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Study of a High Order Family: Local Convergence and Dynamics

Author

Listed:
  • Cristina Amorós

    (Escuela Superior de Ingeniería y Tecnología, Universidad Internacional de La Rioja, 26006 Logroño, Spain)

  • Ioannis K. Argyros

    (Department of Mathematics Sciences, Cameron University, Lawton, OK 73505, USA)

  • Ruben González

    (Escuela Superior de Ingeniería y Tecnología, Universidad Internacional de La Rioja, 26006 Logroño, Spain)

  • Á. Alberto Magreñán

    (Departamento de Matemáticas y Computación, Universidad de La Rioja, 26004 Logroño, Spain)

  • Lara Orcos

    (Facultad de Educación, Universidad Internacional de La Rioja, 26006 Logroño, Spain)

  • Íñigo Sarría

    (Escuela Superior de Ingeniería y Tecnología, Universidad Internacional de La Rioja, 26006 Logroño, Spain)

Abstract

The study of the dynamics and the analysis of local convergence of an iterative method, when approximating a locally unique solution of a nonlinear equation, is presented in this article. We obtain convergence using a center-Lipschitz condition where the ball radii are greater than previous studies. We investigate the dynamics of the method. To validate the theoretical results obtained, a real-world application related to chemistry is provided.

Suggested Citation

  • Cristina Amorós & Ioannis K. Argyros & Ruben González & Á. Alberto Magreñán & Lara Orcos & Íñigo Sarría, 2019. "Study of a High Order Family: Local Convergence and Dynamics," Mathematics, MDPI, vol. 7(3), pages 1-14, February.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:3:p:225-:d:209715
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    References listed on IDEAS

    as
    1. S. Artidiello & A. Cordero & Juan R. Torregrosa & M. P. Vassileva, 2014. "Optimal High-Order Methods for Solving Nonlinear Equations," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-9, May.
    2. Jovana Džunić & Miodrag S. Petković, 2012. "A Family of Three-Point Methods of Ostrowski's Type for Solving Nonlinear Equations," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-9, January.
    3. Budzko, Dzmitry & Cordero, Alicia & Torregrosa, Juan R., 2015. "A new family of iterative methods widening areas of convergence," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 405-417.
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