A New Family of Nonlinear Fifth-Order Solvers for Finding Simple Roots

摘要

In this paper, we present a new family of iterative methods for solving nonlinear equations. It is proved that the order of convergence of this family is five. Two functions and two derivative evaluations should be computed per iteration. To demonstrate convergence properties of the proposed family of methods, some numerical examples are given. Further numerical comparisons are made with several other existing fifth-order methods.