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Stability analysis of a parametric family of seventh-order iterative methods for solving nonlinear systems

Author

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  • Amiri, Abdolreza
  • Cordero, Alicia
  • Taghi Darvishi, M.
  • Torregrosa, Juan R.

Abstract

In this paper, a parametric family of seventh-order of iterative method to solve systems of nonlinear equations is presented. Its local convergence is studied and quadratic polynomials are used to investigate its dynamical behavior. The study of the fixed and critical points of the rational function associated to this class allows us to obtain regions of the complex plane where the method is stable. By depicting parameter planes and dynamical planes we obtain complementary information of the analytical results. These results are used to solve some nonlinear problems.

Suggested Citation

  • Amiri, Abdolreza & Cordero, Alicia & Taghi Darvishi, M. & Torregrosa, Juan R., 2018. "Stability analysis of a parametric family of seventh-order iterative methods for solving nonlinear systems," Applied Mathematics and Computation, Elsevier, vol. 323(C), pages 43-57.
    • Handle: RePEc:eee:apmaco:v:323:y:2018:i:c:p:43-57
    DOI: 10.1016/j.amc.2017.11.040
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    References listed on IDEAS

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    1. Cordero, Alicia & Gutiérrez, José M. & Magreñán, Á. Alberto & Torregrosa, Juan R., 2016. "Stability analysis of a parametric family of iterative methods for solving nonlinear models," Applied Mathematics and Computation, Elsevier, vol. 285(C), pages 26-40.
    2. Geum, Young Hee & Kim, Young Ik & Neta, Beny, 2016. "A sixth-order family of three-point modified Newton-like multiple-root finders and the dynamics behind their extraneous fixed points," Applied Mathematics and Computation, Elsevier, vol. 283(C), pages 120-140.
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    Cited by:

    1. Amiri, Abdolreza & Argyros, Ioannis K., 2021. "On the approximation of mth power divided differences preserving the local order of convergence," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    2. Francisco I. Chicharro & Alicia Cordero & Neus Garrido & Juan R. Torregrosa, 2019. "Generalized High-Order Classes for Solving Nonlinear Systems and Their Applications," Mathematics, MDPI, vol. 7(12), pages 1-14, December.
    3. Ramandeep Behl & Ioannis K. Argyros & Fouad Othman Mallawi, 2021. "Some High-Order Convergent Iterative Procedures for Nonlinear Systems with Local Convergence," Mathematics, MDPI, vol. 9(12), pages 1-13, June.
    4. Francisco I. Chicharro & Rafael A. Contreras & Neus Garrido, 2020. "A Family of Multiple-Root Finding Iterative Methods Based on Weight Functions," Mathematics, MDPI, vol. 8(12), pages 1-17, December.

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