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Some High-Order Convergent Iterative Procedures for Nonlinear Systems with Local Convergence

Author

Listed:
  • Ramandeep Behl

    (Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
    These authors contributed equally to this work.)

  • Ioannis K. Argyros

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

  • Fouad Othman Mallawi

    (Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia)

Abstract

In this study, we suggested the local convergence of three iterative schemes that works for systems of nonlinear equations. In earlier results, such as from Amiri et al. (see also the works by Behl et al., Argryos et al., Chicharro et al., Cordero et al., Geum et al., Guitiérrez, Sharma, Weerakoon and Fernando, Awadeh), authors have used hypotheses on high order derivatives not appearing on these iterative procedures. Therefore, these methods have a restricted area of applicability. The main difference of our study to earlier studies is that we adopt only the first order derivative in the convergence order (which only appears on the proposed iterative procedure). No work has been proposed on computable error distances and uniqueness in the aforementioned studies given on R k . We also address these problems too. Moreover, by using Banach space, the applicability of iterative procedures is extended even further. We have examined the convergence criteria on several real life problems along with a counter problem that completes this study.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:12:p:1375-:d:574613
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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. Behl, Ramandeep & Cordero, Alicia & Motsa, Sandile S. & Torregrosa, Juan R., 2017. "Stable high-order iterative methods for solving nonlinear models," Applied Mathematics and Computation, Elsevier, vol. 303(C), pages 70-88.
    3. 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.
    4. 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.
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