On the local convergence of Kung-Traub's two-point method and its dynamics

Parandoosh Ataei Delshad; Taher Lotfi

Applications of Mathematics (2020)

  • Volume: 65, Issue: 4, page 379-406
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Ataei Delshad, Parandoosh, and Lotfi, Taher. "On the local convergence of Kung-Traub's two-point method and its dynamics." Applications of Mathematics 65.4 (2020): 379-406. <http://eudml.org/doc/297302>.

@article{AtaeiDelshad2020,
abstract = {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.},
author = {Ataei Delshad, Parandoosh, Lotfi, Taher},
journal = {Applications of Mathematics},
keywords = {local convergence; Kung-Traub's method; complex dynamics; parameter space; basins of attraction; stability},
language = {eng},
number = {4},
pages = {379-406},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the local convergence of Kung-Traub's two-point method and its dynamics},
url = {http://eudml.org/doc/297302},
volume = {65},
year = {2020},
}

TY - JOUR
AU - Ataei Delshad, Parandoosh
AU - Lotfi, Taher
TI - On the local convergence of Kung-Traub's two-point method and its dynamics
JO - Applications of Mathematics
PY - 2020
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 65
IS - 4
SP - 379
EP - 406
AB - 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.
LA - eng
KW - local convergence; Kung-Traub's method; complex dynamics; parameter space; basins of attraction; stability
UR - http://eudml.org/doc/297302
ER -

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