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A NEW THREE-STEP ITERATIVE METHOD FOR SOLVING NONLINEAR EQUATIONS

Matinfar Mashaallah, Mohammad Aminzadeh, Sasan Asadpour

Open publisher page 6 citations

Abstract

In this paper, a new three-step iterative method for find- ing a simple root of the nonlinear equation of f(x) = 0 will be intro- duced. 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 eciency in- dex will respectively be 8, and 1.5157. Some numerical experiments are given to illustrate the performance of the three-step iterative method.

About this research paper

What this paper is about

In this paper, a new three-step iterative method for find- ing a simple root of the nonlinear equation of f(x) = 0 will be intro- duced. 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 eciency in- dex will respectively be 8, and 1.5157. Some numerical experiments are given to illustrate the performance of the three-step iterative method.

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OpenAlex reports 6 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

In this paper, a new three-step iterative method for find- ing a simple root of the nonlinear equation of f(x) = 0 will be intro- duced. 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 eciency in- dex will respectively be 8, and 1.5157. Some numerical experiments are given to illustrate the performance of the three-step iterative method.

Key concepts: Iterative method, Local convergence, Mathematics, Newton's method in optimization, Root-finding algorithm, Nonlinear system, Convergence (economics), Simple (philosophy)

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