Özban,A.Y.Mathematics2024-07-052024-07-0520040893-965910.1016/S0893-9659(04)90104-82-s2.0-14544290341https://doi.org/10.1016/S0893-9659(04)90104-8https://hdl.handle.net/20.500.14411/3526Some new variants of Newton's method based on harmonic mean and midpoint integration rule have been developed and their convergence properties have been discussed. The order of convergence of the proposed methods are three. In addition to numerical tests verifying the theory, a comparison of the results for the proposed methods and some of the existing ones have also been given. © 2004 Elsevier Ltd. All rights reserved.eninfo:eu-repo/semantics/openAccessFunction evaluationsIteration functionNewton's methodOrder of convergenceArticleQ1176677682215