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Study of Local Convergence and Dynamics of a King-Like Two-Step Method with Applications

Author

Listed:
  • Ioannis K. Argyros

    (Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA
    These authors contributed equally to this work.)

  • Ángel Alberto Magreñán

    (Departamento de Matemáticas y Computación, Universidad de La Rioja, Madre de Dios 53, 26006 Logroño (La Rioja), Spain
    These authors contributed equally to this work.)

  • Alejandro Moysi

    (Departamento de Matemáticas y Computación, Universidad de La Rioja, Madre de Dios 53, 26006 Logroño (La Rioja), Spain
    These authors contributed equally to this work.)

  • Íñigo Sarría

    (Escuela Superior de Ingeniería y Tecnología, Universidad Internacional de La Rioja, Avenida de la Paz 123, 26006 Logroño (La Rioja), Spain)

  • Juan Antonio Sicilia Montalvo

    (Escuela Superior de Ingeniería y Tecnología, Universidad Internacional de La Rioja, Avenida de la Paz 123, 26006 Logroño (La Rioja), Spain)

Abstract

In this paper, we present the local results of the convergence of the two-step King-like method to approximate the solution of nonlinear equations. In this study, we only apply conditions to the first derivative, because we only need this condition to guarantee convergence. As a result, the applicability of the method is expanded. We also use different convergence planes to show family behavior. Finally, the new results are used to solve some applications related to chemistry.

Suggested Citation

  • Ioannis K. Argyros & Ángel Alberto Magreñán & Alejandro Moysi & Íñigo Sarría & Juan Antonio Sicilia Montalvo, 2020. "Study of Local Convergence and Dynamics of a King-Like Two-Step Method with Applications," Mathematics, MDPI, vol. 8(7), pages 1-12, July.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:7:p:1062-:d:379062
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    References listed on IDEAS

    as
    1. 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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