Periodic solution for strongly nonlinear vibration systems by He's variational iteration method

2009 ◽  
Vol 32 (18) ◽  
pp. 2339-2349 ◽  
Author(s):  
SHA. Hashemi Kachapi ◽  
D. D. Ganji ◽  
A. G. Davodi ◽  
S. M. Varedi
Keyword(s):  
Periodic Solution ◽  
Nonlinear Vibration ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Strongly Nonlinear ◽  
Variational Iteration ◽  
He’S Variational Iteration Method

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 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 Applying He's variational iteration method to FRW cosmology

2019 ◽  
Vol 7 (2) ◽  
pp. 39
Author(s):  
V. K.Shchigolev
Keyword(s):  
Iteration Method ◽  
System Analysis ◽  
Variational Iteration Method ◽  
Cosmological Models ◽  
Frw Cosmology ◽  
Variational Iteration ◽  
Barotropic Fluids ◽  
He’S Variational Iteration Method ◽  
High Degree ◽  
The Universe

This work is devoted to the investigation of Friedmann-Robertson-Walker (FRW) cosmological models with the help of the so-called Variational Iteration Method (VIM). For this end, we briefly recall the main equations of the cosmological models and the basic idea of VIM. In order to approbate the VIM in FRW cosmology and demonstrate the main steps in solving by this method, we consider the test example of the universe with dust for which the exact solution of the model is known. Then, a solution for the spatially flat FRW model of the universe filled with the dust and quintessence is obtained when the exact analytic solution cannot be found. A comparison of our solution with the corresponding numerical solution shows that it is of a high degree of accuracy. Moreover, the Dynamical System Analysis to the dynamics of the homogeneous and isotropic FRW universes is used as a special case of generalized Lotka–Volterra system where the competitive species are the barotropic fluids filling the Universe. With the help of VIM, we have found the iterative formulae for the density parameters of the cosmological analog of the generalized Lotka–Volterra set of equations. All solutions illustrated graphically by means of Maple software.  

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