Period-doubling bifurcations in the family of Chebyshev-Halley-type methods

被引：5

作者：

Cordero, Alicia ^{[1
]}

Torregrosa, Juan R. ^{[1
]}

Vindel, P. ^{[2
]}

机构：

[1] Univ Politecn Valencia, Inst Matemat Multidisciplinar, E-46071 Valencia, Spain

[2] Univ Jaume 1, Inst Matemat & Aplicac Castellon, Castellon de La Plana, Spain

来源：

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS | 2013年 / 90卷 / 10期

关键词：

numerical methods; Chebyshev-Halley methods; bifurcations; dynamics of numerical method; period-doubling bifurcation; 37F10; 37G15; ITERATIVE METHODS; DYNAMICS;

D O I：

10.1080/00207160.2012.745518

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The choice of a member of a parametric family of iterative methods is not always easy. The family of Chebyshev-Halley schemes is a good example of it. The analysis of bifurcation points of this family allows us to define a real interval in which there exist several problematic behaviours: attracting points that become doubled, other ones that become periodic orbits, etc. These aspects should be avoided in an iterative procedure, so it is important to determine the regions where this conduct takes place. In this paper, we obtain that this family admits attractive 2-cycles in two different intervals, for real values of the parameter.

引用

页码：2061 / 2071

页数：11

共 38 条

[31] An optimized Chebyshev-Halley type family of multiple solvers: Extensive analysis and applications [J].

Rani, Litika ;

Soleymani, Fazlollah ;

Kansal, Munish ;

Nashine, Hemant Kumar .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2025, 48 (07) :7037-7055

[32] Cascade of spatio-temporal period-doubling bifurcations in connection with the appearance and dynamics of non-concentric multiple double layers in plasma [J].

Dimitriu, D. G. ;

Ivan, L. M. .

PLASMA 2007, 2008, 993 :93-96

[33] A study on the local convergence and the dynamics of Chebyshev–Halley–type methods free from second derivative [J].

Ioannis K. Argyros ;

Á. Alberto Magreñán .

Numerical Algorithms, 2016, 71 :1-23

[34] A stable class of improved second-derivative free Chebyshev-Halley type methods with optimal eighth order convergence [J].

Cordero, Alicia ;

Kansal, Munish ;

Kanwar, Vinay ;

Torregrosa, Juan R. .

NUMERICAL ALGORITHMS, 2016, 72 (04) :937-958

[35] Highly efficient classes of Chebyshev-Halley type methods free from second-order derivative [J].

Behl, Ramandeep ;

Kanwar, V. .

2014 RECENT ADVANCES IN ENGINEERING AND COMPUTATIONAL SCIENCES (RAECS), 2014,

[36] New two-parameter Chebyshev-Halley-like family of fourth and sixth-order methods for systems of nonlinear equations [J].

Narang, Mona ;

Bhatia, Saurabh ;

Kanwar, V. .

APPLIED MATHEMATICS AND COMPUTATION, 2016, 275 :394-403

[37] Higher-order derivative-free families of Chebyshev-Halley type methods with or without memory for solving nonlinear equations [J].

Argyros, Ioannis K. ;

Kansal, Munish ;

Kanwar, Vinay ;

Bajaj, Sugandha .

APPLIED MATHEMATICS AND COMPUTATION, 2017, 315 :224-245

[38] On a two-parameter Chebyshev-Halley-like family of optimal two-point fourth order methods free from second derivatives [J].

Babajee D.K.R. .

Afrika Matematika, 2015, 26 (5-6) :689-697

← 1 2 3 4 →