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 Application of He's Variational Iteration Method to Solve Semidifferential Equations of th Order

2008 ◽  
Vol 2008 ◽  
pp. 1-9 ◽  
Author(s):  
Asghar Ghorbani ◽  
Abdolsaeed Alavi
Keyword(s):  
Iteration Method ◽  
Present Method ◽  
Variational Iteration Method ◽  
Convergent Series ◽  
Mathematical Tool ◽  
Spline Method ◽  
Weak Nonlinearity ◽  
Variational Iteration ◽  
He’S Variational Iteration Method ◽  
Powerful Mathematical Tool

He's variational iteration method is applied to solve th order semidifferential equations. Comparison is made between collocation spline method based on Lagrange interpolation and the present method. In this method, the solution is calculated in the form of a convergent series with an easily computable component. This approach does not need linearization, weak nonlinearity assumptions, or perturbation theory. Some examples are given to illustrate the effectiveness of the method; the results show that He's method provides a straightforward and powerful mathematical tool for solving various semidifferential equations of the th order.

On the Reconstruction of the First Term in the Variational Iteration Method for Solving Differential Equations

2010 ◽  
Vol 65 (3) ◽  
pp. 203-208 ◽  
Author(s):  
Mehdi Tatari ◽  
Mehdi Dehghan
Keyword(s):  
Nonlinear System ◽  
Differential Equations ◽  
Nonlinear Problem ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
System Of Equations ◽  
Nonlinear System Of Equations ◽  
Variational Iteration ◽  
Initial Term ◽  
He’S Variational Iteration Method

The well-known He’s variational iteration method is an efficient and easy technique for finding the solution of various kinds of problems. In this method the solution of a nonlinear problem is found without any need to solve a linear or nonlinear system of equations. In the current work we present an idea for accelerating the convergence of the resulted sequence to the solution of the problem by choosing a suitable initial term. The efficiency of the method will be shown by testing the new algorithm on several examples.

Application of the Variational Iteration Method to Nonlinear Volterra’s Integro-Differential Equations

2008 ◽  
Vol 63 (9) ◽  
pp. 538-542 ◽  
Author(s):  
Saeid Abbasbandy ◽  
Elyas Shivanian
Keyword(s):  
Differential Equations ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Variational Iteration ◽  
He’S Variational Iteration Method

He’s variational iteration method is proposed to solve nonlinear Volterra’s integro-differential equations. The results reveal that this method is very effective and convenient in comparison with other methods.

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.

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