{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,11]],"date-time":"2026-01-11T02:03:54Z","timestamp":1768097034079,"version":"3.49.0"},"reference-count":38,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2024,9,30]],"date-time":"2024-09-30T00:00:00Z","timestamp":1727654400000},"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>This study introduces a novel, iterative algorithm that achieves fourth-order convergence for solving nonlinear equations. Satisfying the Kung\u2013Traub conjecture, the proposed technique achieves an optimal order of four with an efficiency index (I) of 1.587, requiring three function evaluations. An analysis of convergence is presented to show the optimal fourth-order convergence. To verify the theoretical results, in-depth numerical comparisons are presented for both real and complex domains. The proposed algorithm is specifically examined on a variety of polynomial functions, and it is shown by the efficient and accurate results that it outperforms many existing algorithms in terms of speed and accuracy. The study not only explores the proposed method\u2019s convergence properties, computational efficiency, and stability but also introduces a novel perspective by considering the count of black points as an indicator of a method\u2019s divergence. By analyzing the mean number of iterations necessary for methods to converge within a cycle and measuring CPU time in seconds, this research provides a holistic assessment of both the efficiency and speed of iterative methods. Notably, the analysis of basins of attraction illustrates that our proposed method has larger sets of initial points that yield convergence.<\/jats:p>","DOI":"10.3390\/axioms13100675","type":"journal-article","created":{"date-parts":[[2024,9,30]],"date-time":"2024-09-30T07:19:37Z","timestamp":1727680777000},"page":"675","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["A Robust and Optimal Iterative Algorithm Employing a Weight Function for Solving Nonlinear Equations with Dynamics and Applications"],"prefix":"10.3390","volume":"13","author":[{"given":"Shahid","family":"Abdullah","sequence":"first","affiliation":[{"name":"School of Advanced Sciences and Languages, VIT Bhopal University, Kothri-Kalan, Sehore 466114, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Neha","family":"Choubey","sequence":"additional","affiliation":[{"name":"School of Advanced Sciences and Languages, VIT Bhopal University, Kothri-Kalan, Sehore 466114, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Suresh","family":"Dara","sequence":"additional","affiliation":[{"name":"School of Advanced Sciences and Languages, VIT Bhopal University, Kothri-Kalan, Sehore 466114, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1251-1532","authenticated-orcid":false,"given":"Moin-ud-Din","family":"Junjua","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Zhejiang Normal University, Jinhua 321004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tawseef","family":"Abdullah","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, National Institute of Technology, Hazratbal, Srinagar 190006, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,9,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2465","DOI":"10.1016\/j.nonrwa.2009.08.003","article-title":"On locating all roots of systems of nonlinear equations inside bounded domain using global optimization methods","volume":"11","author":"Tsoulos","year":"2010","journal-title":"Nonlinear Anal. 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