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Convergence and Stability of a Parametric Class of Iterative Schemes for Solving Nonlinear Systems

Author

Listed:
  • Alicia Cordero

    (Multidisciplinary Institute of Mathematics, Universitat Politènica de València, 46022 València, Spain)

  • Eva G. Villalba

    (Multidisciplinary Institute of Mathematics, Universitat Politènica de València, 46022 València, Spain)

  • Juan R. Torregrosa

    (Multidisciplinary Institute of Mathematics, Universitat Politènica de València, 46022 València, Spain)

  • Paula Triguero-Navarro

    (Multidisciplinary Institute of Mathematics, Universitat Politènica de València, 46022 València, Spain)

Abstract

A new parametric class of iterative schemes for solving nonlinear systems is designed. The third- or fourth-order convergence, depending on the values of the parameter being proven. The analysis of the dynamical behavior of this class in the context of scalar nonlinear equations is presented. This study gives us important information about the stability and reliability of the members of the family. The numerical results obtained by applying different elements of the family for solving the Hammerstein integral equation and the Fisher’s equation confirm the theoretical results.

Suggested Citation

  • Alicia Cordero & Eva G. Villalba & Juan R. Torregrosa & Paula Triguero-Navarro, 2021. "Convergence and Stability of a Parametric Class of Iterative Schemes for Solving Nonlinear Systems," Mathematics, MDPI, vol. 9(1), pages 1-18, January.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:1:p:86-:d:474055
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    Citations

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    Cited by:

    1. Lucas Jódar & Rafael Company, 2022. "Preface to “Mathematical Methods, Modelling and Applications”," Mathematics, MDPI, vol. 10(9), pages 1-2, May.
    2. Alicia Cordero & Miguel A. Leonardo-Sepúlveda & Juan R. Torregrosa & María P. Vassileva, 2023. "Enhancing the Convergence Order from p to p + 3 in Iterative Methods for Solving Nonlinear Systems of Equations without the Use of Jacobian Matrices," Mathematics, MDPI, vol. 11(20), pages 1-18, October.

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