Fourth- and fifth-order iterative schemes for nonlinear equations in coupled systems: A novel Adomian decomposition approach

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dc.authoridAllahviranloo, Tofigh/0000-0002-6673-3560
dc.authoridAhmad, Daud/0000-0003-0966-8237
dc.authorwosidAllahviranloo, Tofigh/V-4843-2019
dc.authorwosidAhmad, Daud/ABD-3422-2021
dc.contributor.authorSaqib, Muhammad
dc.contributor.authorAhmad, Daud
dc.contributor.authorAl-Kenani, Ahmad N.
dc.contributor.authorAllahviranloo, Tofigh
dc.date.accessioned2024-05-19T14:46:03Z
dc.date.available2024-05-19T14:46:03Z
dc.date.issued2023
dc.departmentİstinye Üniversitesien_US
dc.description.abstractIn the fields of numerical analysis and applied science, approximating the roots of nonlinear equations is a fundamental and intriguing challenge. With the rapid advancement of computing power, solving nonlinear equations using numerical techniques has become increasingly important.Numerical methods for nonlinear equations play a critical role in many areas of research and industry, enabling scientists and engineers to model and understand complex systems and make accurate predictions about their behavior. This paper aims to propose novel fourth- and fifth-order iterative schemes for approximating solutions to nonlinear equations in coupled systems using Adomian decomposition methods. The proposed method's convergence is examined and numerical examples are provided to demonstrate the effectiveness of the new schemes. We compare these iterative techniques with some previous schemes in the literature, and our results show that the new schemes are more efficient. Our findings represent a significant improvement over previously reported results. Polynomiography is an important tool for visualizing the roots of complex polynomials. It is widely used by researchers, mathematicians and engineers, as it provides a way to visualize complex equations understand their behavior. Our proposed method is capable of generating polynomiographs of complex polynomials, revealing interesting patterns that provide clear visual representations of the roots of complex polynomials. (C) 2023 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).en_US
dc.identifier.doi10.1016/j.aej.2023.05.047
dc.identifier.endpage760en_US
dc.identifier.issn1110-0168
dc.identifier.issn2090-2670
dc.identifier.scopus2-s2.0-85160703007en_US
dc.identifier.scopusqualityQ1en_US
dc.identifier.startpage751en_US
dc.identifier.urihttps://doi.org10.1016/j.aej.2023.05.047
dc.identifier.urihttps://hdl.handle.net/20.500.12713/5428
dc.identifier.volume74en_US
dc.identifier.wosWOS:001020588200001en_US
dc.identifier.wosqualityN/Aen_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherElsevieren_US
dc.relation.ispartofAlexandria Engineering Journalen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.snmz20240519_kaen_US
dc.subjectNumerical Methodsen_US
dc.subjectAdomian Decompositionen_US
dc.subjectConvergence Analysisen_US
dc.titleFourth- and fifth-order iterative schemes for nonlinear equations in coupled systems: A novel Adomian decomposition approachen_US
dc.typeArticleen_US

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