Construction of solitary solutions for nonlinear dispersive equations by variational iteration method

2008 ◽  
Vol 372 (22) ◽  
pp. 4045-4052 ◽  
Author(s):  
Zaid M. Odibat
Keyword(s):  
Iteration Method ◽  
Variational Iteration Method ◽  
Dispersive Equations ◽  
Nonlinear Dispersive Equations ◽  
Variational Iteration ◽  
Solitary Solutions

HPM AND VIM METHODS FOR FINDING THE EXACT SOLUTIONS OF THE NONLINEAR DISPERSIVE EQUATIONS AND SEVENTH-ORDER SAWADA–KOTERA EQUATION

2009 ◽  
Vol 23 (01) ◽  
pp. 39-52 ◽  
Author(s):  
D. D. GANJI ◽  
N. JAMSHIDI ◽  
Z. Z. GANJI
Keyword(s):  
Iteration Method ◽  
Decomposition Method ◽  
Homotopy Perturbation Method ◽  
Adomian Decomposition Method ◽  
Variational Iteration Method ◽  
Dispersive Equations ◽  
Nonlinear Dispersive Equations ◽  
Homotopy Perturbation ◽  
Adomian Decomposition ◽  
Seventh Order

In this paper, nonlinear dispersive equations and seventh-order Sawada–Kotera equation are solved using homotopy perturbation method (HPM) and variational iteration method (VIM). The results obtained by the proposed methods are then compared with that of Adomian decomposition method (ADM). The comparisons demonstrate that the two obtained solutions are in excellent agreement. The numerical results calculated show that the methods can be accurately implemented to these types of nonlinear equations. The results of HPM and VIM confirm the correctness of those obtained by Adomian decomposition method.

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

Sign in / Sign up

Export Citation Format

Share Document