# Two Modified Three-Step Iterative Methods for Solving Nonlinear Equations

### Liang Fang, Rui Chen, Jing Meng

#### Abstract

With the rapid development of information and engineering technology and wide application of science and technology, nonlinear problems become an important direction of research in the field of numerical calculation and analysis. In this paper, we mainly study modified iterative methods for solving nonlinear equations. We present and analyze a sixth-order convergent modified three-step Newton-type method for solving nonlinear equations. Then we give a seventh-order convergence algorithm. The convergence analysis of the presented algorithms are given. Both of the given methods are free from second derivatives. The efficiency indices of the presented methods are 1.431 and 1.476, respectively, which are better than that of the classical Newton’s method 1.414. Some numerical experiments illustrate the efficiency and performance of the proposed two methods.

Download#### Paper Citation

#### in Harvard Style

Fang L., Chen R. and Meng J. (2018). **Two Modified Three-Step Iterative Methods for Solving Nonlinear Equations**.In *Proceedings of the 2nd International Conference on Intelligent Manufacturing and Materials - Volume 1: ICIMM,* ISBN 978-989-758-345-2, pages 207-210. DOI: 10.5220/0007529102070210

#### in Bibtex Style

@conference{icimm18,

author={Liang Fang and Rui Chen and Jing Meng},

title={Two Modified Three-Step Iterative Methods for Solving Nonlinear Equations},

booktitle={Proceedings of the 2nd International Conference on Intelligent Manufacturing and Materials - Volume 1: ICIMM,},

year={2018},

pages={207-210},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0007529102070210},

isbn={978-989-758-345-2},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 2nd International Conference on Intelligent Manufacturing and Materials - Volume 1: ICIMM,

TI - Two Modified Three-Step Iterative Methods for Solving Nonlinear Equations

SN - 978-989-758-345-2

AU - Fang L.

AU - Chen R.

AU - Meng J.

PY - 2018

SP - 207

EP - 210

DO - 10.5220/0007529102070210