{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:15:22Z","timestamp":1760058922903,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2025,5,10]],"date-time":"2025-05-10T00:00:00Z","timestamp":1746835200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Umm Al-Qura University, Saudi Arabia","award":["25UQU4340243GSSR07"],"award-info":[{"award-number":["25UQU4340243GSSR07"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, we study the convergence and complex dynamics of a novel higher-order multipoint iteration scheme to solve nonlinear equations. The approach is based upon utilizing cubic interpolation in the second step of the King\u2013Werner method to improve its convergence order from 2.414 to 3 and the efficiency index from 1.554 to 1.732, which is higher than the efficiency of optimal fourth- and eighth-order iterative schemes. The proposed method is validated through numerical and dynamic experiments concerning the absolute error, approximated computational order, regions of convergence, and CPU time (sec) on the real-world problems, including Kepler\u2019s equation, isentropic supersonic flow, and law of population growth, demonstrating superior performance compared to some existing well-known methods. Commonly, regions of convergence of iterative methods are investigated and compared by plotting attractor basins of iteration schemes in the complex plane on polynomial functions of the type zn\u22121. However, in this paper, the attractor basins of the proposed method are investigated on diverse nonlinear functions. The proposed scheme creates portraits of basins of attraction faster with wider convergence areas outperforming existing well-known iteration schemes.<\/jats:p>","DOI":"10.3390\/axioms14050360","type":"journal-article","created":{"date-parts":[[2025,5,12]],"date-time":"2025-05-12T09:13:38Z","timestamp":1747041218000},"page":"360","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["An Improved King\u2013Werner-Type Method Based on Cubic Interpolation: Convergence Analysis and Complex Dynamics"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1251-1532","authenticated-orcid":false,"given":"Moin-ud-Din","family":"Junjua","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Zhejiang Normal University, Jinhua 321004, Zhejiang, China"},{"name":"Department of Mathematics, Ghazi University, Dera Ghazi Khan 32200, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2174-6915","authenticated-orcid":false,"given":"Ibraheem M.","family":"Alsulami","sequence":"additional","affiliation":[{"name":"Mathematics Department, Faculty of Science, Umm Al-Qura University, Makkah 21955, Saudi Arabia"}]},{"given":"Amer","family":"Alsulami","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Turabah University College, Taif University, Taif 21944, Saudi Arabia"}]},{"given":"Sangeeta","family":"Kumari","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Chandigarh University, Gharuan, Mohali 140301, India"}]}],"member":"1968","published-online":{"date-parts":[[2025,5,10]]},"reference":[{"key":"ref_1","unstructured":"Ostrowski, A.M. 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