Multi-Step Interval Iteration Methods for Nonlinear Equation

2020 ◽  
Vol 09 (08) ◽  
pp. 1124-1133
Author(s):  
雪 楚
Keyword(s):  
Nonlinear Equation ◽  
Interval Iteration ◽  
Step Interval ◽  
Iteration Methods

scholarly journals Iteration Methods with an Auxiliary Function for Nonlinear Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Faisal Ali ◽  
Waqas Aslam ◽  
Imran Khalid ◽  
Akbar Nadeem
Keyword(s):  
Nonlinear Equation ◽  
Iterative Methods ◽  
Nonlinear Equations ◽  
Auxiliary Function ◽  
New Family ◽  
Special Cases ◽  
Engineering Models ◽  
Iteration Methods ◽  
Scientific Engineering ◽  
Taylor’S Series

Various iterative methods have been introduced by involving Taylor’s series on the auxiliary function g x to solve the nonlinear equation f x = 0 . In this paper, we introduce the expansion of g x with the inclusion of weights w i such that ∑ i = 1 p w i = 1 and knots τ i ∈ 0,1 in order to develop a new family of iterative methods. The methods proposed in the present paper are applicable for different choices of auxiliary function g x , and some already known methods can be viewed as the special cases of these methods. We consider the diverse scientific/engineering models to demonstrate the efficiency of the proposed methods.

scholarly journals Further development on Traub’s method for solving system of nonlinear equations and ODE’s

2020 ◽  
Author(s):  
Kalyanasundaram Madhu ◽  
Mo'tassem Al-arydah
Keyword(s):  
Nonlinear Equation ◽  
Dynamical Behavior ◽  
Basins Of Attraction ◽  
System Of Nonlinear Equations ◽  
Functional Evaluation ◽  
Order Method ◽  
Eighth Order ◽  
Numerical Examples ◽  
First Derivative ◽  
Iteration Methods

Abstract The foremost objective of this work is to propose a eighth and sixteenth order scheme for handling a nonlinear equation. The eighth order method uses three evaluations of the function and one assessment of the first derivative and sixteenth order method uses four evaluations of the function and one appraisal of the first derivative. Kung-Traub conjecture is satisfied, theoretical analysis of the methods are presented and numerical examples are added to confirm the order of convergence. The performance and efficiency of our iteration methods are compared with the equivalent existing methods on some standard academic problems. We tested projectile motion problem, Planck’s radiation law problem as an application. The basins of attraction are also given to demonstrate their dynamical behavior in the complex plane. Further, we attempt to proposed a sixteenth order iterative method for solving system of nonlinear equation with four functional evaluation, namely two F and two F 0 and only one inverse of Jacobian. The theoretical proof of the method is given and numerical examples are included to confirm the convergence order of the presented methods. We apply the new scheme to find solution on 1-D bratu problem. The performance and efficiency of our iteration methods are compared.

Determination of Approximated Root of Nonlinear Equation by Interpolation Technique

2018 ◽  
Vol 50 (001) ◽  
pp. 133-136
Author(s):  
M. B. BROHI ◽  
A. A. SHAIKH ◽  
S. BHATTI ◽  
S. QUERSHI
Keyword(s):  
Nonlinear Equation ◽  
Interpolation Technique

A possible modification of groundwater flow equation using coordinate transformations

2014 ◽  
Vol 15 (2) ◽  
pp. 278-287 ◽  
Author(s):  
Abdon Atangana ◽  
Ernestine Alabaraoye
Keyword(s):  
Groundwater Flow ◽  
Prolate Spheroid ◽  
Flow Equation ◽  
Time Space ◽  
Adomian Decomposition ◽  
Iteration Methods ◽  
Groundwater Flow Equation ◽  
Factor Α ◽  
Modified Equation ◽  
Good Agreement

We described a groundwater model with prolate spheroid coordinates, and introduced a new parameter, namely τ the silhouette influence of the geometric under which the water flows. At first, we supposed that the silhouette influence approaches zero; under this assumption, the modified equation collapsed to the ordinary groundwater flow equation. We proposed an analytical solution to the standard version of groundwater as a function of time, space and uncertainty factor α. Our proposed solution was in good agreement with experimental data. We presented a good approximation to the exponential integral. We obtained an asymptotic special solution to the modified equation by means of the Adomian decomposition and variational iteration methods.

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