Seventh-order iterative algorithm free from second derivative for solving algebraic nonlinear equations

seventh-order iterative algorithm free from second derivative for solving algebraic nonlinear equations

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seventh-order iterative algorithm free from second derivative for solving algebraic nonlinear equations

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 Ninth-Order Iterative Method Free from Second Derivative for Solving Nonlinear Equations

Abstract In this paper, we study and analyze an iterative method for solving nonlinear equations with ninth order of convergence. The new proposed method is obtained by composing an iterative method obtained in Noor et al. [9] with Newton’s method and approximating the first-appeared derivative in the last step by a combination of already evaluated function values. The convergence analysis of o...

A Note on Some Higher-Order Iterative Methods Free from Second Derivative for Solving Nonlinear Equations

In the recent paper [M. A. Noor, W. A. Khan, K. I. Noor and Eisa Al-Said, Higher-order iterative methods free from second derivative for solving nonlinear equations, International Journal of the Physical Sciences, Vol. 6 (8) (2011), 1887-1893] several iterative methods for solving nonlinear equations are presented. One of the methods is the three-step iterative method given in Algorithm (2.10) ...

New iterative methods with seventh-order convergence for solving nonlinear equations

In this paper, seventh-order iterative methods for the solution ofnonlinear equations are presented. The new iterative methods are developed byusing weight function method and using an approximation for the last derivative,which reduces the required number of functional evaluations per step. Severalexamples are given to illustrate the eciency and the performance of the newiterative methods.