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A New Class of Iterative Processes for Solving Nonlinear Systems by Using One Divided Differences Operator

Author

Listed:
  • Alicia Cordero

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

  • Cristina Jordán

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

  • Esther Sanabria

    (Department of Applied Mathematics, Universitat Politènica de València, 46022 València, Spain)

  • Juan R. Torregrosa

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

Abstract

In this manuscript, a new family of Jacobian-free iterative methods for solving nonlinear systems is presented. The fourth-order convergence for all the elements of the class is established, proving, in addition, that one element of this family has order five. The proposed methods have four steps and, in all of them, the same divided difference operator appears. Numerical problems, including systems of academic interest and the system resulting from the discretization of the boundary problem described by Fisher’s equation, are shown to compare the performance of the proposed schemes with other known ones. The numerical tests are in concordance with the theoretical results.

Suggested Citation

  • Alicia Cordero & Cristina Jordán & Esther Sanabria & Juan R. Torregrosa, 2019. "A New Class of Iterative Processes for Solving Nonlinear Systems by Using One Divided Differences Operator," Mathematics, MDPI, vol. 7(9), pages 1-12, August.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:9:p:776-:d:260327
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    Cited by:

    1. R. H. Al-Obaidi & M. T. Darvishi, 2022. "Constructing a Class of Frozen Jacobian Multi-Step Iterative Solvers for Systems of Nonlinear Equations," Mathematics, MDPI, vol. 10(16), pages 1-13, August.

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