The Variational Iteration Method and the Variational Homotopy Perturbation Method for Solving the KdV-Burgers Equation and the Sharma-Tasso-Olver Equation

2010 ◽  
Vol 65 (1-2) ◽  
pp. 25-33 ◽  
Author(s):  
Elsayed M. E. Zayed ◽  
Hanan M. Abdel Rahman
Keyword(s):  
Perturbation Method ◽  
Iteration Method ◽  
Homotopy Perturbation Method ◽  
Numerical Solutions ◽  
Burgers Equation ◽  
Nonlinear Problems ◽  
Variational Iteration Method ◽  
Alternative Methods ◽  
Variational Iteration ◽  
Homotopy Perturbation

AbstractIn this article, two powerful analytical methods called the variational iteration method (VIM) and the variational homotopy perturbation method (VHPM) are introduced to obtain the exact and the numerical solutions of the (2+1)-dimensional Korteweg-de Vries-Burgers (KdVB) equation and the (1+1)-dimensional Sharma-Tasso-Olver equation. The main objective of the present article is to propose alternative methods of solutions, which avoid linearization and physical unrealistic assumptions. The results show that these methods are very efficient, convenient and can be applied to a large class of nonlinear problems.

scholarly journals Solving the Fractional Rosenau-Hyman Equation via Variational Iteration Method and Homotopy Perturbation Method

2012 ◽  
Vol 2012 ◽  
pp. 1-14
Author(s):  
R. Yulita Molliq ◽  
M. S. M. Noorani
Keyword(s):  
Perturbation Method ◽  
Iteration Method ◽  
Homotopy Perturbation Method ◽  
Applied Mathematics ◽  
Analytical Techniques ◽  
Variational Iteration Method ◽  
Convergent Series ◽  
Alternative Methods ◽  
Variational Iteration ◽  
Homotopy Perturbation

In this study, fractional Rosenau-Hynam equations is considered. We implement relatively new analytical techniques, the variational iteration method and the homotopy perturbation method, for solving this equation. The fractional derivatives are described in the Caputo sense. The two methods in applied mathematics can be used as alternative methods for obtaining analytic and approximate solutions for fractional Rosenau-Hynam equations. In these schemes, the solution takes the form of a convergent series with easily computable components. The present methods perform extremely well in terms of efficiency and simplicity.

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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