Stability of a fourth order bi-parametric family of iterative methods

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

new family of two-parameters iterative methods for non-linear equations with fourth-order convergence

new family of two-parameters iterative methods for non-linear equations with fourth-order convergence

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Real qualitative behavior of a fourth-order family of iterative methods by using the convergence plane

The real dynamics of a family of fourth-order iterative methods is studied when it is applied on quadratic polynomials. A Scaling Theorem is obtained and the conjugacy classes are analyzed. The convergence plane is used to obtain the same kind of information as from the parameter space, and even more, in complex dynamics.

A family of composite fourth-order iterative methods for solving nonlinear equations

In this paper, we present a family of new fourth-order iterative methods for solving nonlinear equations. Per iteration the methods consisting of the family require only two evaluations of the function and one evaluation of its derivative. Several numerical examples are given to illustrate the efficiency and performance of some of the presented methods. 2006 Elsevier Inc. All rights reserved.