scholarly journals A Simple Modification of Homotopy Perturbation Method for the Solution of Blasius Equation in Semi-Infinite Domains

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
M. Aghakhani ◽  
M. Suhatril ◽  
M. Mohammadhassani ◽  
M. Daie ◽  
A. Toghroli
Keyword(s):  
Boundary Condition ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Simple Modification ◽  
Infinite Domains ◽  
Homotopy Perturbation ◽  
Blasius Equation ◽  
Fifth Order ◽  
Adomian’S Polynomials ◽  
Good Agreement

A simple modification of the homotopy perturbation method is proposed for the solution of the Blasius equation with two different boundary conditions. Padé approximate is used to deal with the boundary condition at infinity. The results obtained from the analytical method are compared to Howarth’s numerical solution and fifth order Runge-Kutta Fehlberg method indicating a very good agreement. The proposed method is a simple and reliable modification of homotopy perturbation method, which does not require the existence of a small parameter, linearization of the equation, or computation of Adomian’s polynomials.

scholarly journals Solution of the inverse heat conduction problem with Neumann boundary condition by using the homotopy perturbation method

2013 ◽  
Vol 17 (3) ◽  
pp. 643-650 ◽  
Author(s):  
Edyta Hetmaniok ◽  
Iwona Nowak ◽  
Damian Slota ◽  
Roman Witula ◽  
Adam Zielonka
Keyword(s):  
Boundary Condition ◽  
Heat Conduction ◽  
Perturbation Method ◽  
Neumann Boundary Condition ◽  
Homotopy Perturbation Method ◽  
Heat Conduction Problem ◽  
Neumann Boundary ◽  
Inverse Heat Conduction Problem ◽  
Inverse Heat Conduction ◽  
Homotopy Perturbation

In the paper a solution of the inverse heat conduction problem with the Neumann boundary condition is presented. For finding this solution the homotopy perturbation method is applied. Investigated problem consists in calculation of the temperature distribution in considered domain, as well as in reconstruction of the functions describing the temperature and the heat flux on the boundary, in case when the temperature measurements in some points of the domain are known. An example confirming usefulness of the homotopy perturbation method for solving problems of this kind are also included.

Solution for Celebrated Blasius Problem Using Homotopy Perturbation Method

2020 ◽  
Vol 12 (2) ◽  
pp. 284-287
Author(s):  
Monika Rani ◽  
Vikramjeet Singh ◽  
Rakesh Goyal
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Perturbation Method ◽  
High Speed ◽  
Homotopy Perturbation Method ◽  
Initial Slope ◽  
Moving Wall ◽  
Homotopy Perturbation ◽  
Blasius Problem ◽  
Blasius Equation

In this manuscript, we have analyzed Celebrated Blasius boundary problem with moving wall or high speed 2D laminar viscous flow over gasifying flat plate. To find the way out of this nonlinear differential equation, a version of semi-analytical homotopy perturbation method has been applied. It has been observed that the precision of the solution would be achieved with increasing approximations. On comparison with literature, our solution has been proven highly accurate and valid with faster rate of convergence. It has been revealed that the second order approximate solution of Blasius equation in terms of initial slope is obtained as 0.33315 reducing the error by 0.32%.

scholarly journals Solving Heat and Wave-Like Equations Using He's Polynomials

2009 ◽  
Vol 2009 ◽  
pp. 1-12 ◽  
Author(s):  
Syed Tauseef Mohyud-Din
Keyword(s):  
Perturbation Method ◽  
Decomposition Method ◽  
Homotopy Perturbation Method ◽  
Iterative Scheme ◽  
Nonlinear Problems ◽  
Homotopy Perturbation ◽  
He’S Polynomials ◽  
Clear Advantage ◽  
Suggested Technique ◽  
Adomian’S Polynomials

We use He's polynomials which are calculated form homotopy perturbation method (HPM) for solving heat and wave-like equations. The proposed iterative scheme finds the solution without any discretization, linearization, or restrictive assumptions. Several examples are given to verify the reliability and efficiency of the method. The fact that suggested technique solves nonlinear problems without using Adomian's polynomials is a clear advantage of this algorithm over the decomposition method.

Numerical inversion method for the Laplace transform based on Boubaker polynomials operational matrix

2021 ◽  
Author(s):  
Rachid Belgacem ◽  
Ahmed Bokhari ◽  
Salih Djilali ◽  
Sunil Kumar
Keyword(s):  
Laplace Transform ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Operational Matrix ◽  
Inversion Method ◽  
Numerical Inversion ◽  
Homotopy Perturbation ◽  
Boubaker Polynomials ◽  
The Laplace Transform ◽  
Good Agreement

We investigate through this research the numerical inversion technique for the Laplace transforms cooperated by the integration Boubaker polynomials operational matrix. The efficiency of the presented approach is demonstrated by solving some differential equations. Also, this technique is combined with the standard Laplace Homotopy Perturbation Method. The numerical results highlight that there is a very good agreement between the estimated solutions with exact solutions.

scholarly journals Homotopy perturbation method for a Stefan problem with variable latent heat

2014 ◽  
Vol 18 (2) ◽  
pp. 391-398 ◽  
Author(s):  
R Rajeev
Keyword(s):  
Approximate Solution ◽  
Analytical Solution ◽  
Perturbation Method ◽  
Latent Heat ◽  
Stefan Problem ◽  
Homotopy Perturbation Method ◽  
Homotopy Perturbation ◽  
Variable Latent Heat ◽  
Good Agreement

In this paper, homotopy perturbation method is successfully applied to find an approximate solution of one phase Stefan problem with variable latent heat. The results thus obtained are compared graphically with a published analytical solution and are in good agreement.

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