scholarly journals Interval and Speed of Convergence on Iterative Methods

2017 ◽  
pp. 112-114
Author(s):  
Iswarmani Adhikari
Keyword(s):  
Iterative Method ◽  
Iterative Methods ◽  
Linear Equations ◽  
Initial Guess ◽  
Similar Process ◽  
Speed Of Convergence ◽  
Non Linear ◽  
Non Linear Equations

The iterative method is a tool of solving the non-linear equations to get their approximate roots with some errors of tolerance. Repetition of the similar process is applied successively on such iterations to compute a sequence of increasingly accurate estimates of the roots. In this paper, the construction of an iterative method for solving an equation, its convergence and the determination of interval of convergence for the approximate choice of initial guess and the speed of convergence are highlighted.The Himalayan Physics Vol. 6 & 7, April 2017 (112-114)

scholarly journals On Efficient Iterative Numerical Methods for Simultaneous Determination of all Roots of Non-Linear Function

2020 ◽  
Author(s):  
Mudassir Shams ◽  
Nazir Mir ◽  
Naila Rafiq
Keyword(s):  
Simultaneous Determination ◽  
Iterative Methods ◽  
Linear Equations ◽  
Basin Of Attraction ◽  
Numerical Test ◽  
Computational Cost ◽  
Single Root ◽  
Non Linear ◽  
Non Linear Equations

We construct a family of two-step optimal fourth order iterative methods for finding single root of non-linear equations. We generalize these methods to simultaneous iterative methods for determining all the distinct as well as multiple roots of single variable non-linear equations. Convergence analysis is present for both cases to show that the order of convergence is four in case of single root finding method and is twelve for simultaneous determination of all roots of non-linear equation. The computational cost, Basin of attraction, efficiency, log of residual and numerical test examples shows, the newly constructed methods are more efficient as compared to the existing methods in literature.

scholarly journals Five-point thirty-two optimal order iterative method for solving non-linear equations

2021 ◽  
Vol 25 (Spec. issue 2) ◽  
pp. 401-409
Author(s):  
Malik Ullah ◽  
Fayyaz Ahmad
Keyword(s):  
Iterative Method ◽  
Linear Equations ◽  
Initial Guess ◽  
Convergence Order ◽  
Optimal Order ◽  
Order Convergence ◽  
Derivative Free ◽  
Non Linear ◽  
High Order Convergence ◽  
Non Linear Equations

A five-point thirty-two convergence order derivative-free iterative method to find simple roots of non-linear equations is constructed. Six function evaluations are performed to achieve optimal convergence order 26-1 = 32 conjectured by Kung and Traub [1]. Secant approximation to the derivative is computed around the initial guess. High order convergence is attained by constructing polynomials of quotients for functional values.

Comparative Study of Iterative Methods for Solving Non-Linear Equations

2021 ◽  
Vol 23 (07) ◽  
pp. 858-866
Author(s):  
Gauri Thakur ◽  
◽  
J.K. Saini ◽  
Keyword(s):  
Numerical Analysis ◽  
Iterative Methods ◽  
Linear Equations ◽  
Bisection Method ◽  
Practical Applications ◽  
Non Linear ◽  
False Position ◽  
Newton Raphson ◽  
Raphson Method ◽  
Non Linear Equations

In numerical analysis, methods for finding roots play a pivotal role in the field of many real and practical applications. The efficiency of numerical methods depends upon the convergence rate (how fast the particular method converges). The objective of this study is to compare the Bisection method, Newton-Raphson method, and False Position Method with their limitations and also analyze them to know which of them is more preferred. Limitations of these methods have allowed presenting the latest research in the area of iterative processes for solving non-linear equations. This paper analyzes the field of iterative methods which are developed in recent years with their future scope.

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