Ball convergence of a sixth-order Newton-like method based on means under weak conditions

2018 ◽  
Vol 56 (7) ◽  
pp. 2117-2131 ◽  
Author(s):  
Á. A. Magreñán ◽  
I. K. Argyros ◽  
J. J. Rainer ◽  
J. A. Sicilia
Keyword(s):  
Sixth Order ◽  
Ball Convergence

scholarly journals Ball convergence for a sixth-order multi-point method in Banach spaces under weak conditions

2020 ◽  
Vol 47 (1) ◽  
pp. 133-144
Author(s):  
Ioannis K. Argyros ◽  
Santhosh George
Keyword(s):  
Banach Spaces ◽  
Point Method ◽  
Sixth Order ◽  
Ball Convergence

An Efficient Sixth-Order Convergent Newton-Type Iterative Method for Nonlinear Equations

2012 ◽  
Vol 220-223 ◽  
pp. 2585-2588
Author(s):  
Zhong Yong Hu ◽  
Fang Liang ◽  
Lian Zhong Li ◽  
Rui Chen
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations ◽  
Newton’S Method ◽  
Newton's Method ◽  
Efficiency Index ◽  
Sixth Order ◽  
Type Method ◽  
Second Derivatives ◽  
Better Than

In this paper, we present a modified sixth order convergent Newton-type method for solving nonlinear equations. It is free from second derivatives, and requires three evaluations of the functions and two evaluations of derivatives per iteration. Hence the efficiency index of the presented method is 1.43097 which is better than that of classical Newton’s method 1.41421. Several results are given to illustrate the advantage and efficiency the algorithm.

A modified Chebyshev’s iterative method with at least sixth order of convergence

2008 ◽  
Vol 206 (1) ◽  
pp. 164-174 ◽  
Author(s):  
S. Amat ◽  
M.A. Hernández ◽  
N. Romero
Keyword(s):  
Iterative Method ◽  
Order Of Convergence ◽  
Sixth Order

scholarly journals Weak Solutions for a Sixth Order Cahn-Hilliard Type Equation with Degenerate Mobility

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Aibo Liu ◽  
Changchun Liu
Keyword(s):  
Existence Result ◽  
Type Equation ◽  
Initial Boundary ◽  
Sixth Order ◽  
Surfactant Mixtures ◽  
Initial Boundary Problem ◽  
Degenerate Mobility ◽  
Oil Water ◽  
Three Space ◽  
Diffusional Mobility

We study an initial-boundary problem for a sixth order Cahn-Hilliard type equation, which arises in oil-water-surfactant mixtures. An existence result for the problem with a concentration dependent diffusional mobility in three space dimensions is presented.

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