On the variational iteration method and other iterative techniques for nonlinear differential equations

2008 ◽  
Vol 199 (1) ◽  
pp. 39-69 ◽  
Author(s):  
J.I. Ramos
Keyword(s):  
Differential Equations ◽  
Iteration Method ◽  
Nonlinear Differential Equations ◽  
Variational Iteration Method ◽  
Iterative Techniques ◽  
Variational Iteration

scholarly journals New analytical solution for natural convection of Darcian fluid in porous media prescribed surface heat flux

2011 ◽  
Vol 15 (suppl. 2) ◽  
pp. 221-227 ◽  
Author(s):  
Domiry Ganji ◽  
Hasan Sajjadi
Keyword(s):  
Heat Flux ◽  
Porous Media ◽  
Differential Equations ◽  
Iteration Method ◽  
Surface Heat Flux ◽  
Nonlinear Differential Equations ◽  
Variational Iteration Method ◽  
Surface Heat ◽  
Variational Iteration ◽  
He’S Variational Iteration Method

A new analytical method called He's Variational Iteration Method is introduced to be applied to solve nonlinear equations. In this method, general Lagrange multipliers are introduced to construct correction functional for the problems. It is strongly and simply capable of solving a large class of linear or nonlinear differential equations without the tangible restriction of sensitivity to the degree of the nonlinear term and also is very user friend because it reduces the size of calculations besides; its iterations are direct and straightforward. In this paper the powerful method called Variational Iteration Method is used to obtain the solution for a nonlinear Ordinary Differential Equations that often appear in boundary layers problems arising in heat and mass transfer which these kinds of the equations contain infinity boundary condition. The boundary layer approximations of fluid flow and heat transfer of vertical full cone embedded in porous media give us the similarity solution for full cone subjected to surface heat flux boundary conditions. The obtained Variational Iteration Method solution in comparison with the numerical ones represents a remarkable accuracy.

scholarly journals Solution of Space-Time-Fractional Problem by Shehu Variational Iteration Method

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Suleyman Cetinkaya ◽  
Ali Demir ◽  
Hulya Kodal Sevindir
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Iteration Method ◽  
Nonlinear Differential Equations ◽  
Variational Iteration Method ◽  
Space Time ◽  
Variational Iteration ◽  
Mathematical Problems ◽  
Fractional Differential ◽  
Time Fractional Differential Equations

In this study, we deal with the problem of constructing semianalytical solution of mathematical problems including space-time-fractional linear and nonlinear differential equations. The method, called Shehu Variational Iteration Method (SVIM), applied in this study is a combination of Shehu transform (ST) and variational iteration method (VIM). First, ST is utilized to reduce the time-fractional differential equation with fractional derivative in Liouville-Caputo sense into an integer-order differential equation. Later, VIM is implemented to construct the solution of reduced differential equation. The convergence analysis of this method and illustrated examples confirm that the proposed method is one of best procedures to tackle space-time-fractional differential equations.

scholarly journals Application of He’s Variational Iteration Method to Nonlinear Integro-Differential Equations

2010 ◽  
Vol 65 (5) ◽  
pp. 418-430 ◽  
Author(s):  
Ahmet Yildirim
Keyword(s):  
Differential Equations ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Mathematical Tool ◽  
Variational Iteration ◽  
He’S Variational Iteration Method ◽  
Powerful Mathematical Tool

In this paper, an application of He’s variational iteration method is applied to solve nonlinear integro-differential equations. Some examples are given to illustrate the effectiveness of the method. The results show that the method provides a straightforward and powerful mathematical tool for solving various nonlinear integro-differential equations

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.

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