A NEW OPTIMAL EIGHTH-ORDER FAMILY OF MULTIPLE ROOT FINDERS

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.