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<p>Xiao and Yin in 2016 constructed a new iterative technique using extended Newton’s method. Their study proves the order of convergence to be five, using Taylors expansion and takes into account the fourth derivative of the involved operator. In this paper, the convergence analysis is not based on the conventional Taylor’s expansion and requires the operator to be just two times differentiable, making it applicable to a wider range of problems. Moreover, the theory is justified by numerical examples. Finally, the dynamics for the method are explored.</p>

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Enhancing the Practicality of Xiao and Yin’s Iterative Method

  • 期刊论文

  • 发表日期：

    2026年6月19日

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  • Ramya Sadananda,
  • Santhosh George,
  • Ajil Kunnarath,
  • P Jidesh,
  • Ioannis K. Argyros

摘要

Xiao and Yin in 2016 constructed a new iterative technique using extended Newton’s method. Their study proves the order of convergence to be five, using Taylors expansion and takes into account the fourth derivative of the involved operator. In this paper, the convergence analysis is not based on the conventional Taylor’s expansion and requires the operator to be just two times differentiable, making it applicable to a wider range of problems. Moreover, the theory is justified by numerical examples. Finally, the dynamics for the method are explored.