Abstract
The purpose of this paper is to derive and discuss a three-step iterative expression for solving nonlinear equations. In fact, we derive a derivative-free form for one of the existing optimal eighth-order methods and preserve its convergence order. Theoretical results will be upheld by numerical experiments.
Highlights
Assume that f : D ⊆ R → R is sufficiently smooth and that α ∈ D is its simple zero; that is, f(α) = 0
Considering a known optimal eighthorder method with derivative and the conjecture of Cordero and Torregrosa [1], we construct a family of derivative-free methods without memory for solving a nonlinear equation
Kung and Traub in [2] have provided a class of nstep derivative-involved methods including n evaluations of the function and one of its first derivatives per full iteration to reach the convergence rate 2n
Summary
Considering a known optimal eighthorder method with derivative and the conjecture of Cordero and Torregrosa [1], we construct a family of derivative-free methods without memory for solving a nonlinear equation. Kung and Traub in [2] have provided a class of nstep derivative-involved methods including n evaluations of the function and one of its first derivatives per full iteration to reach the convergence rate 2n. They have given a nstep derivative-free family of one parameter (consuming n+1 evaluations of the function) to again achieve the optimal convergence rate 2n
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
