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Derivative Free Conformable Iterative Methods for Solving Nonlinear Equations
Version 1
: Received: 22 June 2023 / Approved: 22 June 2023 / Online: 22 June 2023 (12:56:52 CEST)
A peer-reviewed article of this Preprint also exists.
Candelario, G.; Cordero, A.; Torregrosa, J.R.; Vassileva, M.P. Derivative-Free Conformable Iterative Methods for Solving Nonlinear Equations. Fractal Fract. 2023, 7, 578. Candelario, G.; Cordero, A.; Torregrosa, J.R.; Vassileva, M.P. Derivative-Free Conformable Iterative Methods for Solving Nonlinear Equations. Fractal Fract. 2023, 7, 578.
Abstract
In the last years, a recent growing line of research has been developed with fruitful results by using fractional and conformable derivatives in the iterative procedures of classical methods for solving nonlinear equations. In that sense, the use of conformable derivatives has shown better behavior than fractional ones, not only in the theory, but also in the practice. In this work, we adapt the approximation of conformable derivatives in order to design the first conformable derivative-free iterative schemes to solve nonlinear equations: a Steffensen’s type method and a Secant type method; the latter with memory. Convergence analysis is made, preserving the order of classical cases, and the numerical performance is studied in order to confirm the results in the theory. It is shown that these methods can present some numerical advantages versus their classical partners, with wide sets of converging initial estimations.
Keywords
Nonlinear equations; conformable derivative; derivative free conformable methods; conformable method with memory; stability.
Subject
Computer Science and Mathematics, Applied Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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