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

José J. Padilla, Francisco I. Chicharro, Alicia Cordero, Alejandro M. Hernández-Díaz and Juan R. Torregrosa ()
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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

Mathematics, 2024, vol. 12, issue 3, 1-16

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.

Keywords: nonlinear systems; iterative methods; reinforced concrete; shear behaviour; convergence order; efficiency (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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