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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Giro Candelario & Alicia Cordero & Juan R. Torregrosa & María P. Vassileva, 2023. "Solving Nonlinear Transcendental Equations by Iterative Methods with Conformable Derivatives: A General Approach," Mathematics, MDPI, vol. 11(11), pages 1-29, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:11:p:2568-:d:1163306
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    References listed on IDEAS

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    1. A.M. Mathai & H.J. Haubold, 2017. "Fractional and Multivariable Calculus," Springer Optimization and Its Applications, Springer, number 978-3-319-59993-9, June.
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