A Three-Point Iterative Method for Solving Nonlinear Equations with High Efficiency Index

Authors

  • Kabir Saminu Department of‎ ‎Mathematics‎, ‎School of General Studies, ‎‎Dr‎. ‎Yusufu Bala Usman College Daura‎, ‎Katsina, Katsina‎, ‎Nigeria
  • Mohammed waziri Yusuf Department of‎ ‎Mathematical sciences, ‎‎Faculty of Science‎, ‎Bayero University Kano, Kano‎, ‎Nigeria
Abstract:

In this paper, we proposed a three-point iterative method for finding the simple roots of non- linear equations via mid-point and interpolation approach. The method requires one evaluation of the derivative and three(3) functions evaluation with efficiency index of 81/4 ≈ 1.682. Numerical results reported here, between the proposed method with some other existing methods shows that our method is promising.

Upgrade to premium to download articles

Sign up to access the full text

Already have an account?login

similar resources

A NEW TWO STEP CLASS OF METHODS WITH MEMORY FOR SOLVING NONLINEAR EQUATIONS WITH HIGH EFFICIENCY INDEX

It is attempted to extend a two-step without memory method to it's with memory. Then, a new two-step derivative free class of without memory methods, requiring three function evaluations per step, is suggested by using a convenient weight function for solving nonlinear equations. Eventually, we obtain a new class of methods by employing a self-accelerating parameter calculated in each iterative...

full text

Improving Three-point Iterative Methods for Solving Nonlinear Equations

Abstract. In this article, we report on sixth-order and seventh-order iterative methods for solving nonlinear equations. In particular sixth-order derivative-based and derivative-free iterative families are constructed in such a way that they comprise a wide class of sixth-order methods which were developed in the past years. Weighting functions are introduced to enhance the algorithmic efficie...

full text

Three-Step Iterative Method for Solving Nonlinear Equations

In this paper, a published algorithm is investigated that proposes a three-step iterative method for solving nonlinear equations. This method is considered to be efficient with third order of convergence and an improvement to previous methods. This paper proves that the order of convergence of the previous scheme is two, and the efficiency index is less than the corresponding Newton’s method. I...

full text

AN ITERATIVE METHOD WITH SIX-ORDER CONVERGENCE FOR SOLVING NONLINEAR EQUATIONS

Modification of Newtons method with higher-order convergence is presented. The modification of Newtons method is based on Frontinis three-order method. The new method requires two-step per iteration. Analysis of convergence demonstrates that the order of convergence is 6. Some numerical examples illustrate that the algorithm is more efficient and performs better than classical Newtons method and ...

full text

A New Iterative Method For Solving Fuzzy Integral ‎Equations

In the present work, by applying known Bernstein polynomials and their advantageous properties, we establish an efficient iterative algorithm to approximate the numerical solution of fuzzy Fredholm integral equations of the second kind. The convergence of the proposed method is given and the numerical examples illustrate that the proposed iterative algorithm are ‎valid.‎

full text

A new iterative with memory class for solving nonlinear ‎equations‎

In this work we develop a new optimal without memory class for approximating a simple root of a nonlinear equation. This class includes three parameters. Therefore, we try to derive some with memory methods so that the convergence order increases as high as possible. Some numerical examples are also ‎presented.‎‎

full text

My Resources

Save resource for easier access later

Save to my library Already added to my library

{@ msg_add @}


Journal title

volume 9  issue 3 (SUMMER)

pages  175- 185

publication date 2019-09-30

By following a journal you will be notified via email when a new issue of this journal is published.

Hosted on Doprax cloud platform doprax.com

copyright © 2015-2023