309","authenticated-orcid":false,"given":"Sania","family":"Qureshi","sequence":"first","affiliation":[{"name":"Department of Basic Sciences and Related Studies, Mehran University of Engineering & Technology, Jamshoro 76062, Pakistan"},{"name":"Department of Computer Science and Mathematics, Lebanese American University, Beirut P.O. Box 13-5053, Lebanon"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9116-2870","authenticated-orcid":false,"given":"Francisco I.","family":"Chicharro","sequence":"additional","affiliation":[{"name":"Instituto Universitario de Matem\u00e1tica Multidisciplinar, Universitat Polit\u00e8cnica de Val\u00e8ncia, 46022 Val\u00e8ncia, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9189-9298","authenticated-orcid":false,"given":"Ioannis K.","family":"Argyros","sequence":"additional","affiliation":[{"name":"Department of Computing and Mathematics Sciences, Cameron University, Lawton, OK 73505, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5823-0170","authenticated-orcid":false,"given":"Amanullah","family":"Soomro","sequence":"additional","affiliation":[{"name":"Department of Basic Sciences and Related Studies, Mehran University of Engineering & Technology, Jamshoro 76062, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1457-6927","authenticated-orcid":false,"given":"Jihan","family":"Alahmadi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6175-1455","authenticated-orcid":false,"given":"Evren","family":"Hincal","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Near East University, 99138 Mersin, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,5,21]]},"reference":[{"key":"ref_1","unstructured":"Faires, J., and Burden, R. 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