scholarly journals Optimal homotopy asymptotic method for solving fractional relaxation-oscillation equation

2015 ◽  
Vol 2015 (2) ◽  
pp. 98-111 ◽  
Author(s):  
Mohammad Hamarsheh ◽  
Ahmad Ismail ◽  
Zaid Odibat
Keyword(s):  
Asymptotic Method ◽  
Relaxation Oscillation ◽  
Optimal Homotopy Asymptotic Method ◽  
Fractional Relaxation ◽  
Oscillation Equation

Exact Analytical Solution of Fractional Relaxation-Oscillation Equation by Adomian Decomposition and He’s Variational Technique

2009 ◽  
Author(s):  
K. C. Basak ◽  
P. C. Ray ◽  
R. K. Bera
Keyword(s):  
Exact Solution ◽  
Analytical Solution ◽  
Fractional Order ◽  
Decomposition Method ◽  
Exact Analytical Solution ◽  
Relaxation Oscillation ◽  
Variational Technique ◽  
Adomian Decomposition ◽  
Fractional Relaxation ◽  
Oscillation Equation

Exact solution of linear fractional relaxation-oscillation equation is obtained by the decomposition method of Adomian and also by He’s variational method for fractional order α, for 1 < α ≤ 2. Surface plots of the above solution are drawn for different values of fractional order α and time t. Amplitude of the oscillation increases with α but it decreases as time increases.

scholarly journals Numerical approach for solving fractional relaxation–oscillation equation

2013 ◽  
Vol 37 (8) ◽  
pp. 5927-5937 ◽  
Author(s):  
Mustafa Gülsu ◽  
Yalçın Öztürk ◽  
Ayşe Anapalı
Keyword(s):  
Relaxation Oscillation ◽  
Numerical Approach ◽  
Fractional Relaxation ◽  
Oscillation Equation

Generalized wavelet collocation method for solving fractional relaxation–oscillation equation arising in fluid mechanics

2017 ◽  
Vol 06 (02) ◽  
pp. 1750016
Author(s):  
Firdous A. Shah ◽  
R. Abass
Keyword(s):  
Fluid Mechanics ◽  
Relaxation Oscillation ◽  
Operational Matrix ◽  
Haar Wavelet ◽  
Test Problems ◽  
Operational Matrices ◽  
Algebraic Equations ◽  
Specific Test ◽  
Fractional Relaxation ◽  
Oscillation Equation

In this paper, a generalized wavelet collocation operational matrix method based on Haar wavelets is proposed to solve fractional relaxation–oscillation equation arising in fluid mechanics. Contrary to wavelet operational methods accessible in the literature, we derive an explicit form for the Haar wavelet operational matrices of fractional order integration without using the block pulse functions. The properties of the Haar wavelet expansions together with operational matrix of integration are utilized to convert the problems into systems of algebraic equations with unknown coefficients. The performance of the numerical scheme is assessed and tested on specific test problems and the comparisons are given with other methods existing in the recent literature. The numerical outcomes indicate that the method yields highly accurate results and is computationally more efficient than the existing ones.

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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