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The Optimal Order Newton’s Like Methods with Dynamics

Author

Listed:
  • Manoj Kumar Singh

    (Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi 221005, India)

  • Arvind K. Singh

    (Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi 221005, India)

Abstract

In this paper, we have obtained three optimal order Newton’s like methods of order four, eight, and sixteen for solving nonlinear algebraic equations. The convergence analysis of all the optimal order methods is discussed separately. We have discussed the corresponding conjugacy maps for quadratic polynomials and also obtained the extraneous fixed points. We have considered several test functions to examine the convergence order and to explain the dynamics of our proposed methods. Theoretical results, numerical results, and fractal patterns are in support of the efficiency of the optimal order methods.

Suggested Citation

  • Manoj Kumar Singh & Arvind K. Singh, 2021. "The Optimal Order Newton’s Like Methods with Dynamics," Mathematics, MDPI, vol. 9(5), pages 1-24, March.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:5:p:527-:d:509525
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    Citations

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    Cited by:

    1. Manoj K. Singh & Ioannis K. Argyros, 2022. "The Dynamics of a Continuous Newton-like Method," Mathematics, MDPI, vol. 10(19), pages 1-14, October.
    2. Arseny A. Sorokin & Gerd Leuchs & Joel F. Corney & Nikolay A. Kalinin & Elena A. Anashkina & Alexey V. Andrianov, 2022. "Towards Quantum Noise Squeezing for 2-Micron Light with Tellurite and Chalcogenide Fibers with Large Kerr Nonlinearity," Mathematics, MDPI, vol. 10(19), pages 1-11, September.

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