Geodesic
On the local convergence of Kung-Traub's two-point method and its dynamics
Applications of Mathematics, Tome 65 (2020) no. 4, pp. 379-406.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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.
DOI : 10.21136/AM.2020.0322-18
Classification : 37Fxx, 37P40, 65F10, 65H04
Keywords: local convergence; Kung-Traub's method; complex dynamics; parameter space; basins of attraction; stability 
@article{10_21136_AM_2020_0322_18,
     author = {Ataei Delshad, Parandoosh and Lotfi, Taher},
     title = {On the local convergence of {Kung-Traub's} two-point method and its dynamics},
     journal = {Applications of Mathematics},
     pages = {379--406},
     publisher = {mathdoc},
     volume = {65},
     number = {4},
     year = {2020},
     doi = {10.21136/AM.2020.0322-18},
     mrnumber = {4134140},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.2020.0322-18/}
}
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
SP  - 379
EP  - 406
VL  - 65
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.2020.0322-18/
DO  - 10.21136/AM.2020.0322-18
LA  - en
ID  - 10_21136_AM_2020_0322_18
ER  - 
%0 Journal Article
%A Ataei Delshad, Parandoosh
%A Lotfi, Taher
%T On the local convergence of Kung-Traub's two-point method and its dynamics
%J Applications of Mathematics
%D 2020
%P 379-406
%V 65
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.2020.0322-18/
%R 10.21136/AM.2020.0322-18
%G en
%F 10_21136_AM_2020_0322_18
Ataei Delshad, Parandoosh; Lotfi, Taher. On the local convergence of Kung-Traub's two-point method and its dynamics. Applications of Mathematics, Tome 65 (2020) no. 4, pp. 379-406. doi : 10.21136/AM.2020.0322-18. http://geodesic.mathdoc.fr/articles/10.21136/AM.2020.0322-18/

Cité par Sources :