J. Korean Math. Soc. 2022; 59(6): 1067-1082
Online first article October 23, 2022 Printed November 1, 2022
https://doi.org/10.4134/JKMS.j210607
Copyright © The Korean Mathematical Society.
Dejan \'Cebi\'c , Neboj\v sa M. Ralevi\'c
University of Belgrade; University of Novi Sad
This paper presents a new optimal three-step eighth-order family of iterative methods for finding multiple roots of nonlinear equations. Different from the all existing optimal methods of the eighth-order, the new iterative scheme is constructed using one function and three derivative evaluations per iteration, preserving the efficiency and optimality in the sense of Kung-Traub's conjecture. Theoretical results are verified through several standard numerical test examples. The basins of attraction for several polynomials are also given to illustrate the dynamical behaviour and the obtained results show better stability compared to the recently developed optimal methods.
Keywords: Nonlinear equation, multiple root, optimal methods, eighth-order of convergence
MSC numbers: Primary 65H05
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