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Two-Step Fifth-Order Efficient Jacobian-Free Iterative Method for Solving Nonlinear Systems

Author

Listed:
  • Alicia Cordero

    (Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera, s/n, 46022 Valencia, Spain)

  • Javier G. Maimó

    (Area de Ciencias Básicas y Ambientales, Instituto Tecnológico de Santo Domingo (INTEC), Av. Los Próceres, Gala, Santo Domingo 10602, Dominican Republic)

  • Antmel Rodríguez-Cabral

    (Area de Ciencias Básicas y Ambientales, 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)

Abstract

This article introduces a novel two-step fifth-order Jacobian-free iterative method aimed at efficiently solving systems of nonlinear equations. The method leverages the benefits of Jacobian-free approaches, utilizing divided differences to circumvent the computationally intensive calculation of Jacobian matrices. This adaptation significantly reduces computational overhead and simplifies the implementation process while maintaining high convergence rates. We demonstrate that this method achieves fifth-order convergence under specific parameter settings, with broad applicability across various types of nonlinear systems. The effectiveness of the proposed method is validated through a series of numerical experiments that confirm its superior performance in terms of accuracy and computational efficiency compared to existing methods.

Suggested Citation

  • Alicia Cordero & Javier G. Maimó & Antmel Rodríguez-Cabral & Juan R. Torregrosa, 2024. "Two-Step Fifth-Order Efficient Jacobian-Free Iterative Method for Solving Nonlinear Systems," Mathematics, MDPI, vol. 12(21), pages 1-20, October.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:21:p:3341-:d:1506060
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