Iterative Methods for Solving Non-Linear Equations

1989 ◽  
pp. 351-387
Author(s):  
Aleksandr A. Samarskii ◽  
Evgenii S. Nikolaev
Keyword(s):  
Iterative Methods ◽  
Linear Equations ◽  
Non Linear ◽  
Non Linear Equations

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.

scholarly journals Some multistep higher order iterative methods for non-linear equations

2014 ◽  
Vol 9 (17) ◽  
pp. 752-757 ◽  
Author(s):  
Ahmad Mir Nazir ◽  
Rafiq Naila
Keyword(s):  
Iterative Methods ◽  
Linear Equations ◽  
Higher Order ◽  
Non Linear ◽  
Non Linear Equations

scholarly journals Rootfinding : An Iterative Tool to Solve Different Problems

2015 ◽  
Vol 5 ◽  
pp. 121-125
Author(s):  
Iswarmani Adhikari
Keyword(s):  
Numerical Analysis ◽  
Iterative Methods ◽  
Linear Equations ◽  
Secant Method ◽  
Root Finding ◽  
Non Linear ◽  
Iteration Methods ◽  
False Position ◽  
The Common ◽  
Non Linear Equations

The aim of this paper is to apply the iteration methods for the solution of non-linear equations. Among the various root finding techniques, two of the common iterative methods Regula-falsi (false position) and the Secant method are used in two different problems to show the applications of numerical analysis in different fields. The Himalayan Physics Vol. 5, No. 5, Nov. 2014 Page: 121-125

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.

A note on some quadrature based three-step iterative methods for non-linear equations

2009 ◽  
Vol 215 (1) ◽  
pp. 53-57 ◽  
Author(s):  
Heng-fei Ding ◽  
Yu-xin Zhang ◽  
San-fu Wang ◽  
Xiao-ya Yang
Keyword(s):  
Iterative Methods ◽  
Linear Equations ◽  
Non Linear ◽  
Non Linear Equations

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)

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