A new iterative method for finding the multiple roots of nonlinear equations

2019 ◽  
Vol 30 (5-6) ◽  
pp. 747-753
Author(s):  
Reza Dehghan
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations ◽  
Multiple Roots ◽  
New Iterative Method

scholarly journals A New Iterative Numerical Continuation Technique for Approximating the Solutions of Scalar Nonlinear Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-21 ◽  
Author(s):  
Grégory Antoni
Keyword(s):  
Numerical Analysis ◽  
Iterative Method ◽  
Iterative Algorithm ◽  
Nonlinear Equations ◽  
Numerical Procedure ◽  
Approximate Solutions ◽  
Numerical Continuation ◽  
Stationary Type ◽  
Continuation Technique ◽  
New Iterative Method

The present study concerns the development of a new iterative method applied to a numerical continuation procedure for parameterized scalar nonlinear equations. Combining both a modified Newton’s technique and a stationary-type numerical procedure, the proposed method is able to provide suitable approximate solutions associated with scalar nonlinear equations. A numerical analysis of predictive capabilities of this new iterative algorithm is addressed, assessed, and discussed on some specific examples.

scholarly journals On a New Method for Computing the Numerical Solution of Systems of Nonlinear Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
H. Montazeri ◽  
F. Soleymani ◽  
S. Shateyi ◽  
S. S. Motsa
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations ◽  
Order Of Convergence ◽  
Efficiency Index ◽  
The Other ◽  
Systems Of Nonlinear Equations ◽  
System Of Nonlinear Equations ◽  
Numerical Tests ◽  
Programming Package ◽  
New Iterative Method

We consider a system of nonlinear equationsF(x)=0. A new iterative method for solving this problem numerically is suggested. The analytical discussions of the method are provided to reveal its sixth order of convergence. A discussion on the efficiency index of the contribution with comparison to the other iterative methods is also given. Finally, numerical tests illustrate the theoretical aspects using the programming package Mathematica.

Fifth-order iterative method for finding multiple roots of nonlinear equations

2010 ◽  
Vol 57 (3) ◽  
pp. 389-398 ◽  
Author(s):  
Xiaowu Li ◽  
Chunlai Mu ◽  
Jinwen Ma ◽  
Linke Hou
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations ◽  
Multiple Roots ◽  
Fifth Order

scholarly journals New Iterative Method for Solving Nonlinear Equations

2014 ◽  
Vol 11 (4) ◽  
pp. 1649-1654 ◽  
Author(s):  
Baghdad Science Journal
Keyword(s):  
Nonlinear Equation ◽  
Iterative Method ◽  
Convergence Analysis ◽  
Nonlinear Equations ◽  
Order Of Convergence ◽  
New Method ◽  
New Iterative Method

The aim of this paper is to propose an efficient three steps iterative method for finding the zeros of the nonlinear equation f(x)=0 . Starting with a suitably chosen , the method generates a sequence of iterates converging to the root. The convergence analysis is proved to establish its five order of convergence. Several examples are given to illustrate the efficiency of the proposed new method and its comparison with other methods.

A new iterative method to compute nonlinear equations

2006 ◽  
Vol 173 (1) ◽  
pp. 468-483 ◽  
Author(s):  
Mário Basto ◽  
Viriato Semiao ◽  
Francisco L. Calheiros
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations ◽  
New Iterative Method

scholarly journals New Iterative Method of Solving Nonlinear Equations in Fluid Mechanics

2021 ◽  
Vol 26 (3) ◽  
pp. 163-176
Author(s):  
M. Paliivets ◽  
E. Andreev ◽  
A. Bakshtanin ◽  
D. Benin ◽  
V. Snezhko
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Iterative Method ◽  
Fluid Mechanics ◽  
Nonlinear Equations ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Adomian Decomposition ◽  
Linear And Nonlinear ◽  
New Iterative Method

Abstract This paper presents the results of applying a new iterative method to linear and nonlinear fractional partial differential equations in fluid mechanics. A numerical analysis was performed to find an exact solution of the fractional wave equation and fractional Burgers’ equation, as well as an approximate solution of fractional KdV equation and fractional Boussinesq equation. Fractional derivatives of the order α are described using Caputo's definition with 0 < α ≤ 1 or 1 < α ≤ 2. A comparative analysis of the results obtained using a new iterative method with those obtained by the Adomian decomposition method showed the first method to be more efficient and simple, providing accurate results in fewer computational operations. Given its flexibility and ability to solve nonlinear equations, the iterative method can be used to solve more complex linear and nonlinear fractional partial differential equations.

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