Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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A NEW OPTIMAL EIGHTH-ORDER FAMILY OF MULTIPLE ROOT FINDERS

  • Cebic, Dejan (Department of Applied Mathematics and Informatics Faculty of Mining and Geology University of Belgrade) ;
  • Ralevic, Nebojsa M. (Department of Mathematics Faculty of Techincal Sciences University of Novi Sad)
  • Received : 2021.10.01
  • Accepted : 2022.09.14
  • Published : 2022.11.01
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Abstract

This paper presents a new optimal three-step eighth-order family of iterative methods for finding multiple roots of nonlinear equations. Different from the all existing optimal methods of the eighth-order, the new iterative scheme is constructed using one function and three derivative evaluations per iteration, preserving the efficiency and optimality in the sense of Kung-Traub's conjecture. Theoretical results are verified through several standard numerical test examples. The basins of attraction for several polynomials are also given to illustrate the dynamical behaviour and the obtained results show better stability compared to the recently developed optimal methods.

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References

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