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Title: On the local convergence of Kung-Traub's two-point method and its dynamics (English)
Author: Ataei Delshad, Parandoosh
Author: Lotfi, Taher
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940 (print)
ISSN: 1572-9109 (online)
Volume: 65
Issue: 4
Year: 2020
Pages: 379-406
Summary lang: English
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Category: math
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Summary: In this paper, the local convergence analysis of the family of Kung-Traub's two-point method and the convergence ball for this family are obtained and the dynamical behavior on quadratic and cubic polynomials of the resulting family is studied. We use complex dynamic tools to analyze their stability and show that the region of stable members of this family is vast. Numerical examples are also presented in this study. This method is compared with several widely used solution methods by solving test problems from different chemical engineering application areas, e.g. Planck's radiation law problem, natch distillation at infinite reflux, van der Waal's equation, air gap between two parallel plates and flow in a smooth pipe, in order to check the applicability and effectiveness of our proposed methods. (English)
Keyword: local convergence
Keyword: Kung-Traub's method
Keyword: complex dynamics
Keyword: parameter space
Keyword: basins of attraction
Keyword: stability
MSC: 37Fxx
MSC: 37P40
MSC: 65F10
MSC: 65H04
idZBL: 07250668
idMR: MR4134140
DOI: 10.21136/AM.2020.0322-18
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Date available: 2020-09-07T09:45:14Z
Last updated: 2020-11-18
Stable URL: http://hdl.handle.net/10338.dmlcz/148339
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