WITHDRAWN: Two convergence theorems of variational iteration method for ordinary differential equations

2011 ◽  
Author(s):  
Elçin Yusufoğlu
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Convergence Theorems ◽  
Variational Iteration

scholarly journals Variational Iteration Method Solutions for Certain Thirteenth Order Ordinary Differential Equations

2013 ◽  
Vol 04 (10) ◽  
pp. 1405-1411 ◽  
Author(s):  
Tunde A. Adeosun ◽  
Olugbenga J. Fenuga ◽  
Samuel O. Adelana ◽  
Abosede M. John ◽  
Ogunjimi Olalekan ◽  
...  
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Variational Iteration

scholarly journals The Semianalytical Solutions for Stiff Systems of Ordinary Differential Equations by Using Variational Iteration Method and Modified Variational Iteration Method with Comparison to Exact Solutions

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Mehmet Tarik Atay ◽  
Okan Kilic
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Ordinary Differential Equations ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Stiff Ordinary Differential Equations ◽  
Variational Iteration ◽  
Adomian Decomposition ◽  
Linear And Nonlinear ◽  
Modified Variational Iteration Method

The Variational Iteration Method (VIM) and Modified Variational Iteration Method (MVIM) are used to find solutions of systems of stiff ordinary differential equations for both linear and nonlinear problems. Some examples are given to illustrate the accuracy and effectiveness of these methods. We compare our results with exact results. In some studies related to stiff ordinary differential equations, problems were solved by Adomian Decomposition Method and VIM and Homotopy Perturbation Method. Comparisons with exact solutions reveal that the Variational Iteration Method (VIM) and the Modified Variational Iteration Method (MVIM) are easier to implement. In fact, these methods are promising methods for various systems of linear and nonlinear stiff ordinary differential equations. Furthermore, VIM, or in some cases MVIM, is giving exact solutions in linear cases and very satisfactory solutions when compared to exact solutions for nonlinear cases depending on the stiffness ratio of the stiff system to be solved.

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

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