Dynamics of a fifth-order iterative method

DOI10.1080/00207160.2012.663081zbMath1335.37023OpenAlexW2102762937MaRDI QIDQ4903577

Natalia Romero, José Manuel Gutiérrez Jimenez, Sergio Plaza

Publication date: 22 January 2013

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

Full work available at URL: https://doi.org/10.1080/00207160.2012.663081

zbMATH Keywords

Julia setsnonlinear equationsorder of convergenceiterative processesgeneral convergence

Mathematics Subject Classification ID

Small divisors, rotation domains and linearization in holomorphic dynamics (37F50) Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) General theory of numerical methods in complex analysis (potential theory, etc.) (65E05) Simulation of dynamical systems (37M05) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10) Dynamical systems in numerical analysis (37N30)

Related Items (4)

King-type derivative-free iterative families: real and memory dynamics ⋮ Stability analysis of a parametric family of seventh-order iterative methods for solving nonlinear systems ⋮ Unnamed Item ⋮ Avoiding strange attractors in efficient parametric families of iterative methods for solving nonlinear problems

Cites Work

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• 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
• Dynamics in One Complex Variable. (AM-160)

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