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A Class of Efficient Sixth-Order Iterative Methods for Solving the Nonlinear Shear Model of a Reinforced Concrete Beam

Author

Listed:
  • José J. Padilla

    (Departamento de Ingeniería Civil, UCAM Universidad Católica de Murcia, 30107 Guadalupe, Spain)

  • Francisco I. Chicharro

    (Instituto Universitario de Matemàtica Multidisciplinar, Universitat Politècnica de València, 46022 València, Spain)

  • Alicia Cordero

    (Instituto Universitario de Matemàtica Multidisciplinar, Universitat Politècnica de València, 46022 València, Spain)

  • Alejandro M. Hernández-Díaz

    (Área de Mecánica de Medios Continuos y Teoría de Estructuras, Universidad de La Laguna, 38200 La Laguna, Spain)

  • Juan R. Torregrosa

    (Instituto Universitario de Matemàtica Multidisciplinar, Universitat Politècnica de València, 46022 València, Spain)

Abstract

In this paper, we present a three-step sixth-order class of iterative schemes to estimate the solutions of a nonlinear system of equations. This procedure is designed by means of a weight function technique. We apply this procedure for predicting the shear strength of a reinforced concrete beam. The values for the parameters of the nonlinear system describing this problem were randomly selected inside the prescribed ranges by technical standards for structural concrete. Moreover, some of these parameters were fixed taking into consideration the solvability region of the adopted steel constitutive model. The effectiveness of the new class is also compared with other current schemes in terms of the computational efficiency and numerical performance, with very good results. The advantages of this new class come from the low computational cost, due to the existence of an only inverse operator.

Suggested Citation

  • José J. Padilla & Francisco I. Chicharro & Alicia Cordero & Alejandro M. Hernández-Díaz & Juan R. Torregrosa, 2024. "A Class of Efficient Sixth-Order Iterative Methods for Solving the Nonlinear Shear Model of a Reinforced Concrete Beam," Mathematics, MDPI, vol. 12(3), pages 1-16, February.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:3:p:499-:d:1333902
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    References listed on IDEAS

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    1. Artidiello, Santiago & Cordero, Alicia & Torregrosa, Juan R. & Vassileva, Maria P., 2015. "Multidimensional generalization of iterative methods for solving nonlinear problems by means of weight-function procedure," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 1064-1071.
    2. Narang, Mona & Bhatia, Saurabh & Kanwar, V., 2016. "New two-parameter Chebyshev–Halley-like family of fourth and sixth-order methods for systems of nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 394-403.
    3. Moin-ud-Din Junjua & Saima Akram & Nusrat Yasmin & Fiza Zafar, 2015. "A New Jarratt-Type Fourth-Order Method for Solving System of Nonlinear Equations and Applications," Journal of Applied Mathematics, Hindawi, vol. 2015, pages 1-14, March.
    4. Alzahrani, Abdullah Khamis Hassan & Behl, Ramandeep & Alshomrani, Ali Saleh, 2018. "Some higher-order iteration functions for solving nonlinear models," Applied Mathematics and Computation, Elsevier, vol. 334(C), pages 80-93.
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