{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T00:54:08Z","timestamp":1760057648734,"version":"build-2065373602"},"reference-count":20,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,2,17]],"date-time":"2025-02-17T00:00:00Z","timestamp":1739750400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>This article presents the development of three-step derivative-free techniques with memory, which achieve higher convergence orders for solving systems of nonlinear equations. The suggested approaches enhance an existing seventh-order method (without memory) by incorporating various adjustable, self-correcting parameters in the first iterative step. This modification leads to a significant increase in the convergence order, with new methods reaching values of approximately 7.2749, 7.5311, 7.6056, 8.1231, 8.2749, and 9.2169. Additionally, the computational efficiency of these new approaches is evaluated against other comparable methods. Numerical tests show that the suggested approaches are consistently more efficient.<\/jats:p>","DOI":"10.3390\/computation13020055","type":"journal-article","created":{"date-parts":[[2025,2,17]],"date-time":"2025-02-17T10:26:12Z","timestamp":1739787972000},"page":"55","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Novel Techniques with Memory Extension of Three-Step Derivative-Free Iterative Scheme for Nonlinear Systems"],"prefix":"10.3390","volume":"13","author":[{"given":"Nishant","family":"Kumar","sequence":"first","affiliation":[{"name":"Department of Mathematics, Guru Ghasidas Vishwavidyalaya (A Central University), Bilaspur 495009, C.G., India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jai P.","family":"Jaiswal","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Guru Ghasidas Vishwavidyalaya (A Central University), Bilaspur 495009, C.G., India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ioannis K.","family":"Argyros","sequence":"additional","affiliation":[{"name":"Department of Computing and Mathematical Sciences, Cameron University, Lawton, OK 73505, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,17]]},"reference":[{"key":"ref_1","first-page":"64","article-title":"Remarks on iteration","volume":"1","author":"Steffensen","year":"1993","journal-title":"Scand. 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