Variant of Two Real Parameters Chun-Kim’s Method Free Second Derivative with Fourth-order Convergence

Rahmawati, Septia Utami, Wartono

2018

Abstract

Newton’s method is one of the iterative methods that used to solve a nonlinear equation. In this paper, a new iterative method with two parameters was developed with variant modification of Newton’s method using curvature and second-order Taylor series expansion, then its second derivative was approximated using equality of Newton-Steffensen’s and Halley’s Methods. The result of this study shows that this new iterative method has fourth-order convergence and involves three evaluation of functions with the efficiency index about 1.5874. In numerical simulation, we use several functions to test the performance of this new iterative method and the others compared iterative methods, such as: Newton’s Method (MN), Newton-Steffensen’s Method (MNS), Chun-Kim’s Method (MCK) and Omran’s Method (MO). The result of numerical simulation shows that the performance of this method is better than the others.

Paper Citation

in Harvard Style

Rahmawati., Utami S. and Wartono. (2018). Variant of Two Real Parameters Chun-Kim’s Method Free Second Derivative with Fourth-order Convergence.In Proceedings of the International Conference on Mathematics and Islam - Volume 1: ICMIs, ISBN 978-989-758-407-7, pages 307-313. DOI: 10.5220/0008521203070313

in Bibtex Style

@conference{icmis18,
author={Rahmawati and Septia Utami and Wartono},
title={Variant of Two Real Parameters Chun-Kim’s Method Free Second Derivative with Fourth-order Convergence},
booktitle={Proceedings of the International Conference on Mathematics and Islam - Volume 1: ICMIs,},
year={2018},
pages={307-313},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0008521203070313},
isbn={978-989-758-407-7},
}

in EndNote Style

TY - CONF

JO - Proceedings of the International Conference on Mathematics and Islam - Volume 1: ICMIs,
TI - Variant of Two Real Parameters Chun-Kim’s Method Free Second Derivative with Fourth-order Convergence
SN - 978-989-758-407-7
AU - Rahmawati.
AU - Utami S.
AU - Wartono.
PY - 2018
SP - 307
EP - 313
DO - 10.5220/0008521203070313