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ON HIGHLY EFFICIENT SIMULTANEOUS SCHEMES FOR FINDING ALL POLYNOMIAL ROOTS

MUDASSIR SHAMS

Department of Mathematics and Statistics, Riphah International University, I-14, Islamabad 44000, Pakistan

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NAILA RAFIQ

Department of Mathematics, National University of Modern Languages (NUML), Islamabad, Pakistan

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NASREEN KAUSAR

Department of Mathematics, Faculty of Arts and Science, Yildiz Technical University, Esenler 34210, Istanbul, Turkey

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PRAVEEN AGARWAL

Department of Mathematics, Anand International College of Engineering, Jaipur 303012, Rajasthan, India

Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St., 117198 Moscow, Russia

Russian Federation and Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman, UAE

International Center for Basic and Applied Sciences, Jaipur 302029, India

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NAZIR AHMAD MIR

Department of Mathematics, National University of Modern Languages (NUML), Islamabad, Pakistan

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, and

YONG-MIN LI

Department of Mathematics, Huzhou University, Huzhou 313000, P. R. China

Institute for Advanced Study Honoring Chen Jian Gong, Hangzhou Normal University, Hangzhou 311121, P. R. China

E-mail Address: chenyg@pku.edu.cn

Corresponding author.

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https://doi.org/10.1142/S0218348X22401983Cited by:8 (Source: Crossref)

This article is part of the issue:

Special Issue on Recent Advances on Fractional Linear and Nonlinear Equations: Theory and Application
Guest Editors: Salah Boulaaras and Rashid Jan

Abstract

This paper develops optimal family of fourth-order iterative techniques in order to find a single root and to generalize them for simultaneous finding of all roots of polynomial equation. Convergence study reveals that for single root finding methods, its optimal convergence order is 4, while for simultaneous methods, it is 12. Computational cost and numerical illustrations demonstrate that the newly developed family of methods outperformed the previous methods available in the literature.

Keywords:

References

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Vol. 30, No. 10

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History

Received 29 November 2021

Accepted 20 December 2021

Published: November 25, 2022

Information

This is an Open Access article in the “Special Issue on Recent Advances on Fractional Linear and Nonlinear Equations: Theory and Application”, edited by Salah Boulaaras (Qassim University, Saudi Arabia) & Rashid Jan (Xi’An Jiaotong University, China) published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution 4.0 (CC-BY) License which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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ON HIGHLY EFFICIENT SIMULTANEOUS SCHEMES FOR FINDING ALL POLYNOMIAL ROOTS

Abstract

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