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

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.

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

A Two-Parameter Family of Fourth-Order Iterative Methods with Optimal Convergence for Multiple Zeros

We develop a family of fourth-order iterative methods using the weighted harmonic mean of two derivative functions to compute approximatemultiple roots of nonlinear equations.They are proved to be optimally convergent in the sense of Kung-Traub’s optimal order. Numerical experiments for various test equations confirm well the validity of convergence and asymptotic error constants for the develo...