scholarly journals The Optimal q-Homotopy Analysis Method (Oq-HAM)

2013 ◽  
Vol 11 (8) ◽  
pp. 2859-2866 ◽  
Author(s):  
Shaheed N Huseen ◽  
Said R.Grace ◽  
Magdy A. El-Tawil
Keyword(s):  
Homotopy Analysis Method ◽  
Control Parameter ◽  
Analysis Method ◽  
Optimal Homotopy Analysis Method ◽  
Homotopy Analysis ◽  
Convergence Control ◽  
One Step ◽  
The One ◽  
Convergence Control Parameter

In this paper, an optimal q-homotopy analysis method (Oq-HAM) is proposed. We present some examples to show the reliability and efficiency of the method. It is compared with the one-step optimal homotopy analysis method. The results reveal that the Oq-HAM has more accuracy to determine the convergence-control parameter than the one-step optimal HAM.

scholarly journals An effective approach for evaluation of the optimal convergence control parameter in the homotopy analysis method

Filomat ◽  
2016 ◽  
Vol 30 (6) ◽  
pp. 1633-1650 ◽  
Author(s):  
Mustafa Turkyilmazoglu
Keyword(s):  
Homotopy Analysis Method ◽  
Control Parameter ◽  
Real Life ◽  
Analysis Method ◽  
Level Curves ◽  
Homotopy Analysis ◽  
Convergence Control ◽  
Working Out ◽  
Convergence Control Parameter ◽  
Error Method

A rapid and effective way of working out the optimum parameter of convergence control in the homotopy analysis method (HAM) is introduced in this paper. As compared with the already known ways of evaluating the convergence control parameter in HAM either through the classical h-level curves with h being the convergence control parameter or from the classical squared residual formula as adopted in the HAM society, an elegant way of calculating the convergence control parameter yielding the same optimum values is offered. In most cases, the new method is shown to perform quicker and better against the residual error method when integrations are much harder to evaluate or even by numerical means. Examples originating from real life applications selected from the literature demonstrate the validity and usefulness of the introduced technique.

Modified Homotopy Analysis Method for Nonlinear Aeroelastic Behavior of Two Degree-of-Freedom Airfoils

2016 ◽  
Vol 16 (09) ◽  
pp. 1520001 ◽  
Author(s):  
Yaobin Niu ◽  
Zhongwei Wang ◽  
Dequan Wang ◽  
Bing Liu
Keyword(s):  
Homotopy Analysis Method ◽  
Control Parameter ◽  
Numerical Solutions ◽  
Degree Of Freedom ◽  
Aerodynamic Load ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
Convergence Control ◽  
Two Degree Of Freedom ◽  
Convergence Control Parameter

In this paper, the homotopy analysis method (HAM) is extended to deal with the nonlinear aeroelastic problem of a two degree-of-freedom (DOF) airfoil. To avoid determination of the parameter for the complicated high-order minimization problem, a new modified HAM is proposed based on the idea of minimizing the squared residual. Using this method, the convergence-control parameter is determined by the low order squared residual of the governing equations, and then the problem is solved in a way similar to the basic HAM. The proposed method is used to solve the nonlinear aeroelastic behavior of a supersonic airfoil, with the unsteady aerodynamic load evaluated by the piston theory. Two examples are prepared, for which the frequencies and amplitudes of the limit cycles are obtained. The approximate solutions obtained are demonstrated to agree excellently the numerical solutions, meanwhile, the convergence-control parameter can be easily determined using the present approach.

scholarly journals The One Step Optimal Homotopy Analysis Method to Circular Porous Slider

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Mohammad Ghoreishi ◽  
Ahmad Izani B. Md. Ismail ◽  
Abdur Rashid
Keyword(s):  
Reynolds Number ◽  
Approximate Solution ◽  
Homotopy Analysis Method ◽  
Momentum Equation ◽  
Analysis Method ◽  
Lateral Velocity ◽  
Optimal Homotopy Analysis Method ◽  
Homotopy Analysis ◽  
One Step ◽  
The One

An incompressible Newtonian fluid is forced through the porous of a circular slider which is moving laterally on a horizontal plan. In this paper, we introduce and apply the one step Optimal Homotopy Analysis Method (one step OHAM) to the problem of the circular porous slider where a fluid is injected through the porous bottom. The effects of mass injection and lateral velocity on the heat generated by viscous dissipation are investigated by solving the governing boundary layer equations using one step optimal homotopy technique. The approximate solution for the coupled nonlinear ordinary differential equations resulting from the momentum equation is obtained and discussed for different values of the Reynolds number of the velocity field. The solution obtained is also displayed graphically for various values of the Reynolds number and it is shown that the one step OHAM is capable of finding the approximate solution of circular porous slider.

scholarly journals Homotopy Analysis Solution for Magnetohydrodynamic Squeezing Flow in Porous Medium

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Inayat Ullah ◽  
M. T. Rahim ◽  
Hamid Khan ◽  
Mubashir Qayyum
Keyword(s):  
Porous Medium ◽  
Control Parameter ◽  
Analytical Techniques ◽  
Squeezing Flow ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
Convergence Control ◽  
Flow Through ◽  
Convergence Control Parameter ◽  
Good Agreement

The aim of the present work is to analyze the magnetohydrodynamic (MHD) squeezing flow through porous medium using homotopy analysis method (HAM). Fourth-order boundary value problem is modeled through stream functionψ(r,z)and transformationψ(r,z)=r2f(z). Absolute residuals are used to check the efficiency and consistency of HAM. Other analytical techniques are compared with the present work. It is shown that results of good agreement can be obtained by choosing a suitable value of convergence control parameterhin the valid regionRh. The influence of different parameters on the flow is argued theoretically as well as graphically.

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