Application of optimal homotopy asymptotic method for the analytic solution of singular Lane–Emden type equation

2011 ◽  
Vol 217 (19) ◽  
pp. 7753-7761 ◽  
Author(s):  
S. Iqbal ◽  
A. Javed
Keyword(s):  
Asymptotic Method ◽  
Analytic Solution ◽  
Type Equation ◽  
Optimal Homotopy Asymptotic Method

scholarly journals Optimal Homotopy Asymptotic Method for Solving Delay Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
N. Ratib Anakira ◽  
A. K. Alomari ◽  
I. Hashim
Keyword(s):  
Differential Equations ◽  
Asymptotic Method ◽  
Delay Differential Equations ◽  
Perturbation Methods ◽  
Analytic Solution ◽  
Approximate Analytic Solution ◽  
Initial Value ◽  
Optimal Homotopy Asymptotic Method ◽  
Delay Differential ◽  
First Time

We extend for the first time the applicability of the optimal homotopy asymptotic method (OHAM) to find the algorithm of approximate analytic solution of delay differential equations (DDEs). The analytical solutions for various examples of linear and nonlinear and system of initial value problems of DDEs are obtained successfully by this method. However, this approach does not depend on small or large parameters in comparison to other perturbation methods. This method provides us with a convenient way to control the convergence of approximation series. The results which are obtained revealed that the proposed method is explicit, effective, and easy to use.

An Optimal Homotopy Asymptotic Method Solution of Injection of a Newtonian Fluid Through One Side of a Long Vertical Channel

2011 ◽  
Vol 42 (3) ◽  
pp. 267-283
Author(s):  
Rehan Ali Shah ◽  
Saeed Islam ◽  
A. M. Siddiqui ◽  
Ishtiaq Ali ◽  
Manzoor Ellahi
Keyword(s):  
Newtonian Fluid ◽  
Asymptotic Method ◽  
Vertical Channel ◽  
Optimal Homotopy Asymptotic Method

scholarly journals Optimal Homotopy Asymptotic Method for a thin film flow of a pseudo plastic fluid draining down or lifting up on a cylindrical surface

2013 ◽  
Vol 19 (4) ◽  
pp. 513-527
Author(s):  
Kamran Alam ◽  
M.T. Rahim ◽  
S. Islam ◽  
A.M. Sidiqqui
Keyword(s):  
Thin Film ◽  
Asymptotic Method ◽  
Cylindrical Surface ◽  
Film Flow ◽  
Vertical Cylinder ◽  
Stokes Number ◽  
Velocity Shear ◽  
Thin Film Flow ◽  
Fluid Velocities ◽  
Optimal Homotopy Asymptotic Method

In this study, the pseudo plastic model is used to obtain the solution for the steady thin film flow on the outer surface of long vertical cylinder for lifting and drainage problems. The non-linear governing equations subject to appropriate boundary conditions are solved analytically for velocity profiles by a modified homotopy perturbation method called the Optimal Homotopy Asymptotic method. Expressions for the velocity profile, volume flux, average velocity, shear stress on the cylinder, normal stress differences, force to hold the vertical cylindrical surface in position, have been derived for both the problems. For the non-Newtonian parameter ?=0, we retrieve Newtonian cases for both the problems. We also plotted and discussed the affect of the Stokes number St, the non-Newtonian parameter ? and the thickness ? of the fluid film on the fluid velocities.

Approximate Solutions to a Cantilever Beam Using Optimal Homotopy Asymptotic Method

2013 ◽  
Vol 430 ◽  
pp. 22-26 ◽  
Author(s):  
Vasile Marinca ◽  
Nicolae Herisanu ◽  
Traian Marinca
Keyword(s):  
Small Parameter ◽  
Cantilever Beam ◽  
Asymptotic Method ◽  
Approximate Solutions ◽  
Lumped Mass ◽  
Engineering Problems ◽  
Approximate Frequency ◽  
Optimal Homotopy Asymptotic Method ◽  
Analytical Expressions

The response of a cantilever beam with a lumped mass attached to its free end subject to harmonical excitation at the base is investigated by means of the Optimal Homotopy Asymptotic Method (OHAM). Approximate accurate analytical expressions for the solutions and for approximate frequency are determined. This method does not require any small parameter in the equation. The obtained results prove that our method is very accurate, effective and simple for investigation of such engineering problems.

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