scholarly journals A Rational Iteration Function for Solving Equations

1966 ◽  
Vol 9 (3) ◽  
pp. 304-307 ◽  
Author(s):  
P. Jarratt
Keyword(s):  
Solving Equations ◽  
Iteration Function

scholarly journals A New Family of High-Order Ehrlich-Type Iterative Methods

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1855 ◽  
Author(s):  
Petko D. Proinov ◽  
Maria T. Vasileva
Keyword(s):  
Iterative Methods ◽  
Local Convergence ◽  
Semilocal Convergence ◽  
High Order ◽  
Convergence Theorems ◽  
New Family ◽  
Special Cases ◽  
Iteration Functions ◽  
Iteration Function ◽  
Local Convergence Analysis

One of the famous third-order iterative methods for finding simultaneously all the zeros of a polynomial was introduced by Ehrlich in 1967. In this paper, we construct a new family of high-order iterative methods as a combination of Ehrlich’s iteration function and an arbitrary iteration function. We call these methods Ehrlich’s methods with correction. The paper provides a detailed local convergence analysis of presented iterative methods for a large class of iteration functions. As a consequence, we obtain two types of local convergence theorems as well as semilocal convergence theorems (with computer verifiable initial condition). As special cases of the main results, we study the convergence of several particular iterative methods. The paper ends with some experiments that show the applicability of our semilocal convergence theorems.

Semi-local convergence of a Newton-like method for solving equations with a singular derivative

2018 ◽  
Vol 27 (1) ◽  
pp. 01-08
Author(s):  
IOANNIS K. ARGYROS ◽  
◽  
GEORGE SANTHOSH ◽  
Keyword(s):  
Banach Space ◽  
Convergence Analysis ◽  
Real Line ◽  
Local Convergence ◽  
Approximate Solutions ◽  
Convergence Domain ◽  
Solving Equations ◽  
Solutions Of Equations ◽  
Local Convergence Analysis ◽  
Special Case

We present a semi-local convergence analysis for a Newton-like method to approximate solutions of equations when the derivative is not necessarily non-singular in a Banach space setting. In the special case when the equation is defined on the real line the convergence domain is improved for this method when compared to earlier results. Numerical results where earlier results cannot apply but the new results can apply to solve nonlinear equations are also presented in this study.

Solving Equations on Words with Morphisms and Antimorphisms

2014 ◽  
pp. 186-197 ◽  
Author(s):  
Alexandre Blondin Massé ◽  
Sébastien Gaboury ◽  
Sylvain Hallé ◽  
Michaël Larouche
Keyword(s):  
Solving Equations

Investigation of Sinkage and Trim by Ships in Shallow Water Based on Overset Grid

2015 ◽  
Vol 713-715 ◽  
pp. 2126-2132
Author(s):  
Da Ming Sun ◽  
Ji Yong Liu ◽  
Qing Wen Kong
Keyword(s):  
Shallow Water ◽  
Equations Of Motion ◽  
Navier Stokes ◽  
Overset Grid ◽  
Ship Hulls ◽  
Surface Ship ◽  
Solving Equations ◽  
Sinkage And Trim ◽  
Volume Method ◽  
Good Agreement

A study on the navigation behavior for ships in shallow water had been carried out on CFD. The problem of surface ship hulls free of sinkage and trim in shallow water is analyzed numerically by simultaneously solving equations of the Reynolds averaged Navier-Stokes (RANS). The computations, based on the single-phase level set and overset grid, are discretized by finite volume method (FVM). An earth-based reference system is used for the solution to the fluid flow, while a ship-based reference is used to compute the rigid-body equations of motion. A S60 CB=0.6 ship model is taken as an example to the numerical simulation. Numerical results of the sinkage and trim of the seven Froude Numbers (Fn=0.5~0.8) are compared against experimental data, which have a good agreement.

Solving Equations with Waves in Collections of Mach-Zehnder Interferometers

2018 ◽  
Author(s):  
Mario Junior Mencagli ◽  
Nasim Mohammadi Estakhri ◽  
Brian Edwards ◽  
Nader Engheta
Keyword(s):  
Solving Equations
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