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Korean Mathematical Society JKMS

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J. Korean Math. Soc. 2011; 48(3): 487-497

Printed May 1, 2011

https://doi.org/10.4134/JKMS.2011.48.3.487

Copyright © The Korean Mathematical Society.

A quadratically convergent iterative method for nonlinear equations

Beong In Yun and Miodrag S. Petkovi\'c

Kunsan National University, University of Ni\v s

Abstract

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In this paper we propose a simple iterative method for finding a root of a nonlinear equation. It is shown that the new method, which does not require any derivatives, has a quadratic convergence order. In addition, one can find that a hybrid method combined with the non-iterative method can further improve the convergence rate. To show the efficiency of the presented method we give some numerical examples.

Keywords: nonlinear equation, iterative method, quadratic convergence, hybrid method

MSC numbers: 65H05, 68W25

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