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.

Series Solution of the System of Integro-Differential Equations

2009 ◽  
Vol 64 (12) ◽  
pp. 811-818 ◽  
Author(s):  
Saeid Abbasbandy ◽  
Elyas Shivanian
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Homotopy Analysis Method ◽  
Series Solution ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
Linear And Nonlinear

This investigation presents a mathematical model describing the homotopy analysis method (HAM) for systems of linear and nonlinear integro-differential equations. Some examples are analyzed to illustrate the ability of the method for such systems. The results reveal that this method is very effective and highly promising

scholarly journals A two-parameter mathematical model for immobilizedenzymes and Homotopy analysis method

2011 ◽  
Vol 03 (07) ◽  
pp. 556-565 ◽  
Author(s):  
Rathinasamy Angel Joy ◽  
Athimoolam Meena ◽  
Shunmugham Loghambal ◽  
Lakshmanan Rajendran
Keyword(s):  
Mathematical Model ◽  
Homotopy Analysis Method ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
Two Parameter

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 A semi-analytical method applied to turbocharger engine model

2020 ◽  
Vol 18 (4) ◽  
pp. 178-186
Author(s):  
OPhir Nave
Keyword(s):  
Differential Equations ◽  
Physical Model ◽  
Homotopy Analysis Method ◽  
Asymptotic Methods ◽  
System Of Equations ◽  
Analysis Method ◽  
Engine Model ◽  
Homotopy Analysis ◽  
The Right ◽  
Sum Of Functions

In this study, we apply a new version of the Homotopy Analysis Method called decomposition of the homotopy analysis method (DHAM). The DHAM method is based on the decomposition of the right-hand side of a given system of differential equations into a sum of functions. After the decomposition one can apply the HAM method. The physical model that we investigate in this paper is a complex system of equations that contains nonlinear ordinary differential equations of the first order. The system of equations takes into account the important variables such as the pressure, the temperature, the mass flow, the torque due to the turbine turbocharger, the torque from the compressor, the speed of turbocharger, etc. This system is very complex and cannot be solved analytically. The HAM method includes an artificial small parameter that inserts into the physical model and hence it enables one to apply different asymptotic methods. We compared the results of DHAM and HAM to numerical simulations analyses. We concluded that the DHAM results are closer to the numerical simulation 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.

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