Optimizing Nonlinear Root Finding: A Novel Fourth Order Derivative-Free Iterative Method with Maximum Efficiency Index and Comparative Analysis

Optimizing Nonlinear Root Finding: A Novel Fourth Order Derivative-Free Iterative Method with Maximum Efficiency Index and Comparative Analysis | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Optimizing Nonlinear Root Finding: A Novel Fourth Order Derivative-Free Iterative Method with Maximum Efficiency Index and Comparative Analysis Muhammad Raza, Daanish Toheed, Najma Abdul Rehman This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7439716/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This paper proposes a novel optimal fourth order derivative free iterative method to find simple roots of nonlinear equations. Based on Kung-Traub conjecture, this fourth order method has maximum efficiency index and it involves three functional evaluations per iteration. The performance and accuracy of this innovative method is compared with wide range of existing methods of same order including Traub-Ostrowski method, modified family of Traub-Ostrowski method and modified family of King’s method. 2020 Mathematics Subject Classification: 65H04, 65H05 Applied Mathematics Computational Mathematics Nonlinear equations Iterative methods Order of convergence Kung-Traub conjecture Full Text Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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