Enhancing the Convergence Order from p to p + 3 in Iterative Methods for Solving Nonlinear Systems of Equations without the Use of Jacobian Matrices

Alicia Cordero (), Miguel A. Leonardo-Sepúlveda, Juan R. Torregrosa and María P. Vassileva
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Alicia Cordero: Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera, s/n, 46022 Valencia, Spain
Miguel A. Leonardo-Sepúlveda: Área de Ciencia Básica y Ambiental, Instituto Tecnológico de Santo Domingo (INTEC), Av. Los Próceres, Gala, Santo Domingo 10602, Dominican Republic
Juan R. Torregrosa: Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera, s/n, 46022 Valencia, Spain
María P. Vassileva: Área de Ciencia Básica y Ambiental, Instituto Tecnológico de Santo Domingo (INTEC), Av. Los Próceres, Gala, Santo Domingo 10602, Dominican Republic

Mathematics, 2023, vol. 11, issue 20, 1-18

Abstract: In this paper, we present an innovative technique that improves the convergence order of iterative schemes that do not require the evaluation of Jacobian matrices. As far as we know, this is the first technique that allows us the achievement of an increase, from p to p + 3 units, in the order of convergence. This is constructed from any Jacobian-free scheme of order p . We conduct comprehensive numerical tests first in academical examples to validate the theoretical results, showing the efficiency and effectiveness of the new Jacobian-free schemes. Then, we apply them on the non-differentiable partial differential equations that models the nutrient diffusion in a biological substrate.

Keywords: iterative methods; nonlinear systems; local convergence; Jacobian-free scheme (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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