scholarly journals Solution of the Local Fractional Generalized KDV Equation Using Homotopy Analysis Method

Fractals ◽  
2021 ◽  
Author(s):  
Hossein Jafari ◽  
Pranay Goswami ◽  
Ravi Shanker Dubey ◽  
Jyoti Geetesh Prasad
Keyword(s):  
Homotopy Analysis Method ◽  
Kdv Equation ◽  
Analysis Method ◽  
Generalized Kdv Equation ◽  
Homotopy Analysis

scholarly journals A New Homotopy Analysis Method for Approximating the Analytic Solution of KdV Equation

2014 ◽  
Vol 7 (4) ◽  
pp. 826-831
Author(s):  
Vahid Barati ◽  
Mojtaba Nazari ◽  
Vincent Daniel David ◽  
Zainal Abdul Aziz
Keyword(s):  
Homotopy Analysis Method ◽  
Analytic Solution ◽  
Kdv Equation ◽  
Analysis Method ◽  
Homotopy Analysis

Solving the discrete KdV equation with homotopy analysis method

2007 ◽  
Vol 370 (3-4) ◽  
pp. 287-294 ◽  
Author(s):  
L. Zou ◽  
Z. Zong ◽  
Z. Wang ◽  
L. He
Keyword(s):  
Homotopy Analysis Method ◽  
Kdv Equation ◽  
Analysis Method ◽  
Homotopy Analysis

HOMOTOPY ANALYSIS METHOD TO SOLVE BOUSSINESQ EQUATIONS

2015 ◽  
Vol 10 (3) ◽  
pp. 2825-2833
Author(s):  
Achala Nargund ◽  
R Madhusudhan ◽  
S B Sathyanarayana
Keyword(s):  
Homotopy Analysis Method ◽  
Degrees Of Freedom ◽  
Initial Approximation ◽  
Boussinesq Equations ◽  
Convergent Series ◽  
Boussinesq System ◽  
Analysis Method ◽  
Analytical Technique ◽  
Homotopy Analysis ◽  
Region Of Convergence

In this paper, Homotopy analysis method is applied to the nonlinear coupleddifferential equations of classical Boussinesq system. We have applied Homotopy analysis method (HAM) for the application problems in [1, 2, 3, 4]. We have also plotted Domb-Sykes plot for the region of convergence. We have applied Pade for the HAM series to identify the singularity and reflect it in the graph. The HAM is a analytical technique which is used to solve non-linear problems to generate a convergent series. HAM gives complete freedom to choose the initial approximation of the solution, it is the auxiliary parameter h which gives us a convenient way to guarantee the convergence of homotopy series solution. It seems that moreartificial degrees of freedom implies larger possibility to gain better approximations by HAM.

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