A triparametric family of optimal fourth-order multiple-root finders and their dynamics

DOI10.1155/2016/8436759zbMath1418.65067OpenAlexW2320467171WikidataQ59123676 ScholiaQ59123676MaRDI QIDQ2314736

Publication date: 30 July 2019

Published in: Discrete Dynamics in Nature and Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2016/8436759

Mathematics Subject Classification ID

Numerical computation of solutions to single equations (65H05) Iteration theory, iterative and composite equations (39B12)

Related Items (2)

Stability analysis of a family of optimal fourth-order methods for multiple roots ⋮ Modified optimal class of Newton-like fourth-order methods for multiple roots

Uses Software

Mathematica

Cites Work

Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
On the convergence of an optimal fourth-order family of methods and its dynamics
On a numerical technique for finding multiple zeros and its dynamic
Basin attractors for various methods
Three-point methods with and without memory for solving nonlinear equations
On some modified families of multipoint iterative methods for multiple roots of nonlinear equations
Basins of attraction for several methods to find simple roots of nonlinear equations
One-point Newton-type iterative methods: a unified point of view
Basin of attraction of a cusp-fold singularity in 3D piecewise smooth vector fields
Constructing higher-order methods for obtaining the multiple roots of nonlinear equations
Modified Jarratt method for computing multiple roots
A new fourth-order iterative method for finding multiple roots of nonlinear equations
New optimal class of higher-order methods for multiple roots, permitting \(f'(x_{n})=0\)
Some fourth-order nonlinear solvers with closed formulae for multiple roots
Extraneous fixed points, basin boundaries and chaotic dynamics for Schröder and König rational iteration functions
On extraneous fixed-points of the basic family of iteration functions
On developing fourth-order optimal families of methods for multiple roots and their dynamics
Dynamics of the King and Jarratt iterations
Basins of attraction in forced systems with time-varying dissipation
Basins of attraction for several optimal fourth order methods for multiple roots
Real qualitative behavior of a fourth-order family of iterative methods by using the convergence plane
A new biparametric family of two-point optimal fourth-order multiple-root finders
Chaos in King's iterative family
A two-parameter family of fourth-order iterative methods with optimal convergence for multiple zeros
Complex dynamics of derivative-free methods for nonlinear equations
Convergence of the Newton process to multiple solutions
Optimal Order of One-Point and Multipoint Iteration

This page was built for publication: A triparametric family of optimal fourth-order multiple-root finders and their dynamics