A High-Efficiency Fourth-Order Iterative Method for Nonlinear Equations: Convergence and Computational Gains

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dc.authorscopusid 56989208700
dc.authorscopusid 35174554200
dc.authorscopusid 57204460693
dc.authorscopusid 7004530784
dc.authorscopusid 60113721800
dc.authorscopusid 57226820219
dc.authorscopusid 36903183800
dc.contributor.author Naseem, A.
dc.contributor.author Gdawiec, K.
dc.contributor.author Qureshi, S.
dc.contributor.author Argyros, I.K.
dc.contributor.author Ur Rehman, M.A.
dc.contributor.author Soomro, A.
dc.contributor.author Hinçal, E.
dc.date.accessioned 2025-10-15T16:45:38Z
dc.date.available 2025-10-15T16:45:38Z
dc.date.issued 2026
dc.department Okan University en_US
dc.department-temp [Naseem] Amir, Department of Mathematics, University of Management and Technology Lahore, Lahore, Pakistan; [Gdawiec] Krzysztof J., Uniwersytet Śląski w Katowicach, Katowice, Poland; [Qureshi] Sania, Department of Basic Sciences and Related Studies, Mehran University of Engineering & Technology, Jamshoro, Pakistan, Mathematics Research Center, Near East University TRNC, Nicosia, Turkey, Research Center of Applied Mathematics, Khazar University, Baku, Azerbaijan; [Argyros] Ioannis Konstantinos, Department of Mathematics and Computer Science, Cameron University, Lawton, United States; [Ur Rehman] Muhammad Aziz, Department of Mathematics, University of Management and Technology Lahore, Lahore, Pakistan; [Soomro] Amanullah, Department of Basic Sciences and Related Studies, Mehran University of Engineering & Technology, Jamshoro, Pakistan; [Hinçal] Evren, Mathematics Research Center, Near East University TRNC, Nicosia, Turkey; [Hosseini] K., Mathematics Research Center, Near East University TRNC, Nicosia, Turkey, Research Center of Applied Mathematics, Khazar University, Baku, Azerbaijan, Faculty of Engineering and Natural Sciences, Istanbul Okan University, Tuzla, Turkey; [Padder] Ausif, Symbiosis Institute of Technology, Pune, India en_US
dc.description.abstract This study introduces an optimal fourth-order iterative method derived by combining two established methods, resulting in enhanced convergence when solving nonlinear equations. Through rigorous convergence analysis using both Taylor expansion and the Banach space framework, the fourth-order optimality condition is verified. We demonstrate the superior efficiency and stability of this new method compared to traditional alternatives. Numerical experiments confirm its effectiveness, showing a reduction in the average number of iterations and computational time. Visual analysis with polynomiographs confirms the method's robustness, focusing on convergence area index, iteration count, computational time, fractal dimension, and Wada measure of basins. These findings underscore the potential of this optimal method for tackling complex nonlinear problems in various scientific and engineering fields. © 2025 Elsevier B.V., All rights reserved. en_US
dc.identifier.doi 10.1016/j.jco.2025.101994
dc.identifier.issn 1090-2708
dc.identifier.scopus 2-s2.0-105016993225
dc.identifier.scopusquality Q2
dc.identifier.uri https://doi.org/10.1016/j.jco.2025.101994
dc.identifier.uri https://hdl.handle.net/20.500.14517/8482
dc.identifier.volume 92 en_US
dc.identifier.wosquality Q1
dc.language.iso en en_US
dc.publisher Academic Press Inc. en_US
dc.relation.ispartof Journal of Complexity en_US
dc.relation.publicationcategory Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı en_US
dc.rights info:eu-repo/semantics/closedAccess en_US
dc.subject Efficiency Index en_US
dc.subject Kung-Traub Conjecture en_US
dc.subject Local and Semi-Local Convergence Analysis en_US
dc.subject Nonlinear Equations en_US
dc.subject Numerical Measures en_US
dc.subject Polynomiography en_US
dc.title A High-Efficiency Fourth-Order Iterative Method for Nonlinear Equations: Convergence and Computational Gains en_US
dc.type Article en_US
dspace.entity.type Publication

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