scholarly journals Comment on “A New Second-Order Iteration Method for Solving Nonlinear Equations”

2013 ◽  
Vol 2013 ◽  
pp. 1-2
Author(s):  
Haibin Li
Keyword(s):  
Nonlinear Equations ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Second Order ◽  
Algebraic Equations ◽  
Variational Iteration ◽  
Nonlinear Algebraic Equations ◽  
New Formulation

Kang et al. claimed that they obtained a new iteration formulation for nonlinear algebraic equations; however the “new” formulation was first derived in 2007 by the variational iteration method.

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.

scholarly journals Convergence of Variational Iteration Method for Fractional Delay Integrodifferential-Algebraic Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Yayun Fu ◽  
Hongliang Liu ◽  
Aiguo Xiao
Keyword(s):  
Iteration Method ◽  
Time Lag ◽  
Variational Iteration Method ◽  
Good Choice ◽  
Algebraic Equations ◽  
Science And Engineering ◽  
Variational Iteration ◽  
Fractional Delay ◽  
Restricted Variation ◽  
Algebraic Constraint

Fractional order delay integrodifferential-algebraic equations are often used for many practical modeling problems in science and engineering, which have time lag, memory, constraint limit, and so forth. These yield some difficulties in numerical computation. The iterative methods are good choice. In the present paper, we construct variational iteration method for solving them by using the appropriate restricted variation. This overcomes the difficulties caused by limitations of large storage amount and algebraic constraint and extends the previous conclusions.

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.

scholarly journals Variational Iteration Method forq-Difference Equations of Second Order

2012 ◽  
Vol 2012 ◽  
pp. 1-5 ◽  
Author(s):  
Guo-Cheng Wu
Keyword(s):  
Lagrange Multiplier ◽  
Difference Equations ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Second Order ◽  
Iteration Formula ◽  
Strongly Nonlinear ◽  
Variational Iteration ◽  
He’S Variational Iteration Method ◽  
Oscillation Equation

Recently, Liu extended He's variational iteration method to strongly nonlinearq-difference equations. In this study, the iteration formula and the Lagrange multiplier are given in a more accurate way. Theq-oscillation equation of second order is approximately solved to show the new Lagrange multiplier's validness.

scholarly journals On the Numerical Solution of Differential-Algebraic Equations with Hessenberg Index-3

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Melike Karta ◽  
Ercan Çelik
Keyword(s):  
Exact Solutions ◽  
Numerical Solution ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Variational Iteration

Numerical solution of differential-algebraic equations with Hessenberg index-3 is considered by variational iteration method. We applied this method to two examples, and solutions have been compared with those obtained by exact solutions.

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