Exact and analytical solution for nonlinear dispersive equations using homotopy perturbation method

2007 ◽  
Vol 368 (3-4) ◽  
pp. 266-270 ◽  
Author(s):  
Ganji Domairry ◽  
M. Ahangari ◽  
M. Jamshidi
Keyword(s):  
Analytical Solution ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Dispersive Equations ◽  
Nonlinear Dispersive Equations ◽  
Homotopy Perturbation

Homotopy perturbation method for the nonlinear dispersive K(m, n, 1) equations with fractional time derivatives

2010 ◽  
Vol 20 (2) ◽  
pp. 174-185 ◽  
Author(s):  
Hüseyin Koçak ◽  
Turgut Öziş ◽  
Ahmet Yıldırım
Keyword(s):  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Time Derivative ◽  
Approximate Solutions ◽  
Dispersive Equations ◽  
Content Type ◽  
Nonlinear Dispersive Equations ◽  
Homotopy Perturbation ◽  
Solitary Solutions ◽  
Fractional Time Derivative

PurposeThis paper aims to apply He's homotopy perturbation method (HPM) to obtain solitary solutions for the nonlinear dispersive equations with fractional time derivatives.Design/methodology/approachThe authors choose as an example the nonlinear dispersive and equations with fractional time derivatives to illustrate the validity and the advantages of the proposed method.FindingsThe paper extends the application of the HPM to obtain analytic and approximate solutions to the nonlinear dispersive equations with fractional time derivatives.Originality/valueThis paper extends the HPM to the equation with fractional time derivative.

Application of He’s Homotopy Perturbation Method to Stiff Systems of Ordinary Differential Equations

2008 ◽  
Vol 63 (1-2) ◽  
pp. 19-23 ◽  
Author(s):  
Mohammad Taghi Darvishi ◽  
Farzad Khani
Keyword(s):  
Analytical Solution ◽  
Differential Equations ◽  
Perturbation Method ◽  
Ordinary Differential Equations ◽  
Homotopy Perturbation Method ◽  
Nonlinear Ordinary Differential Equations ◽  
Stiff Systems ◽  
Homotopy Perturbation ◽  
Linear And Nonlinear

We propose He’s homotopy perturbation method (HPM) to solve stiff systems of ordinary differential equations. This method is very simple to be implemented. HPM is employed to compute an approximation or analytical solution of the stiff systems of linear and nonlinear ordinary differential equations.

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.

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