scholarly journals 7th -Order Caudrey-Dodd-Gibbon Equation and Fisher-Type Equation by Homotopy Analysis Method

2020 ◽  
Vol 5 (2) ◽  
pp. 272-282
Author(s):  
Ankita Sharma ◽  
Rajan Arora
Keyword(s):  
Homotopy Analysis Method ◽  
Type Equation ◽  
Analysis Method ◽  
Nucleation Kinetics ◽  
Reliable Technique ◽  
Analytical Technique ◽  
Closed Form Solutions ◽  
Non Linear ◽  
Homotopy Analysis ◽  
Linear Differential

In this paper, we first describe the methodology of the Homotopy Analysis Method (HAM) which is an analytical technique and then employ it to some of the non-linear problems which are used in different fields of sciences like plasma physics, fluid dynamics, laser optics, biology, chemical kinetics, nucleation kinetics, physiology, etc. Approximate series solutions have been obtained and the results are compared with the closed form solutions of the equations, which show that this technique gives high accurate results. HAM is a reliable technique, easy to use and is widely applicable to a large class of non-linear differential equations. MATHEMATICA software package has been used for computations.

A reliable treatment of the homotopy analysis method for viscous flow over a non-linearly stretching sheet in presence of a chemical reaction and under influence of a magnetic field

Open Physics ◽  
2009 ◽  
Vol 7 (1) ◽  
Author(s):  
Saeed Dinarvand
Keyword(s):  
Magnetic Field ◽  
Differential Equations ◽  
Chemical Reaction ◽  
Homotopy Analysis Method ◽  
Stretching Sheet ◽  
Linear Differential Equations ◽  
Analysis Method ◽  
Non Linear ◽  
Homotopy Analysis ◽  
Linear Differential

AbstractThe similarity solution for the steady two-dimensional flow of an incompressible viscous and electrically conducting fluid over a non-linearly semi-infinite stretching sheet in the presence of a chemical reaction and under the influence of a magnetic field gives a system of non-linear ordinary differential equations. These non-linear differential equations are analytically solved by applying a newly developed method, namely the Homotopy Analysis Method (HAM). The analytic solutions of the system of non-linear differential equations are constructed in the series form. The convergence of the obtained series solutions is carefully analyzed. Graphical results are presented to investigate the influence of the Schmidt number, magnetic parameter and chemical reaction parameter on the velocity and concentration fields. It is noted that the behavior of the HAM solution for concentration profiles is in good agreement with the numerical solution given in reference [A. Raptis, C. Perdikis, Int. J. Nonlinear Mech. 41, 527 (2006)].

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.

Predictor homotopy analysis method for nanofluid flow through expanding or contracting gaps with permeable walls

2015 ◽  
Vol 08 (04) ◽  
pp. 1550050 ◽  
Author(s):  
Navid Freidoonimehr ◽  
Behnam Rostami ◽  
Mohammad Mehdi Rashidi
Keyword(s):  
Homotopy Analysis Method ◽  
Volume Fraction ◽  
Expansion Ratio ◽  
Analysis Method ◽  
Nanofluid Flow ◽  
Analytical Technique ◽  
Study Results ◽  
Permeable Walls ◽  
Homotopy Analysis ◽  
Flow Through

In this paper a definitely new analytical technique, predictor homotopy analysis method (PHAM), is employed to solve the problem of two-dimensional nanofluid flow through expanding or contracting gaps with permeable walls. Moreover, comparison of the PHAM results with numerical results obtained by the shooting method coupled with a Runge–Kutta integration method as well as previously published study results demonstrates high accuracy for this technique. The fluid in the channel is water containing different nanoparticles: silver, copper, copper oxide, titanium oxide, and aluminum oxide. The effects of the nanoparticle volume fraction, Reynolds number, wall expansion ratio, and different types of nanoparticles on the flow are discussed.

scholarly journals Numerical Solutions of Heat Transfer for Magnetohydrodynamic Jeffery-Hamel Flow Using Spectral Homotopy Analysis Method

Processes ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 626 ◽  
Author(s):  
Asad Mahmood ◽  
Md Md Basir ◽  
Umair Ali ◽  
Mohd Mohd Kasihmuddin ◽  
Mohd. Mansor
Keyword(s):  
Heat Transfer ◽  
Temperature Profile ◽  
Homotopy Analysis Method ◽  
Numerical Solutions ◽  
Hartmann Number ◽  
Reynold Number ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
Linear Differential ◽  
Spectral Homotopy Analysis Method

This paper studies heat transfer in a two-dimensional magnetohydrodynamic viscous incompressible flow in convergent/divergent channels. The temperature profile was obtained numerically for both cases of convergent/divergent channels. It was found that the temperature profile increases with an increase in Reynold number, Prandtl number, Nusselt number and angle of the wall but decreases with an increase in Hartmann number. A relatively new numerical method called the spectral homotopy analysis method (SHAM) was used to solve the governing non-linear differential equations. The SHAM 3rd order results matched with the DTM and shooting, showing that SHAM is feasible as a technique to be used.

scholarly journals Two Species Commensalism Model with Harvesting by Homotopy Analysis Method

2019 ◽  
Vol 8 (2S11) ◽  
pp. 3584-3588
Keyword(s):  
Linear System ◽  
Homotopy Analysis Method ◽  
Series Solution ◽  
Analytical Study ◽  
Analysis Method ◽  
Linear Ordinary Differential Equations ◽  
Commensal Species ◽  
Non Linear ◽  
Homotopy Analysis ◽  
Non Linear System

In the present investigation a two species commensalism model was taken up for detailed analytical study in which commensal species was harvested at a rate proportional to its strength. The system under investigation was represented by a coupled non linear ordinary differential equations. The series solution of the non-linear system was approximated by Homotopy Analysis Method.

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.

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