{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,14]],"date-time":"2026-03-14T20:01:23Z","timestamp":1773518483645,"version":"3.50.1"},"reference-count":18,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2016,2,1]],"date-time":"2016-02-01T00:00:00Z","timestamp":1454284800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>In this work, two multi-step derivative-free iterative methods are presented for solving system of nonlinear equations. The new methods have high computational efficiency and low computational cost. The order of convergence of the new methods is proved by a development of an inverse first-order divided difference operator. The computational efficiency is compared with the existing methods. Numerical experiments support the theoretical results. Experimental results show that the new methods remarkably reduce the computing time in the process of high-precision computing.<\/jats:p>","DOI":"10.3390\/a9010014","type":"journal-article","created":{"date-parts":[[2016,2,1]],"date-time":"2016-02-01T10:03:26Z","timestamp":1454321006000},"page":"14","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Two Efficient Derivative-Free Iterative Methods for Solving Nonlinear Systems"],"prefix":"10.3390","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8524-6488","authenticated-orcid":false,"given":"Xiaofeng","family":"Wang","sequence":"first","affiliation":[{"name":"School of Mathematics and Physics, Bohai University, Jinzhou 121013, China"}]},{"given":"Xiaodong","family":"Fan","sequence":"additional","affiliation":[{"name":"School of Mathematics and Physics, Bohai University, Jinzhou 121013, China"}]}],"member":"1968","published-online":{"date-parts":[[2016,2,1]]},"reference":[{"key":"ref_1","unstructured":"Ortega, J.M., and Rheinbolt, W.C. 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