Solving Nonlinear Transcendental Equations by Iterative Methods with Conformable Derivatives: A General Approach

Giro Candelario, Alicia Cordero (), Juan R. Torregrosa and María P. Vassileva
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Giro Candelario: Área de Ciencias Básicas y Ambientales, Instituto Tecnológico de Santo Domingo (INTEC), Av. Los Procéres, Gala, Santo Domingo 10602, Dominican Republic
Alicia Cordero: Institute for Multidisciplinary Mathematics, Universitat Politècnica de València, 46022 València, Spain
Juan R. Torregrosa: Institute for Multidisciplinary Mathematics, Universitat Politècnica de València, 46022 València, Spain
María P. Vassileva: Área de Ciencias Básicas y Ambientales, Instituto Tecnológico de Santo Domingo (INTEC), Av. Los Procéres, Gala, Santo Domingo 10602, Dominican Republic

Mathematics, 2023, vol. 11, issue 11, 1-29

Abstract: In recent years, some Newton-type schemes with noninteger derivatives have been proposed for solving nonlinear transcendental equations by using fractional derivatives (Caputo and Riemann–Liouville) and conformable derivatives. It has also been shown that the methods with conformable derivatives improve the performance of classical schemes. In this manuscript, we design point-to-point higher-order conformable Newton-type and multipoint procedures for solving nonlinear equations and propose a general technique to deduce the conformable version of any classical iterative method with integer derivatives. A convergence analysis is given and the expected orders of convergence are obtained. As far as we know, these are the first optimal conformable schemes, beyond the conformable Newton procedure, that have been developed. The numerical results support the theory and show that the new schemes improve the performance of the original methods in some aspects. Additionally, the dependence on initial guesses is analyzed, and these schemes show good stability properties.

Keywords: nonlinear equations; conformable derivative; higher-order Newton’s procedure; multipoint methods; optimal schemes; stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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