IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v7y2019i8p672-d252320.html
   My bibliography  Save this article

An Optimal Eighth-Order Family of Iterative Methods for Multiple Roots

Author

Listed:
  • Saima Akram

    (Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan 60800, Pakistan)

  • Fiza Zafar

    (Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan 60800, Pakistan)

  • Nusrat Yasmin

    (Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan 60800, Pakistan)

Abstract

In this paper, we introduce a new family of efficient and optimal iterative methods for finding multiple roots of nonlinear equations with known multiplicity ( m ≥ 1 ) . We use the weight function approach involving one and two parameters to develop the new family. A comprehensive convergence analysis is studied to demonstrate the optimal eighth-order convergence of the suggested scheme. Finally, numerical and dynamical tests are presented, which validates the theoretical results formulated in this paper and illustrates that the suggested family is efficient among the domain of multiple root finding methods.

Suggested Citation

  • Saima Akram & Fiza Zafar & Nusrat Yasmin, 2019. "An Optimal Eighth-Order Family of Iterative Methods for Multiple Roots," Mathematics, MDPI, vol. 7(8), pages 1-14, July.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:8:p:672-:d:252320
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/7/8/672/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/7/8/672/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Geum, Young Hee & Kim, Young Ik & Neta, Beny, 2015. "A class of two-point sixth-order multiple-zero finders of modified double-Newton type and their dynamics," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 387-400.
    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.
    3. R. F. Lin & H. M. Ren & Z. Šmarda & Q. B. Wu & Y. Khan & J. L. Hu, 2014. "New Families of Third-Order Iterative Methods for Finding Multiple Roots," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-9, June.
    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. Fiza Zafar & Alicia Cordero & Juan R. Torregrosa, 2018. "An Efficient Family of Optimal Eighth-Order Multiple Root Finders," Mathematics, MDPI, vol. 6(12), pages 1-16, December.
    2. Min-Young Lee & Young Ik Kim & Beny Neta, 2019. "A Generic Family of Optimal Sixteenth-Order Multiple-Root Finders and Their Dynamics Underlying Purely Imaginary Extraneous Fixed Points," Mathematics, MDPI, vol. 7(6), pages 1-26, June.
    3. Ramandeep Behl & Ioannis K. Argyros & Michael Argyros & Mehdi Salimi & Arwa Jeza Alsolami, 2020. "An Iteration Function Having Optimal Eighth-Order of Convergence for Multiple Roots and Local Convergence," Mathematics, MDPI, vol. 8(9), pages 1-21, August.
    4. Young Hee Geum & Young Ik Kim & Beny Neta, 2018. "Developing an Optimal Class of Generic Sixteenth-Order Simple-Root Finders and Investigating Their Dynamics," Mathematics, MDPI, vol. 7(1), pages 1-32, December.
    5. Deepak Kumar & Janak Raj Sharma & Clemente Cesarano, 2019. "One-Point Optimal Family of Multiple Root Solvers of Second-Order," Mathematics, MDPI, vol. 7(7), pages 1-11, July.
    6. Ramandeep Behl & Eulalia Martínez & Fabricio Cevallos & Diego Alarcón, 2019. "A Higher Order Chebyshev-Halley-Type Family of Iterative Methods for Multiple Roots," Mathematics, MDPI, vol. 7(4), pages 1-12, April.
    7. G Thangkhenpau & Sunil Panday & Shubham Kumar Mittal & Lorentz Jäntschi, 2023. "Novel Parametric Families of with and without Memory Iterative Methods for Multiple Roots of Nonlinear Equations," Mathematics, MDPI, vol. 11(9), pages 1-18, April.
    8. 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.
    9. Janak Raj Sharma & Sunil Kumar & Lorentz Jäntschi, 2020. "On Derivative Free Multiple-Root Finders with Optimal Fourth Order Convergence," Mathematics, MDPI, vol. 8(7), pages 1-15, July.
    10. 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.
    11. Himani Arora & Alicia Cordero & Juan R. Torregrosa & Ramandeep Behl & Sattam Alharbi, 2022. "Derivative-Free Iterative Schemes for Multiple Roots of Nonlinear Functions," Mathematics, MDPI, vol. 10(9), pages 1-13, May.
    12. Sharma, Janak Raj & Kumar, Sunil, 2021. "An excellent numerical technique for multiple roots," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 316-324.
    13. Alicia Cordero & Beny Neta & Juan R. Torregrosa, 2021. "Memorizing Schröder’s Method as an Efficient Strategy for Estimating Roots of Unknown Multiplicity," Mathematics, MDPI, vol. 9(20), pages 1-13, October.
    14. 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.
    15. Deepak Kumar & Janak Raj Sharma & Ioannis K. Argyros, 2020. "Optimal One-Point Iterative Function Free from Derivatives for Multiple Roots," Mathematics, MDPI, vol. 8(5), pages 1-14, May.
    16. Vázquez-Lozano, J. Enrique & Cordero, Alicia & Torregrosa, Juan R., 2018. "Dynamical analysis on cubic polynomials of Damped Traub’s method for approximating multiple roots," Applied Mathematics and Computation, Elsevier, vol. 328(C), pages 82-99.
    17. Munish Kansal & Ali Saleh Alshomrani & Sonia Bhalla & Ramandeep Behl & Mehdi Salimi, 2020. "One Parameter Optimal Derivative-Free Family to Find the Multiple Roots of Algebraic Nonlinear Equations," Mathematics, MDPI, vol. 8(12), pages 1-15, December.

    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:7:y:2019:i:8:p:672-:d:252320. 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.