scholarly journals New Iterative Method with Application

2021 ◽  
Vol 20 ◽  
pp. 424-430
Author(s):  
O. Ababneh ◽  
N. Zomot
Keyword(s):  
Nonlinear Equation ◽  
Iterative Method ◽  
Iterative Methods ◽  
Simple Root ◽  
Open Interval ◽  
Scalar Function ◽  
New Iterative Method

In this paper, we consider iterative methods to find a simple root of a nonlinear equation f(x) = 0, where f : D∈R→R for an open interval D is a scalar function.

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.

scholarly journals New Iterative Manner Involving Sunny Nonexpansive Retractions for Pseudocontractive Mappings

2012 ◽  
Vol 2012 ◽  
pp. 1-9
Author(s):  
Yaqin Zheng ◽  
Jinwei Shi
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Iterative Method ◽  
Banach Spaces ◽  
Iterative Methods ◽  
Pseudocontractive Mapping ◽  
Suggested Algorithm ◽  
Pseudocontractive Mappings ◽  
New Iterative Method

Iterative methods for pseudocontractions have been studied by many authors in the literature. In the present paper, we firstly propose a new iterative method involving sunny nonexpansive retractions for pseudocontractions in Banach spaces. Consequently, we show that the suggested algorithm converges strongly to a fixed point of the pseudocontractive mapping which also solves some variational inequality.

scholarly journals Modifikasi Metode Householder Tiga Parameter yang Bebas Turunan Kedua dengan Orde Konvergensi Optimal

2021 ◽  
Vol 18 (1) ◽  
pp. 62-74
Author(s):  
Wartono ◽  
M Zulianti ◽  
Rahmawati
Keyword(s):  
Numerical Simulation ◽  
Iterative Method ◽  
Iterative Methods ◽  
Efficiency Index ◽  
New Method ◽  
Third Order ◽  
The Third ◽  
New Iterative Method ◽  
Better Than ◽  
Taylor’S Series

The Householder’s method is one of the iterative methods with a third-order convergence that used to solve a nonlinear equation. In this paper, the authors modified the iterative method using the expansion of second order Taylor’s series and approximated its second derivative using equality of two the third-order iterative methods. Based on the results of the study, it was found that the new iterative method has a fourth-order of convergence and requires three evaluations of function with an efficiency index of 1,587401. Numerical simulation is given by using several functions to compare the performance between the new method with other iterative methods. The results of numerical simulation show that the performance of the new method is better than other iterative methods.

scholarly journals A new iterative method for computing the Drazin inverse

Filomat ◽  
2012 ◽  
Vol 26 (3) ◽  
pp. 597-606 ◽  
Author(s):  
Jin Zhong ◽  
Xiaoji Liu ◽  
Guangping Zhou ◽  
Yaoming Yu
Keyword(s):  
Iterative Method ◽  
Iterative Methods ◽  
Error Bounds ◽  
Drazin Inverse ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient ◽  
New Iterative Method

In this paper, we construct a new iterative method for computing the Drazin inverse and deduce the necessary and sufficient condition for its convergence to Ad. Moreover, we present the error bounds of the iterative methods for approximating Ad.

scholarly journals Aboodh Transform Iterative Method for Spatial Diffusion of a Biological Population with Fractional-Order

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 155
Author(s):  
Gbenga O. Ojo ◽  
Nazim I. Mahmudov
Keyword(s):  
Iterative Method ◽  
Fractional Order ◽  
Population Model ◽  
Numerical Solutions ◽  
Computational Effort ◽  
Spatial Diffusion ◽  
Transform Method ◽  
Biological Population ◽  
The Laplace Transform ◽  
New Iterative Method

In this paper, a new approximate analytical method is proposed for solving the fractional biological population model, the fractional derivative is described in the Caputo sense. This method is based upon the Aboodh transform method and the new iterative method, the Aboodh transform is a modification of the Laplace transform. Illustrative cases are considered and the comparison between exact solutions and numerical solutions are considered for different values of alpha. Furthermore, the surface plots are provided in order to understand the effect of the fractional order. The advantage of this method is that it is efficient, precise, and easy to implement with less computational effort.

A new modified group explicit iterative method for the numerical solution of time dependent viscous Burgers' equation

2014 ◽  
Vol 05 (02) ◽  
pp. 1350029 ◽  
Author(s):  
Jyoti Talwar ◽  
R. K. Mohanty
Keyword(s):  
Iterative Method ◽  
Numerical Solution ◽  
Convergence Analysis ◽  
Iterative Methods ◽  
Iteration Method ◽  
Burgers Equation ◽  
Time Dependent ◽  
Alternating Group ◽  
Explicit Method ◽  
Rectangular Coordinates

In this article, we discuss a new smart alternating group explicit method based on off-step discretization for the solution of time dependent viscous Burgers' equation in rectangular coordinates. The convergence analysis for the new iteration method is discussed in details. We compared the results of Burgers' equation obtained by using the proposed iterative method with the results obtained by other iterative methods to demonstrate computationally the efficiency of the proposed method.

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