On the approximation of mth power divided differences preserving the local order of convergence

2021 ◽  
Vol 410 ◽  
pp. 126415
Author(s):  
Abdolreza Amiri ◽  
Ioannis K. Argyros
Keyword(s):  
Order Of Convergence ◽  
Divided Differences ◽  
Local Order

scholarly journals Preliminary Orbit Determination of Artificial Satellites: A Vectorial Sixth-Order Approach

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Carlos Andreu ◽  
Noelia Cambil ◽  
Alicia Cordero ◽  
Juan R. Torregrosa
Keyword(s):  
Iterative Methods ◽  
Orbit Determination ◽  
Order Of Convergence ◽  
Classical Method ◽  
Numerical Approach ◽  
Original Method ◽  
Weight Functions ◽  
Artificial Satellites ◽  
Local Order ◽  
The Stability

A modified classical method for preliminary orbit determination is presented. In our proposal, the spread of the observations is considerably wider than in the original method, as well as the order of convergence of the iterative scheme involved. The numerical approach is made by using matricial weight functions, which will lead us to a class of iterative methods with a sixth local order of convergence. This is a process widely used in the design of iterative methods for solving nonlinear scalar equations, but rarely employed in vectorial cases. The numerical tests confirm the theoretical results, and the analysis of the dynamics of the problem shows the stability of the proposed schemes.

LOCAL ORDER IN THE EUTECTIC Mg.72 Zn.28 ALLOY

1985 ◽  
Vol 46 (C8) ◽  
pp. C8-81-C8-86 ◽  
Author(s):  
P. Andonov ◽  
P. Chieux
Keyword(s):  
Local Order

scholarly journals Fractional Newton–Raphson Method Accelerated with Aitken’s Method

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 47
Author(s):  
A. Torres-Hernandez ◽  
F. Brambila-Paz ◽  
U. Iturrarán-Viveros ◽  
R. Caballero-Cruz
Keyword(s):  
Fractional Derivative ◽  
Iterative Methods ◽  
Fractional Integral ◽  
Order Of Convergence ◽  
Fractional Operators ◽  
Speed Of Convergence ◽  
Newton Raphson ◽  
Raphson Method

In the following paper, we present a way to accelerate the speed of convergence of the fractional Newton–Raphson (F N–R) method, which seems to have an order of convergence at least linearly for the case in which the order α of the derivative is different from one. A simplified way of constructing the Riemann–Liouville (R–L) fractional operators, fractional integral and fractional derivative is presented along with examples of its application on different functions. Furthermore, an introduction to Aitken’s method is made and it is explained why it has the ability to accelerate the convergence of the iterative methods, in order to finally present the results that were obtained when implementing Aitken’s method in the F N–R method, where it is shown that F N–R with Aitken’s method converges faster than the simple F N–R.

scholarly journals Derivative-Free King’s Scheme for Multiple Zeros of Nonlinear Functions

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1242
Author(s):  
Ramandeep Behl ◽  
Sonia Bhalla ◽  
Eulalia Martínez ◽  
Majed Aali Alsulami
Keyword(s):  
Iterative Methods ◽  
Fourth Order ◽  
Order Of Convergence ◽  
Real Life ◽  
Multiple Roots ◽  
Computational Results ◽  
Nonlinear Functions ◽  
First Order ◽  
Life Problems ◽  
Derivative Free

There is no doubt that the fourth-order King’s family is one of the important ones among its counterparts. However, it has two major problems: the first one is the calculation of the first-order derivative; secondly, it has a linear order of convergence in the case of multiple roots. In order to improve these complications, we suggested a new King’s family of iterative methods. The main features of our scheme are the optimal convergence order, being free from derivatives, and working for multiple roots (m≥2). In addition, we proposed a main theorem that illustrated the fourth order of convergence. It also satisfied the optimal Kung–Traub conjecture of iterative methods without memory. We compared our scheme with the latest iterative methods of the same order of convergence on several real-life problems. In accordance with the computational results, we concluded that our method showed superior behavior compared to the existing methods.

Monitoring local order in the liquid-X interface

2021 ◽  
pp. e1875076
Author(s):  
Linsey Nowack ◽  
Stuart A. Rice
Keyword(s):  
Local Order ◽  
X Interface

Time and space meshes adaptivity for the resolution of a semi-linear heat equation

2021 ◽  
pp. 1-10
Author(s):  
Nejmeddine Chorfi
Keyword(s):  
Parabolic Equation ◽  
Heat Equation ◽  
Order Of Convergence ◽  
Linear Parabolic Equation ◽  
Spectral Elements ◽  
Euler Scheme ◽  
Time Step ◽  
Implicit Euler Scheme ◽  
Linear Heat ◽  
Error Indicators

The aim of this work is to highlight that the adaptivity of the time step when combined with the adaptivity of the spectral mesh is optimal for a semi-linear parabolic equation discretized by an implicit Euler scheme in time and spectral elements method in space. The numerical results confirm the optimality of the order of convergence. The later is similar to the order of the error indicators.

scholarly journals Interplay of local order and topology in the extended Haldane-Hubbard model

2021 ◽  
Vol 103 (3) ◽  
Author(s):  
Can Shao ◽  
Eduardo V. Castro ◽  
Shijie Hu ◽  
Rubem Mondaini
Keyword(s):  
Hubbard Model ◽  
Local Order ◽  
And Topology
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