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RESEARCH ARTICLE

A novel ninth-order root-finding algorithm for nonlinear equations with implementations in various software tools

Srinivasarao Thota1 ,  Amir Naseem2 ,  Thumati Gopi3 ,  Kashireddy Sai NandanReddy3 ,  Padarthi Sai Kousik3 ,  Thulasi Bikku3 ,  Shanmugasundaram Palanisamy4*
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1 Department of Mathematics, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Amaravati, Andhra Pradesh, India
2 Department of Mathematics, University of Management and Technology, Lahore, Punjab, Pakistan
3 Department of Computer Science and Engineering, Amrita School of Computing, Amrita Vishwa Vidyapeetham, Amaravati, Andhra Pradesh, India
4 Department of Mathematics, College of Natural Computational Sciences, MizanTepi University, Mizan-Aman, South West Ethiopia Peoples’ Region, Ethiopia
IJOCTA, 8171 https://doi.org/10.36922/ijocta.8171
Received: 24 December 2024 | Revised: 9 May 2025 | Accepted: 14 May 2025 | Published online: 19 June 2025
© 2025 by the Author(s). This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
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Abstract

Nonlinear phenomena are prevalent in numerous fields, including economics, engineering, and natural sciences. Computational science continues to advance through the development of novel numerical schemes and the refinement of existing ones. Ideally, these numerical systems should offer both high-order convergence and computational efficiency. This article introduces a new three step algorithm for solving nonlinear scalar equations, aiming to meet these criteria. The proposed approach requires six function evaluations per iteration and achieves ninth-order convergence. To demonstrate the efficiency of the technique, various numerical examples are shown. Implementations of the method are available in both Maple and Python, and it can be readily adapted for use in other computational environments.

Keywords
Root-finding algorithm
Nonlinear equations
Implementations
Halley method
Exponential method
Funding
None.
Conflict of interest
The authors declare that they have no competing interests.
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An International Journal of Optimization and Control: Theories & Applications, Electronic ISSN: 2146-5703 Print ISSN: 2146-0957, Published by AccScience Publishing
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