{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:53:30Z","timestamp":1760147610853,"version":"build-2065373602"},"reference-count":26,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,2,18]],"date-time":"2023-02-18T00:00:00Z","timestamp":1676678400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61976027","2022-MS-371","LJKMZ20221492","LJKMZ20221498","0522xn078"],"award-info":[{"award-number":["61976027","2022-MS-371","LJKMZ20221492","LJKMZ20221498","0522xn078"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100005047","name":"Natural Science Foundation of Liaoning Province","doi-asserted-by":"publisher","award":["61976027","2022-MS-371","LJKMZ20221492","LJKMZ20221498","0522xn078"],"award-info":[{"award-number":["61976027","2022-MS-371","LJKMZ20221492","LJKMZ20221498","0522xn078"]}],"id":[{"id":"10.13039\/501100005047","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Educational Commission Foundation of Liaoning Province of China","award":["61976027","2022-MS-371","LJKMZ20221492","LJKMZ20221498","0522xn078"],"award-info":[{"award-number":["61976027","2022-MS-371","LJKMZ20221492","LJKMZ20221498","0522xn078"]}]},{"name":"Key Project of Bohai University","award":["61976027","2022-MS-371","LJKMZ20221492","LJKMZ20221498","0522xn078"],"award-info":[{"award-number":["61976027","2022-MS-371","LJKMZ20221492","LJKMZ20221498","0522xn078"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, the stability of a class of Liu\u2013Wang\u2019s optimal eighth-order single-parameter iterative methods for solving simple roots of nonlinear equations was studied by applying them to arbitrary quadratic polynomials. Under the Riemann sphere and scaling theorem, the complex dynamic behavior of the iterative method was analyzed by fractals. We discuss the stability of all fixed points and the parameter spaces starting from the critical points with the Mathematica software. The dynamical planes of the elements with good and bad dynamical behavior are given, and the optimal parameter element with stable behavior was obtained. Finally, a numerical experiment and practical application were carried out to prove the conclusion.<\/jats:p>","DOI":"10.3390\/axioms12020215","type":"journal-article","created":{"date-parts":[[2023,2,20]],"date-time":"2023-02-20T02:29:08Z","timestamp":1676860148000},"page":"215","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Stability Analysis of Simple Root Seeker for Nonlinear Equation"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8524-6488","authenticated-orcid":false,"given":"Xiaofeng","family":"Wang","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Bohai University, Jinzhou 121013, China"}]},{"given":"Wenshuo","family":"Li","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Bohai University, Jinzhou 121013, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Sidorov, N. 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