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

E. Azadegan , R. Ezzati Department of Mathematics, Islamic Azad University-Karaj Branch, Karaj, Iran |||||||||||||||||||||||||||||||Abstract In this paper, we present a new two-parameters family of iterative methods for solving non-linear equations and prove that the order of convergence of these methods is at least four. Per iteration of these new methods require two evaluations of the functio...

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.

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...

A new optimal method of fourth-order convergence for solving nonlinear equations

In this paper, we present a fourth order method for computing simple roots of nonlinear equations by using suitable Taylor and weight function approximation. The method is based on Weerakoon-Fernando method [S. Weerakoon, G.I. Fernando, A variant of Newton's method with third-order convergence, Appl. Math. Lett. 17 (2000) 87-93]. The method is optimal, as it needs three evaluations per iterate,...