IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i7p1062-d379062.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/7/1062/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/7/1062/
    Download Restriction: no
    ---><---

    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Artidiello, S. & Cordero, Alicia & Torregrosa, Juan R. & Vassileva, M.P., 2017. "Design and multidimensional extension of iterative methods for solving nonlinear problems," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 194-203.
    2. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:8:y:2020:i:7:p:1062-:d:379062. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.