Higher-order iterative methods by using Householder's method for solving certain nonlinear equations

2013 ◽  
Vol 2 (2) ◽  
pp. 107-120
Author(s):  
Waseem Asghar Khan ◽  
Muhammad Aslam Noor ◽  
Adnan Rauf
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Higher Order

A family of higher order multi-point iterative methods based on power mean for solving nonlinear equations

2015 ◽  
Vol 27 (5-6) ◽  
pp. 865-876 ◽  
Author(s):  
Diyashvir Kreetee Rajiv Babajee ◽  
Kalyanasundaram Madhu ◽  
Jayakumar Jayaraman
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Higher Order ◽  
Power Mean

Higher order multi-step interval iterative methods for solving nonlinear equations in $$R^n$$ R n

SeMA Journal ◽  
2016 ◽  
Vol 74 (2) ◽  
pp. 133-146
Author(s):  
Sukhjit Singh ◽  
D. K. Gupta ◽  
Falguni Roy
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Higher Order ◽  
Step Interval

scholarly journals Two Higher Order Iterative Methods for Solving Nonlinear Equations

2018 ◽  
Vol 14 (1) ◽  
pp. 179-187
Author(s):  
Jivandhar Jnawali ◽  
Chet Raj Bhatta
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Order Of Convergence ◽  
Higher Order ◽  
Secant Method ◽  
Subject Classification ◽  
Numerical Examples ◽  
Ams Subject Classification

 The main purpose of this paper is to derive two higher order iterative methods for solving nonlinear equations as variants of Mir, Ayub and Rafiq method. These methods are free from higher order derivatives. We obtain these methods by amalgamating Mir, Ayub and Rafiq method with standard secant method and modified secant method given by Amat and Busquier. The order of convergence of new variants are four and six. Also, numerical examples are given to compare the performance of newly introduced methods with the similar existing methods. 2010 AMS Subject Classification: 65H05 Journal of the Institute of Engineering, 2018, 14(1): 179-187

scholarly journals New Higher Order Iterative Methods for Solving Nonlinear Equations

2017 ◽  
Vol 4 (46) ◽  
Author(s):  
Shuliang Huang ◽  
Arif Rafiq ◽  
Muhammad Rizwan Shahzad ◽  
Faisal Ali
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Higher Order

scholarly journals Higher-Order Root-Finding Algorithms and Their Basins of Attraction

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Amir Naseem ◽  
M. A. Rehman ◽  
Thabet Abdeljawad
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Basins Of Attraction ◽  
Higher Order ◽  
Complex Polynomials ◽  
Convergence Criteria ◽  
Root Finding ◽  
Variational Iteration ◽  
Order Root ◽  
Iteration Technique

In this paper, we proposed and analyzed three new root-finding algorithms for solving nonlinear equations in one variable. We derive these algorithms with the help of variational iteration technique. We discuss the convergence criteria of these newly developed algorithms. The dominance of the proposed algorithms is illustrated by solving several test examples and comparing them with other well-known existing iterative methods in the literature. In the end, we present the basins of attraction using some complex polynomials of different degrees to observe the fractal behavior and dynamical aspects of the proposed algorithms.

Higher Order Convergent Newton Type Iterative Methods

2018 ◽  
Vol 1 (2) ◽  
pp. 32-39
Author(s):  
Jivandhar Jnawali
Keyword(s):  
Numerical Methods ◽  
Iterative Methods ◽  
Nonlinear Equations ◽  
Newton Method ◽  
Order Of Convergence ◽  
Higher Order ◽  
Predictor Corrector ◽  
Appl Math

Newton method is one of the most widely used numerical methods for solving nonlinear equations. McDougall and Wotherspoon [Appl. Math. Lett., 29 (2014), 20-25] modified this method in predictor-corrector form and get an order of convergence 1+√2. More on the PDF

scholarly journals Introduction to Higher-Order Iterative Methods for Finding Multiple Roots of Nonlinear Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-3 ◽  
Author(s):  
Rajinder Thukral
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Higher Order ◽  
Multiple Roots ◽  
Multiple Zeros ◽  
New Methods

We introduce two higher-order iterative methods for finding multiple zeros of nonlinear equations. Per iteration the new methods require three evaluations of function and one of its first derivatives. It is proved that the two methods have a convergence of order five or six.

Iterative Methods of Higher Order for Nonlinear Equations

2015 ◽  
Vol 44 (2) ◽  
pp. 387-398 ◽  
Author(s):  
Sukhjit Singh ◽  
Dharmendra Kumar Gupta
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Higher Order
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