Implementation of the Method of Fundamental Solutions and Homotopy Analysis Method for Solving a Torsion Problem of a Rod Made of Functionally Graded Material

2010 ◽  
Vol 123-125 ◽  
pp. 551-554 ◽  
Author(s):  
Anita Uscilowska
Keyword(s):  
Homotopy Analysis Method ◽  
Circular Cross Section ◽  
Numerical Procedure ◽  
Fundamental Solutions ◽  
Functionally Graded ◽  
Method Of Fundamental Solutions ◽  
Torsion Problem ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
Graded Material

The purpose of this paper is the application of Method of Fundamental Solutions (MFS) to the torsion problem of hollow rods made with functionally graded materials. This method belongs to so-called meshless methods. The proposal of the paper is to solve the problem by numerical procedure, which is proper combinations of the Method of Fundamental Solutions, the approximation by Radial Basis Functions (RBF) and Homotopy Analysis Method. The numerical experiment has been performed for the bar with circular cross-section.

scholarly journals The Approximate Solutions of Fredholm Integrodifferential-Difference Equations with Variable Coefficients via Homotopy Analysis Method

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Seydi Battal Gazi Karakoç ◽  
Aytekin Eryılmaz ◽  
Musa Başbük
Keyword(s):  
Difference Equations ◽  
Homotopy Analysis Method ◽  
Algebraic System ◽  
Numerical Solutions ◽  
Numerical Procedure ◽  
Approximate Solutions ◽  
Variable Coefficients ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
Linear And Nonlinear

Numerical solutions of linear and nonlinear integrodifferential-difference equations are presented using homotopy analysis method. The aim of the paper is to present an efficient numerical procedure for solving linear and nonlinear integrodifferential-difference equations. The reliability and efficiency of the proposed scheme are demonstrated by some numerical experiments and performed on the computer algebraic system.

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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