scholarly journals Analytic approximate solution for the Bratu's problem by optimal homotopy analysis method

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Hany N. Hassan ◽  
Mourad S. Semary
Keyword(s):  
Approximate Solution ◽  
Homotopy Analysis Method ◽  
Analysis Method ◽  
Optimal Homotopy Analysis Method ◽  
Bratu’S Problem ◽  
Homotopy Analysis

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.

Optimal Homotopic Exploration of features of Cattaneo-Christov model in Second Grade Nanofluid flow via Darcy-Forchheimer medium subject to Viscous Dissipation and Thermal Radiation

2021 ◽  
Vol 24 ◽  
Author(s):  
Ghulam Rasool ◽  
Anum Shafiq ◽  
Yu-Ming Chu ◽  
Muhammad Shoaib Bhutta ◽  
Amjad Ali
Keyword(s):  
Temperature Distribution ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Skin Friction ◽  
Homotopy Analysis Method ◽  
Stream Velocity ◽  
Analysis Method ◽  
Nanofluid Flow ◽  
Optimal Homotopy Analysis Method ◽  
Homotopy Analysis

Introduction: In this article Optimal Homotopy analysis method (oHAM) is used for exploration of the features of Cattaneo-Christov model in viscous and chemically reactive nanofluid flow through a porous medium with stretching velocity at the solid/sheet surface and free stream velocity at the free surface. Methods: The two important aspects, Brownian motion and Thermophoresis are considered. Thermal radiation is also included in present model. Based on the heat and mass flux, the Cattaneo-Christov model is implemented on the Temperature and Concentration distributions. The governing Partial Differential Equations (PDEs) are converted into Ordinary Differential Equations (ODEs) using similarity transformations. The results are achieved using the optimal homotopy analysis method (oHAM). The optimal convergence and residual errors have been calculated to preserve the validity of the model. Results: The results are plotted graphically to see the variations in three main profiles i.e. momentum, temperature and concentration profile. Conclusion: The outcomes indicate that skin friction enhances due to implementation of Darcy medium. It is also noted that the relaxation time parameter results in enhancement of the temperature distribution. Thermal radiation enhances the temperature distribution and so is the case with skin friction.

Application of Optimal Homotopy Analysis Method for Solitary Wave Solutions of Kuramoto-Sivashinsky Equation

2011 ◽  
Vol 66 (1-2) ◽  
pp. 117-122
Author(s):  
Qi Wang
Keyword(s):  
Solitary Wave ◽  
Homotopy Analysis Method ◽  
Solitary Wave Solutions ◽  
Analysis Method ◽  
Convergence Region ◽  
Optimal Method ◽  
Optimal Homotopy Analysis Method ◽  
Wave Solutions ◽  
Homotopy Analysis ◽  
Sivashinsky Equation

In this paper, the optimal homotopy analysis method is applied to find the solitary wave solutions of the Kuramoto-Sivashinsky equation. With three auxiliary convergence-control parameters, whose possible optimal values can be obtained by minimizing the averaged residual error, the method used here provides us with a simple way to adjust and control the convergence region of the solution. Compared with the usual homotopy analysis method, the optimal method can be used to get much faster convergent series solutions.

scholarly journals Application of the Homotopy Method for Fractional Inverse Stefan Problem

Energies ◽  
2020 ◽  
Vol 13 (20) ◽  
pp. 5474
Author(s):  
Damian Słota ◽  
Agata Chmielowska ◽  
Rafał Brociek ◽  
Marcin Szczygieł
Keyword(s):  
Heat Flux ◽  
Approximate Solution ◽  
Temperature Distribution ◽  
Continuous Function ◽  
Homotopy Analysis Method ◽  
Input Data ◽  
Sufficient Condition ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
The One

The paper presents an application of the homotopy analysis method for solving the one-phase fractional inverse Stefan design problem. The problem was to determine the temperature distribution in the domain and functions describing the temperature and the heat flux on one of the considered area boundaries. It was demonstrated that if the series constructed for the method is convergent then its sum is a solution of the considered equation. The sufficient condition of this convergence was also presented as well as the error of the approximate solution estimation. The paper also includes the example presenting the application of the described method. The obtained results show the usefulness of the proposed method. The method is stable for the input data disturbances and converges quickly. The big advantage of this method is the fact that it does not require discretization of the area and the solution is a continuous function.

Homotopy analysis method approximate solution for fuzzy pantograph equation

2021 ◽  
Vol 14 (3) ◽  
pp. 286
Author(s):  
A.H. Shather ◽  
A.F. Jameel ◽  
N.R. Anakira ◽  
A.K. Alomari ◽  
Azizan Saaban
Keyword(s):  
Approximate Solution ◽  
Homotopy Analysis Method ◽  
Analysis Method ◽  
Pantograph Equation ◽  
Homotopy Analysis
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