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.

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

He’s Variational Iteration Method for Solving a Partial Differential Equation Arising in Modelling of theWater Waves

2009 ◽  
Vol 64 (12) ◽  
pp. 783-787 ◽  
Author(s):  
Abbas Saadatmandi ◽  
Mehdi Dehghan
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Small Perturbation ◽  
Efficient Method ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Convergent Series ◽  
Kawahara Equation ◽  
Variational Iteration ◽  
He’S Variational Iteration Method

The variational iteration method is applied to solve the Kawahara equation. This method produces the solutions in terms of convergent series and does not require linearization or small perturbation. Some examples are given. The comparison with the theoretical solution shows that the variational iteration method is an efficient method

scholarly journals He's Variational Iteration Method for Solving Fractional Riccati Differential Equation

2010 ◽  
Vol 2010 ◽  
pp. 1-8 ◽  
Author(s):  
H. Jafari ◽  
H. Tajadodi
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Iteration Method ◽  
Present Method ◽  
Variational Iteration Method ◽  
Riccati Differential Equation ◽  
Variational Iteration ◽  
Optimal Value ◽  
He’S Variational Iteration Method ◽  
Sequence Of Functions

We will consider He's variational iteration method for solving fractional Riccati differential equation. This method is based on the use of Lagrange multipliers for identification of optimal value of a parameter in a functional. This technique provides a sequence of functions which converges to the exact solution of the problem. The present method performs extremely well in terms of efficiency and simplicity.

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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