Variational iteration technique for solving nonlinear equations

2008 ◽  
Vol 31 (1-2) ◽  
pp. 247-254 ◽  
Author(s):  
Muhammad Aslam Noor ◽  
Farooq Ahmed Shah
Keyword(s):  
Nonlinear Equations ◽  
Variational Iteration ◽  
Iteration Technique

A family of fifth-order convergent methods for solving nonlinear equations using variational iteration technique

2018 ◽  
Vol 39 (3) ◽  
pp. 673-694 ◽  
Author(s):  
Xiujun Zhang ◽  
Farooq Ahmed Shah ◽  
Yingfang Li ◽  
Li Yan ◽  
Abdul Qudair Baig ◽  
...  
Keyword(s):  
Nonlinear Equations ◽  
Variational Iteration ◽  
Fifth Order ◽  
Iteration Technique

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.

Variational iteration technique for solving a system of nonlinear equations

2012 ◽  
Vol 7 (5) ◽  
pp. 991-1007 ◽  
Author(s):  
Muhammad Aslam Noor ◽  
Muhammad Waseem ◽  
Khalida Inayat Noor ◽  
Eisa Al-Said
Keyword(s):  
Nonlinear Equations ◽  
System Of Nonlinear Equations ◽  
Variational Iteration ◽  
Iteration Technique

scholarly journals The variational iteration method for solving n-th order fuzzy differential equations

Open Physics ◽  
2012 ◽  
Vol 10 (1) ◽  
Author(s):  
Hossein Jafari ◽  
Mohammad Saeidy ◽  
Dumitru Baleanu
Keyword(s):  
Differential Equations ◽  
Nonlinear Equations ◽  
Analytical Method ◽  
Iteration Method ◽  
Initial Conditions ◽  
Variational Iteration Method ◽  
Linear Differential Equations ◽  
Variational Iteration ◽  
Linear And Nonlinear ◽  
Linear Differential

AbstractThe variational iteration method (VIM) proposed by Ji-Huan He is a new analytical method for solving linear and nonlinear equations. In this paper, the variational iteration method has been applied in solving nth-order fuzzy linear differential equations with fuzzy initial conditions. This method is illustrated by solving several examples.

The estimation of the length constant of a long cooling fin by variational iteration method

2015 ◽  
Vol 25 (4) ◽  
pp. 887-891 ◽  
Author(s):  
Yan Zhang ◽  
Qiaoling Chen ◽  
Fujuan Liu ◽  
Ping Wang
Keyword(s):  
Nonlinear Equation ◽  
Nonlinear Equations ◽  
Iteration Method ◽  
Design Methodology ◽  
Variational Iteration Method ◽  
Engineering Problem ◽  
Content Type ◽  
Variational Iteration ◽  
Length Constant ◽  
Good Agreement

Purpose – The purpose of this paper is to validate the variational iteration method (VIM) is suitable for various nonlinear equations. Design/methodology/approach – The He’s VIM is applied to solve nonlinear equation which is derived from actual engineering problem. The result was compared with other method. Findings – The result obtained from VIM shows good agreement with Xu’s result which provide a solid evidence that VIM is convenient and effective for solving nonlinear equation in the engineering. Originality/value – The VIM can be extended to many academic and engineering fields for nonlinear equations solving.

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