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

DOI10.1080/00207160.2012.745518zbMath1291.37090OpenAlexW2030648424MaRDI QIDQ5416451

Alicia Cordero, Pura Vindel, Juan Ramón Torregrosa Sánchez

Publication date: 20 May 2014

Published in: International Journal of Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00207160.2012.745518

zbMATH Keywords

numerical methodsbifurcationsperiod-doubling bifurcationChebyshev-Halley methodsdynamics of numerical method

Mathematics Subject Classification ID

Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Computational methods for bifurcation problems in dynamical systems (37M20)

Related Items (6)

Dynamics of the family of c-iterative methods ⋮ Bulbs of period two in the family of Chebyshev-Halley iterative methods on quadratic polynomials ⋮ Convergence regions for the Chebyshev-Halley family ⋮ Connectivity of the Julia set for the Chebyshev-Halley family on degree \(n\) polynomials ⋮ Study of a biparametric family of iterative methods ⋮ Dynamics of a family of Chebyshev-Halley type methods

Cites Work

• Graphic and numerical comparison between iterative methods
• A construction of attracting periodic orbits for some classical third-order iterative methods
• Dynamics of a new family of iterative processes for quadratic polynomials
• Dynamics of a higher-order family of iterative methods
• Attracting cycles for the relaxed Newton's method
• On the dynamics of the Euler iterative function
• The Mandelbrot Set, the Farey Tree, and the Fibonacci Sequence
• Complex analytic dynamics on the Riemann sphere
• On the dynamics of a family of third-order iterative functions
• Julia sets for the super-Newton method, Cauchy’s method, and Halley’s method

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