A new sixth-order scheme for nonlinear equations

DOI10.1016/J.AML.2011.08.012zbMath1260.65048OpenAlexW2154639108MaRDI QIDQ659836

Changbum Chun, Beny Neta

Publication date: 24 January 2012

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2011.08.012

zbMATH Keywords

convergenceNewton's methoditerative methodsnonlinear equationsroot-finding methods

Mathematics Subject Classification ID

Numerical computation of solutions to single equations (65H05)

Related Items (13)

An analysis of a new family of eighth-order optimal methods ⋮ Improved Chebyshev-Halley methods with sixth and eighth order convergence ⋮ An efficient method based on progressive interpolation for solving non-linear equations ⋮ An optimal and efficient general eighth-order derivative free scheme for simple roots ⋮ Unification of sixth-order iterative methods ⋮ On improved three-step schemes with high efficiency index and their dynamics ⋮ Necessary and sufficient conditions for the convergence of two- and three-point Newton-type iterations ⋮ Basin attractors for various methods ⋮ A new optimal eighth-order family of iterative methods for the solution of nonlinear equations ⋮ A new family of optimal eighth order methods with dynamics for nonlinear equations ⋮ Comparing the geometry of the basins of attraction, the speed and the efficiency of several numerical methods ⋮ Efficient \(n\)-point iterative methods with memory for solving nonlinear equations ⋮ COMPARATIVE STUDY OF METHODS OF VARIOUS ORDERS FOR FINDING SIMPLE ROOTS OF NONLINEAR EQUATIONS

Cites Work

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• Regarding the accuracy of optimal eighth-order methods
• Sixth order derivative free family of iterative methods
• A new two-step biparametric family of sixth-order iterative methods free from second derivatives for solving nonlinear algebraic equations
• Several new methods for solving equations
• A sixth-order family of methods for nonlinear equations
• Optimal Order of One-Point and Multipoint Iteration
• A Family of Fourth Order Methods for Nonlinear Equations
• A variant of Newton's method with accelerated third-order convergence

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