Homotopy perturbation method to obtain new solitary solutions with compact support for Boussinesq-like B(2n, 2n) equations with fully nonlinear dispersion

2011 ◽  
Vol 65 (6) ◽  
pp. 699-706
Author(s):  
Ahmet Yıldırım ◽  
Yağmur Gülkanat
Keyword(s):  
Perturbation Method ◽  
Compact Support ◽  
Homotopy Perturbation Method ◽  
Nonlinear Dispersion ◽  
Fully Nonlinear ◽  
Homotopy Perturbation ◽  
Solitary Solutions ◽  
Solutions With Compact Support

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.

On Spectral-Homotopy Perturbation Method Solution of Nonlinear Differential Equations in Bounded Domains

2013 ◽  
Vol 1 (1) ◽  
pp. 25-37
Author(s):  
Ahmed A. Khidir
Keyword(s):  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Nonlinear Boundary ◽  
Nonlinear Differential Equations ◽  
Iteration Algorithm ◽  
Test Problems ◽  
Nonlinear Boundary Value Problems ◽  
Homotopy Perturbation ◽  
Spectral Technique ◽  
Homotopy Analysis

In this study, a combination of the hybrid Chebyshev spectral technique and the homotopy perturbation method is used to construct an iteration algorithm for solving nonlinear boundary value problems. Test problems are solved in order to demonstrate the efficiency, accuracy and reliability of the new technique and comparisons are made between the obtained results and exact solutions. The results demonstrate that the new spectral homotopy perturbation method is more efficient and converges faster than the standard homotopy analysis method. The methodology presented in the work is useful for solving the BVPs consisting of more than one differential equation in bounded domains. 

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