Derivative-Free Conformable Iterative Methods for Solving Nonlinear Equations

Abstract

[EN] In this manuscript, we use approximations of conformable derivatives for designing iterative methods to solve nonlinear algebraic or trascendental equations. We adapt the approximation of conformable derivatives in order to design conformable derivative-free iterative schemes to solve nonlinear equations: Steffensen and Secant-type methods. To our knowledge, these are the first conformable derivative-free schemes in the literature, where the Steffensen conformable method is also optimal; moreover, the Secant conformable scheme is also a procedure with memory. A convergence analysis is made, preserving the order of classical cases, and the numerical performance is studied in order to confirm the theoretical results. It is shown that these methods can present some numerical advantages versus their classical partners, with wide sets of converging initial estimations.