Numerical assessment of Dirac equation system by means of homotopy analysis method

2015 ◽  
Author(s):  
Etibar S. Panakhov ◽  
Mine Babaoglu
Keyword(s):  
Dirac Equation ◽  
Homotopy Analysis Method ◽  
Equation System ◽  
Analysis Method ◽  
Numerical Assessment ◽  
Homotopy Analysis

scholarly journals A New Piecewise-Spectral Homotopy Analysis Method for Solving Chaotic Systems of Initial Value Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
H. Saberi Nik ◽  
Sohrab Effati ◽  
Sandile S. Motsa ◽  
Stanford Shateyi
Keyword(s):  
Homotopy Analysis Method ◽  
Initial Value Problems ◽  
System Modeling ◽  
Equation System ◽  
Analysis Method ◽  
Initial Value ◽  
Homotopy Analysis ◽  
Highly Oscillatory ◽  
First Time ◽  
Spectral Homotopy Analysis Method

An accurate algorithm for solving initial value problems (IVPs) which are highly oscillatory is proposed. The proposed method is based on a novel technique of extending the standard spectral homotopy analysis method (SHAM) and adapting it to a sequence of multiple intervals. In this new application the method is referred to as the piecewise spectral homotopy analysis method (PSHAM). The applicability of the proposed method is examined on the differential equation system modeling HIV infection of CD4+T cells and the Genesio-Tesi system which is known to be chaotic and highly oscillatory. Also, for the first time, we present here a convergence proof for SHAM. We treat in detail Legendre collocation and Chebyshev collocation. The method is compared to MATLAB’sode45inbuilt solver as a measure of accuracy and efficiency.

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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