Application of Homotopy Analysis Method to Solve Relativistic Toda Lattice System

2010 ◽  
Vol 53 (6) ◽  
pp. 1111-1116 ◽  
Author(s):  
Wang Qi
Keyword(s):  
Homotopy Analysis Method ◽  
Toda Lattice ◽  
Lattice System ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
Relativistic Toda Lattice

Homotopy Analysis Method for Ablowitz–Ladik Lattice

2011 ◽  
Vol 66 (10-11) ◽  
pp. 599-605
Author(s):  
Benny Y. C. Hon ◽  
Engui Fan ◽  
Qi Wang
Keyword(s):  
Exact Solutions ◽  
Difference Equations ◽  
Homotopy Analysis Method ◽  
Lattice System ◽  
Analysis Method ◽  
Homotopy Analysis

In this paper, the homotopy analysis method is successfully applied to solve the systems of differential-difference equations. The Ablowitz-Ladik lattice system are chosen to illustrate the method. Comparisons between the results of the proposed method and exact solutions reveal that the homotopy analysis method is very effective and simple in solving systems of differential-difference equations.

Application of the Homotopy Analysis Method for Systems of Differential-Difference Equations

2010 ◽  
Vol 65 (10) ◽  
pp. 811-817
Author(s):  
Qi Wang
Keyword(s):  
Difference Equations ◽  
Homotopy Analysis Method ◽  
Lattice System ◽  
Analysis Method ◽  
Homotopy Analysis

The homotopy analysis method is used for solving systems of differential-difference equations. To demonstrate the validity and applicability of the presented technique the Volterra lattice system is taken as example. Analysis results show that the method is very effective and yields very accurate results.

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.

scholarly journals Dynamics with Cattaneo–Christov heat and mass flux theory of bioconvection Oldroyd-B nanofluid

2020 ◽  
Vol 12 (8) ◽  
pp. 168781402093046 ◽  
Author(s):  
Noor Saeed Khan ◽  
Qayyum Shah ◽  
Arif Sohail
Keyword(s):  
Mass Transfer ◽  
Porous Media ◽  
Differential Equations ◽  
Mass Flux ◽  
Homotopy Analysis Method ◽  
Two Dimensional ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
Transfer Flow ◽  
Insight Into

Entropy generation in bioconvection two-dimensional steady incompressible non-Newtonian Oldroyd-B nanofluid with Cattaneo–Christov heat and mass flux theory is investigated. The Darcy–Forchheimer law is used to study heat and mass transfer flow and microorganisms motion in porous media. Using appropriate similarity variables, the partial differential equations are transformed into ordinary differential equations which are then solved by homotopy analysis method. For an insight into the problem, the effects of various parameters on different profiles are shown in different graphs.

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