Consideration of transient heat conduction in a semi-infinite medium using homotopy analysis method

2008 ◽  
Vol 29 (12) ◽  
pp. 1625-1632 ◽  
Author(s):  
A. Rezania ◽  
A. Ghorbali ◽  
G. Domairry ◽  
H. Bararnia
Keyword(s):  
Heat Conduction ◽  
Homotopy Analysis Method ◽  
Transient Heat Conduction ◽  
Infinite Medium ◽  
Analysis Method ◽  
Homotopy Analysis

scholarly journals Solutions of the heat-conduction model described by fractional Emden-Fowler type equation

2017 ◽  
Vol 21 (suppl. 1) ◽  
pp. 113-120 ◽  
Author(s):  
Chunfu Wei ◽  
Huanhuan Wang
Keyword(s):  
Heat Conduction ◽  
Homotopy Analysis Method ◽  
Initial Value Problems ◽  
Type Equation ◽  
Approximate Solutions ◽  
Time Dependent ◽  
Analysis Method ◽  
Initial Value ◽  
Conduction Model ◽  
Homotopy Analysis

In this paper, we presented a reliable algorithm to solve the singularity initial value problems of the time-dependent fractional Emden-Fowler type equations by homotopy analysis method. The approximate solutions of the problems are obtained.

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.

Approximate solutions of singular two-point BVPs by modified homotopy analysis method

2008 ◽  
Vol 372 (22) ◽  
pp. 4062-4066 ◽  
Author(s):  
A. Sami Bataineh ◽  
M.S.M. Noorani ◽  
I. Hashim
Keyword(s):  
Homotopy Analysis Method ◽  
Approximate Solutions ◽  
Analysis Method ◽  
Homotopy Analysis
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