Fixed Point Root-Finding Methods of Fourth-Order of Convergence

On the Fourth Order Root Finding Methods of Euler’s Type

A new iterative method of the fourth order for solving nonlinear equations of the form f(x) = 0 is derived. The comparison with other existing methods is performed regarding the computational efficiency and numerical examples. The fourth-order derivative free method for the simultaneous calculation of all polynomial zeros, arising from the proposed method, is also studied. AMS Mathematics Subje...

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

On the fixed point of order 2

This paper  deals with a new type  of fixed point, i.e;"fixed point of order 2" which is introduced in a metric spaceand some results are achieved.

THIRD-ORDER AND FOURTH-ORDER ITERATIVE METHODS FREE FROM SECOND DERIVATIVE FOR FINDING MULTIPLE ROOTS OF NONLINEAR EQUATIONS

In this paper, we present two new families of third-order and fourth-order methods for finding multiple roots of nonlinear equations. Each of them requires one evaluation of the function and two of its first derivative per iteration. Several numerical examples are given to illustrate the performance of the presented methods.    

A new family of four-step fifteenth-order root-finding methods with high efficiency index

‎In this paper a new family of fifteenth-order methods with high efficiency index is presented‎. This family include four evaluations of the function and one evaluation of its first derivative per iteration.‎ ‎Therefore‎, ‎this family of methods has the efficiency index which equals 1.71877‎. ‎In order to show the applicability and validity of the class‎, ‎some numerical examples are discussed‎.