On a bi-parametric class of optimal eighth-order derivative-free methods. (English) Zbl 1248.65050

Soleymani, F.

Int. J. Pure Appl. Math. 72, No. 1, 27-37 (2011).

Given a nonlinear equation of one variate \(f(x)=0\). There are many well-known methods of finding the solution of the equation. Among them are Newton’s method and Steffensen’s method. A new three-step derivative-free class of eighth-order methods is proposed in the paper. Optimality conditions of these methods are established. Numerical examples that illustrate the proposed methods are given at the end of the article.

Reviewer: Michael M. Pahirya (Mukachevo)

MSC:

65H05

Numerical computation of solutions to single equations

Keywords:

nonlinear scalar equations; optimality; order of convergence; derivate-free methods; simple root; without memory iterations; Newton’s method; Steffensen’s method; numerical examples