Ball Convergence for Steffensen-type Fourth-order Methods

Ball Convergence for Steffensen-type Fourth-order Methods

We present a local convergence analysis for a family of Steffensen-type fourth-order methods in order to approximate a solution of a nonlinear equation. We use hypotheses up to the first derivative in contrast to earlier studies such as [1], [5]-[28] using hypotheses up to the fifth derivative. This way the applicability of these methods is extended under weaker hypotheses. Moreover the radius ...

New family of Two-Parameters Iterative Methods for Non-Linear Equations with Fourth-Order Convergence

A class of Steffensen type methods with optimal order of convergence

In this paper, a family of Steffensen type methods of fourth-order convergence for solving nonlinear smooth equations is suggested. In the proposed methods, a linear combination of divided diferences is used to get a better approximation to the derivative of the given function. Each derivative-free member of the family requires only three evaluations of the given function per iteration. Therefo...

Solving Nonlinear Equations Using Steffensen-Type Methods With Optimal Order of Convergence

The author would like to express his deep gratitude to F. Soleymani for his comments which resulted in considerable improvement in the quality of this paper. Thus, he is much grateful for A.E.Alamir for his helpful hints and a great deal of patience in reviewing this paper. The author is also thankful to the reviewer for his constructive remarks and suggestions which have enhanced the present p...

Optimized Steffensen-Type Methods with Eighth-Order Convergence and High Efficiency Index

Steffensen-type methods are practical in solving nonlinear equations. Since, such schemes do not need derivative evaluation per iteration. Hence, this work contributes two new multistep classes of Steffensen-type methods for finding the solution of the nonlinear equation f x 0. New techniques can be taken into account as the generalizations of the one-step method of Steffensen. Theoretical proo...