{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,5]],"date-time":"2026-05-05T19:47:22Z","timestamp":1778010442397,"version":"3.51.4"},"reference-count":22,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2023,7,12]],"date-time":"2023-07-12T00:00:00Z","timestamp":1689120000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Pontificia Universidad Cat\u00f3lica del Ecuador Proyect","award":["UIO2022"],"award-info":[{"award-number":["UIO2022"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, we propose two new hybrid methods for solving nonlinear equations, utilizing the advantages of classical methods (bisection, trisection, and modified false position), i.e., bisection-modified false position (Bi-MFP) and trisection-modified false position (Tri-MFP). We implemented the proposed algorithms for several benchmark problems. We discuss the graphical analysis of these problems with respect to the number of iterations and the average CPU time.<\/jats:p>","DOI":"10.3390\/axioms12070684","type":"journal-article","created":{"date-parts":[[2023,7,13]],"date-time":"2023-07-13T01:58:11Z","timestamp":1689213491000},"page":"684","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Numerical Analysis of New Hybrid Algorithms for Solving Nonlinear Equations"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1567-0264","authenticated-orcid":false,"given":"Miguel","family":"Vivas-Cortez","sequence":"first","affiliation":[{"name":"Escuela de Ciencias Fsicas y Matemticas, Facultad de Ciencias Exactas y Naturales, Pontificia Universidad Catlica del Ecuador, Av. 12 de Octubre 1076, Apartado, Quito 17-01-2184, Ecuador"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Naseem Zulfiqar","family":"Ali","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Government College University, Allama Iqbal Road, Faisalabad 38000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Awais Gul","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Government College University, Allama Iqbal Road, Faisalabad 38000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1019-9485","authenticated-orcid":false,"given":"Muhammad Uzair","family":"Awan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Government College University, Allama Iqbal Road, Faisalabad 38000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,7,12]]},"reference":[{"key":"ref_1","unstructured":"Burden, R.L., and Faires, J.D. 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