%0 Journal Article %T A new fifth-order iterative method for solving non-linear equations using weight function technique and the basins of attraction %A Khirallah, M. Q. %A Alkhomsan, A. M. %J Journal of Mathematics and Computer Science %D 2023 %V 28 %N 3 %@ ISSN 2008-949X %F Khirallah2023 %X In this paper, new iterative method is presented of fifth-order for solving non-linear equations \(f\left(x\right)=0\) a devoid of the second derivative which requires two derivative functions and evaluations for each step, using both weight functions and synthesis techniques together. This method improves Newton's method and thus the efficiency index has been improved from \(1.414\) to \(1.495\). The convergence analysis for the new method is discussed. We provide some numerical examples that illustrate the performance of our proposed method by comparing them with numerical methods of fifth-order also the complex dynamics and basins of attraction is discussed, comparing it with several methods of the same order, thus comparisons show that new method gives the best results. %9 journal article %R 10.22436/jmcs.028.03.06 %U http://dx.doi.org/10.22436/jmcs.028.03.06 %P 281--293 %0 Journal Article %T A class of optimal eighth-order derivative-free methods for solving the Danchick-Gauss problem %A C. Andreu %A N. Cambil %A A. Cordero %A J. R. Torregrosa %J Appl. Math. Comput. %D 2014 %V 232 %F Andreu2014 %0 Book %T Student Solutions Manual and Study Guide: Numerical Analysis %A R. L. Burden %A J. D. Faires %A A. M. Burden %D 2016 %I Cengage Learning %C %F Burden2016 %0 Journal Article %T Wide stability in a new family of optimal fourth-order iterative methods %A F. I. Chicharro %A N. Garrido %A J. R. Torregrosa %J Comput. Math. Methods %D 2019 %V 3 %F Chicharro2019 %0 Journal Article %T On optimal fourth-order iterative methods free from second derivative and their dynamics %A C. B. Chun %A M. Y. Lee %A B. Neta %A J. Dzunic %J Appl. Math. Comput. %D 2012 %V 218 %F Chun2012 %0 Journal Article %T Basins of attraction for several third order methods to find multiple roots of nonlinear equations %A C. B. Chun %A B. Neta %J Appl. Math. Comput. %D 2015 %V 268 %F Chun2015 %0 Journal Article %T The basins of attraction of Murakami’s fifth order family of methods %A C. B. Chun %A B. Neta %J Appl. Numer. Math. %D 2016 %V 110 %F Chun2016 %0 Journal Article %T An efficient Newton-type method with fifth-order convergence for solving nonlinear equations %A L. Fang %A L. Sun %A G. P. He %J Comput. Appl. Math. %D 2008 %V 27 %F Fang2008 %0 Journal Article %T A fifth-order iterative method for solving nonlinear equations %A Y. M. Ham %A C. B. Chun %J Appl. Math. Comput. %D 2007 %V 194 %F Ham2007 %0 Journal Article %T Basins of attraction for several methods to find simple roots of nonlinear equations %A B. Neta %A M. Scott %A C. B. Chun %J Appl. Math. Comput. %D 2012 %V 218 %F Neta2012 %0 Journal Article %T Some fifth and sixth order iterative methods for solving nonlinear equations %A R. Sharma %J Int. J. Eng. Res. Appl. %D 2014 %V 4 %F Sharma2014 %0 Journal Article %T Some New Higher Order Weighted Newton Methods for Solving Nonlinear Equation with Applications %A P. Sivakumar %A J. Jayaraman %J Math. Comput. Appl. %D 2019 %V 24 %F Sivakumar2019 %0 Book %T Attractor basins of various root-finding methods %A B. D. Stewart %D 2001 %I Naval Postgraduate School Monterey %C CA %F Stewart2001 %0 Journal Article %T Book Review: Solution of equations and systems of equations %A D. M. Young %J Bull. Amer. Math. Soc. %D 1962 %V 68 %F Young1962 %0 Journal Article %T A family of fifth-order convergent methods for solving nonlinear equations using variational iteration technique %A X. J. Zhang %A F. A. Shah %A Y. F. Li %A L. Yan %A A. Q. Baig %A M. R. Farahani %J J. Inf. Optim. Sci. %D 2018 %V 39 %F Zhang2018