scholarly journals A combination of two semi-analytical method called “singular perturbed homotopy analysis method, (SPHAM)” applied to combustion of spray fuel droplets

2016 ◽  
Vol 3 (1) ◽  
pp. 1256467
Author(s):  
Ophir Nave ◽  
Vladimir Gol’dshtein ◽  
Shaoyong Lai
Keyword(s):  
Homotopy Analysis Method ◽  
Analytical Method ◽  
Analysis Method ◽  
Fuel Droplets ◽  
Homotopy Analysis

An analytical method with Padé technique for solving of variational problems

2017 ◽  
Vol 6 (4) ◽  
Author(s):  
H. Jaffarian ◽  
K. Sayevand ◽  
Sunil Kumar
Keyword(s):  
Homotopy Analysis Method ◽  
Analytical Method ◽  
Variational Problems ◽  
Analysis Method ◽  
Homotopy Analysis

AbstractIn this paper, the homotopy analysis method (HAM) is employed to solve a class of variational problems (VPs). By using the so-called

scholarly journals An analytical method for solving the two-phase inverse Stefan problem

2015 ◽  
Vol 63 (3) ◽  
pp. 583-590 ◽  
Author(s):  
E. Hetmaniok ◽  
D. Słota ◽  
R. Wituła ◽  
A. Zielonka
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Stefan Problem ◽  
Homotopy Analysis Method ◽  
Analytical Method ◽  
Original Equation ◽  
Sufficient Condition ◽  
Analysis Method ◽  
Two Phase ◽  
Homotopy Analysis

Abstract In the paper we present an application of the homotopy analysis method for solving the two-phase inverse Stefan problem. In the proposed approach a series is created, having elements which satisfy some differential equation following from the investigated problem. We reveal, in the paper, that if this series is convergent then its sum determines the solution of the original equation. A sufficient condition for this convergence is formulated. Moreover, the estimation of the error of the approximate solution, obtained by taking the partial sum of the considered series, is given. Additionally, we present an example illustrating an application of the described method.

scholarly journals Modification of Semi-Analytical Method Applied System of ODE

2020 ◽  
Vol 14 (6) ◽  
pp. 75
Author(s):  
OPhir Nave
Keyword(s):  
Breast Cancer ◽  
Mathematical Model ◽  
Homotopy Analysis Method ◽  
Analytical Method ◽  
Analysis Method ◽  
Analytical Functions ◽  
Ode System ◽  
Homotopy Analysis ◽  
Simulation Results ◽  
The Right

In this study, we modify the well-known semi-analytical method called the Homotopy Analysis Method (HAM), such that the right-hand side of a given ODE system is decomposed to a sum of analytical functions. We called the new semi-analytical method: decomposition of the Homotopy Analysis Method (DHAM). We applied the new method to a breast cancer mathematical model. We compared the DHAM results to HAM and numerical simulations. We concluded that the DHAM results are closer to the numerical simulation results than the HAM.

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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