{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T00:42:16Z","timestamp":1759970536743,"version":"build-2065373602"},"reference-count":24,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,1,21]],"date-time":"2025-01-21T00:00:00Z","timestamp":1737417600000},"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>In this manuscript, we propose a multi-step framework for solving nonlinear systems of algebraic equations. To improve the solver\u2019s efficiency, the Jacobian matrix is held constant during the second sub-step, while a specialized strategy is applied in the third sub-step to maximize convergence speed without necessitating additional Jacobian evaluations. The proposed method achieves fifth-order convergence for simple roots, with its theoretical convergence established. Finally, computational experiments are conducted to illustrate the performance of the proposed solver in addressing nonlinear equation systems.<\/jats:p>","DOI":"10.3390\/axioms14020077","type":"journal-article","created":{"date-parts":[[2025,1,21]],"date-time":"2025-01-21T08:46:26Z","timestamp":1737449186000},"page":"77","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On the Derivation of a Fast Solver for Nonlinear Systems of Equations Utilizing Frozen Substeps with Applications"],"prefix":"10.3390","volume":"14","author":[{"given":"Mingming","family":"Liu","sequence":"first","affiliation":[{"name":"School of Statistics and Big Data, Zhengzhou College of Finance and Economics, Zhengzhou 450000, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5829-8634","authenticated-orcid":false,"given":"Stanford","family":"Shateyi","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Applied Mathematics, School of Mathematical and Natural Sciences, University of Venda, P. 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