Solution of One-Dimensional Time Fractional Advection Dispersion Equation by Homotopy Analysis Method

2017 ◽  
Vol 143 (9) ◽  
pp. 04017103 ◽  
Author(s):  
Mritunjay Kumar Singh ◽  
Ayan Chatterjee ◽  
Vijay P. Singh
Keyword(s):  
Dispersion Equation ◽  
Homotopy Analysis Method ◽  
Analysis Method ◽  
One Dimensional ◽  
Advection Dispersion ◽  
Homotopy Analysis

scholarly journals Approximate Analytical Solution of Advection-Dispersion Equation By Means of OHAM.

2018 ◽  
Vol 7 (1) ◽  
pp. 15-20
Author(s):  
D J Prajapati ◽  
N B Desai
Keyword(s):  
Analytical Solution ◽  
Dispersion Equation ◽  
Graphical Representation ◽  
Approximate Analytical Solution ◽  
Time Dependent ◽  
Analysis Method ◽  
Optimal Homotopy Analysis Method ◽  
Advection Dispersion ◽  
Homotopy Analysis ◽  
Input Source

This work deals with the analytical solution of advection dispersion equation arising in solute transport along unsteady groundwater flow in finite aquifer. A time dependent input source concentration is considered at the origin of the aquifer and it is assumed that the concentration gradient is zero at the other end of the aquifer. The optimal homotopy analysis method (OHAM) is used to obtain numerical and graphical representation.

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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