# A Class of Three-step Root-solvers with Order of Convergence Five for Nonlinear Equations

### Liang Fang, Rui Chen

#### Abstract

The root-finding problem of a univariate nonlinear equation is a fundamental and long-studied problem, and it has wide applications in mathematics and engineering computation. In this paper, a class of modified Newton-type methods for solving nonlinear equations is brought forward. Analytical discussions are reported and the theoretical efficiency of the method is studied. The proposed algorithm requires two evaluations of the functions and two evaluations of derivatives at each iteration. Therefore the efficiency indices of it is 1.4953. Hence, the index of the proposed algorithm is better than that of classical Newton’s method 1.4142. The proposed algorithm in this paper is free from second derivatives. Some numerical results are finally provided to support the theoretical discussions of the proposed method.

Download#### Paper Citation

#### in Harvard Style

Fang L. and Chen R. (2018). **A Class of Three-step Root-solvers with Order of Convergence Five for Nonlinear Equations**.In *Proceedings of the 2nd International Conference on Intelligent Manufacturing and Materials - Volume 1: ICIMM,* ISBN 978-989-758-345-2, pages 470-473. DOI: 10.5220/0007533904700473

#### in Bibtex Style

@conference{icimm18,

author={Liang Fang and Rui Chen},

title={A Class of Three-step Root-solvers with Order of Convergence Five for Nonlinear Equations},

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

year={2018},

pages={470-473},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0007533904700473},

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 - A Class of Three-step Root-solvers with Order of Convergence Five for Nonlinear Equations

SN - 978-989-758-345-2

AU - Fang L.

AU - Chen R.

PY - 2018

SP - 470

EP - 473

DO - 10.5220/0007533904700473