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

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...

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

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...