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A New Optimal Family of Schröder’s Method for Multiple Zeros

Author

Listed:
  • Ramandeep Behl

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

  • Arwa Jeza Alsolami

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

  • Bruno Antonio Pansera

    (Department of Law, Economics and Human Sciences & Decisions Lab, University Mediterranea of Reggio Calabria, 89125 Reggio Calabria, Italy)

  • Waleed M. Al-Hamdan

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

  • Mehdi Salimi

    (Department of Law, Economics and Human Sciences & Decisions Lab, University Mediterranea of Reggio Calabria, 89125 Reggio Calabria, Italy
    Center for Dynamics and Institute for Analysis, Department of Mathematics, Technische Universität Dresden, 01062 Dresden, Germany)

  • Massimiliano Ferrara

    (Department of Law, Economics and Human Sciences & Decisions Lab, University Mediterranea of Reggio Calabria, 89125 Reggio Calabria, Italy
    ICRIOS—The Invernizzi Centre for Research on Innovation, Organization, Strategy and Entrepreneurship, Department of Management and Technology, Bocconi University, Via Sarfatti, 25, 20136 Milano, Italy)

Abstract

Here, we suggest a high-order optimal variant/modification of Schröder’s method for obtaining the multiple zeros of nonlinear uni-variate functions. Based on quadratically convergent Schröder’s method, we derive the new family of fourth -order multi-point methods having optimal convergence order. Additionally, we discuss the theoretical convergence order and the properties of the new scheme. The main finding of the present work is that one can develop several new and some classical existing methods by adjusting one of the parameters. Numerical results are given to illustrate the execution of our multi-point methods. We observed that our schemes are equally competent to other existing methods.

Suggested Citation

  • Ramandeep Behl & Arwa Jeza Alsolami & Bruno Antonio Pansera & Waleed M. Al-Hamdan & Mehdi Salimi & Massimiliano Ferrara, 2019. "A New Optimal Family of Schröder’s Method for Multiple Zeros," Mathematics, MDPI, vol. 7(11), pages 1-14, November.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:11:p:1076-:d:284959
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    References listed on IDEAS

    as
    1. Sharifi, Somayeh & Salimi, Mehdi & Siegmund, Stefan & Lotfi, Taher, 2016. "A new class of optimal four-point methods with convergence order 16 for solving nonlinear equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 119(C), pages 69-90.
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