Application of Homotopy Perturbation Method and Variational Iteration Method to Nonlinear Oscillator Differential Equations

2008 ◽  
Vol 104 (2) ◽  
pp. 161-171 ◽  
Author(s):  
A. Barari ◽  
M. Omidvar ◽  
Abdoul R. Ghotbi ◽  
D. D. Ganji
Keyword(s):  
Differential Equations ◽  
Perturbation Method ◽  
Iteration Method ◽  
Nonlinear Oscillator ◽  
Homotopy Perturbation Method ◽  
Variational Iteration Method ◽  
Variational Iteration ◽  
Homotopy Perturbation

ANALYTICAL COMPARISON BETWEEN THE HOMOTOPY PERTURBATION METHOD AND VARIATIONAL ITERATION METHOD FOR DIFFERENTIAL EQUATIONS OF FRACTIONAL ORDER

2008 ◽  
Vol 22 (23) ◽  
pp. 4041-4058 ◽  
Author(s):  
ZAID ODIBAT ◽  
SHAHER MOMANI
Keyword(s):  
Differential Equations ◽  
Perturbation Method ◽  
Fractional Order ◽  
Iteration Method ◽  
Homotopy Perturbation Method ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
Variational Iteration ◽  
Homotopy Perturbation ◽  
Different Types

Comparison of homotopy perturbation method (HPM) and variational iteration method (VIM) is made, revealing that the two methods can be used as alternative and equivalent methods for obtaining analytic and approximate solutions for different types of differential equations of fractional order. Furthermore, the former is more general and powerful than the latter. Numerical results show that the two approaches are easy to implement and accurate when applied to differential equations of fractional order.

Variational Iteration Method and Homotopy-Perturbation Method for Solving Second-Order Non-Linear Wave Equation

2007 ◽  
Author(s):  
A. Barari ◽  
M. Omidvar ◽  
S. Gholitabar ◽  
D. D. Ganji ◽  
Theodore E. Simos ◽  
...  
Keyword(s):  
Wave Equation ◽  
Perturbation Method ◽  
Iteration Method ◽  
Homotopy Perturbation Method ◽  
Variational Iteration Method ◽  
Second Order ◽  
Linear Wave ◽  
Linear Wave Equation ◽  
Variational Iteration ◽  
Homotopy Perturbation

scholarly journals The Approximate Solution of Fractional Fredholm Integrodifferential Equations by Variational Iteration and Homotopy Perturbation Methods

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Abdelouahab Kadem ◽  
Adem Kilicman
Keyword(s):  
Approximate Solution ◽  
Perturbation Method ◽  
Iteration Method ◽  
Homotopy Perturbation Method ◽  
Perturbation Methods ◽  
Variational Iteration Method ◽  
Integrodifferential Equations ◽  
Variational Iteration ◽  
Homotopy Perturbation ◽  
Constant Coefficients

Variational iteration method and homotopy perturbation method are used to solve the fractional Fredholm integrodifferential equations with constant coefficients. The obtained results indicate that the method is efficient and also accurate.

scholarly journals Variational Homotopy Perturbation Method for Solving Fractional Initial Boundary Value Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Yanqin Liu
Keyword(s):  
Perturbation Method ◽  
Boundary Value Problems ◽  
Iteration Method ◽  
Homotopy Perturbation Method ◽  
Variational Iteration Method ◽  
Initial Boundary ◽  
Initial Boundary Value Problems ◽  
Variational Iteration ◽  
Homotopy Perturbation ◽  
Initial Boundary Value

A variational homotopy perturbation method (VHPM) which is based on variational iteration method and homotopy perturbation method is applied to solve the approximate solution of the fractional initial boundary value problems. The nonlinear terms can be easily handled by the use of He's polynomials. It is observed that the variational iteration method is very efficient and easier to implements; illustrative examples are included to demonstrate the high accuracy and fast convergence of this new algorithm.

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