A New Three-step Iterative Method for Solving Nonlinear Equations

Authors

  • Mashallah Matin Far
  • Mohammad Aminzadeh
  • Sasan Asadpour

DOI:

https://doi.org/10.30495/jme.v6i0.95

Keywords:

Nonlinear equation, iterative method, threestep iterative method, convergence order, efficiency index.

Abstract

In this paper, a new three-step iterative method for finding a simple root of the nonlinear equation of f(x) = 0 will be introduced. This method is based on the two-step method of [C. Chun, Y. Ham, Some fourth-order modifications of Newton’s method, Appl. Math. Comput. 197 (2008) 654-658]. The new method requires three evaluations of the function and two of its first-derivative. We will prove that the order of convergence of the new method and its efficiency index will respectively be 8, and 1.5157. Some numerical experiments are given to illustrate the performance of the three-step iterative method.

Author Biographies

Mashallah Matin Far

Department of Mathematics and Computer Science Assistant Professor of Mathematics University of Mazandaran P.O.Box 47415-95447 Babolsar, Iran

Mohammad Aminzadeh

Department of Mathematics M.Sc. Student Science of Mathematics Faculty University of Mazandaran P.O.Box 47415-95447 Babolsar, Iran

Sasan Asadpour

Department of Mathematics M.Sc. Student Science of Mathematics Faculty University of Mazandaran P.O.Box 47415-95447 Babolsar, Iran

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Published

2012-06-01

Issue

Vol. 6

Section

Vol. 6, No. 1, (2012)

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