scholarly journals A fourth-order nonlinear iterative method in Banach spaces

1993 ◽  
Vol 6 (4) ◽  
pp. 97-98 ◽  
Author(s):  
Dong Chen ◽  
I.K. Argyros
Keyword(s):  
Iterative Method ◽  
Banach Spaces ◽  
Fourth Order ◽  
Nonlinear Iterative Method

scholarly journals Two solutions to Kirchhoff-type fourth-order implusive elastic beam equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Jian Liu ◽  
Wenguang Yu
Keyword(s):  
Iterative Method ◽  
Variational Methods ◽  
Critical Point ◽  
Fourth Order ◽  
Elastic Beam ◽  
Kirchhoff Type ◽  
Newton Iterative Method ◽  
Beam Equations ◽  
Critical Point Theorems ◽  
Elastic Beam Equations

AbstractIn this paper, the existence of two solutions for superlinear fourth-order impulsive elastic beam equations is obtained. We get two theorems via variational methods and corresponding two-critical-point theorems. Combining with the Newton-iterative method, an example is presented to illustrate the value of the obtained theorems.

An Accelerated Iterative Method with Third-Order Convergence

2012 ◽  
Vol 220-223 ◽  
pp. 2658-2661
Author(s):  
Zhong Yong Hu ◽  
Liang Fang ◽  
Lian Zhong Li
Keyword(s):  
Iterative Method ◽  
Fourth Order ◽  
Newton’S Method ◽  
Newton's Method ◽  
New Method ◽  
Order Convergence ◽  
Third Order ◽  
Numerical Examples ◽  
Modified Newton’S Method ◽  
Jarratt Method

We present a new modified Newton's method with third-order convergence and compare it with the Jarratt method, which is of fourth-order. Based on this new method, we obtain a family of Newton-type methods, which converge cubically. Numerical examples show that the presented method can compete with Newton's method and other known third-order modifications of Newton's method.

scholarly journals Ball convergence for a fourth order iterative method

2018 ◽  
Vol 1139 ◽  
pp. 012035
Author(s):  
Ioannis K Argyros ◽  
Ramandeep Behl
Keyword(s):  
Iterative Method ◽  
Fourth Order ◽  
Ball Convergence

scholarly journals A fourth order method for finding a simple root of univariate function

2015 ◽  
Vol 34 (2) ◽  
pp. 197-211
Author(s):  
D. Sbibih ◽  
Abdelhafid Serghini ◽  
A. Tijini ◽  
A. Zidna
Keyword(s):  
Iterative Method ◽  
Fourth Order ◽  
Newton’S Method ◽  
Simple Root ◽  
Newton's Method ◽  
Order Method ◽  
Numerical Examples ◽  
Quadratic Interpolation ◽  
Univariate Function ◽  
Fourth Order Method

In this paper, we describe an iterative method for approximating asimple zero $z$ of a real defined function. This method is aessentially based on the idea to extend Newton's method to be theinverse quadratic interpolation. We prove that for a sufficientlysmooth function $f$ in a neighborhood of $z$ the order of theconvergence is quartic. Using Mathematica with its high precisioncompatibility, we present some numerical examples to confirm thetheoretical results and to compare our method with the others givenin the literature.

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