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A New Derivative-Free Method to Solve Nonlinear Equations

Author

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  • Beny Neta

    (Department of Applied Mathematics, Naval Postgraduate School, Monterey, CA 93943, USA)

Abstract

A new high-order derivative-free method for the solution of a nonlinear equation is developed. The novelty is the use of Traub’s method as a first step. The order is proven and demonstrated. It is also shown that the method has much fewer divergent points and runs faster than an optimal eighth-order derivative-free method.

Suggested Citation

  • Beny Neta, 2021. "A New Derivative-Free Method to Solve Nonlinear Equations," Mathematics, MDPI, vol. 9(6), pages 1-5, March.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:6:p:583-:d:513918
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    References listed on IDEAS

    as
    1. Savin Treanţă, 2020. "Gradient Structures Associated with a Polynomial Differential Equation," Mathematics, MDPI, vol. 8(4), pages 1-10, April.
    2. Biagio Ricceri, 2020. "A Class of Equations with Three Solutions," Mathematics, MDPI, vol. 8(4), pages 1-8, April.
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    Cited by:

    1. Ekta Sharma & Sunil Panday & Shubham Kumar Mittal & Dan-Marian Joița & Lavinia Lorena Pruteanu & Lorentz Jäntschi, 2023. "Derivative-Free Families of With- and Without-Memory Iterative Methods for Solving Nonlinear Equations and Their Engineering Applications," Mathematics, MDPI, vol. 11(21), pages 1-13, November.
    2. Uriel Filobello-Nino & Hector Vazquez-Leal & Jesús Huerta-Chua & Jaime Martínez-Castillo & Agustín L. Herrera-May & Mario Alberto Sandoval-Hernandez & Victor Manuel Jimenez-Fernandez, 2022. "The Enhanced Fixed Point Method: An Extremely Simple Procedure to Accelerate the Convergence of the Fixed Point Method to Solve Nonlinear Algebraic Equations," Mathematics, MDPI, vol. 10(20), pages 1-19, October.

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