Numerical solution of Painlev̀e equation I by optimal homotopy asymptotic method

2013 ◽  
Author(s):  
Fazle Mabood ◽  
Ahmad Izani Md Ismail ◽  
Ishak Hashim
Keyword(s):  
Numerical Solution ◽  
Asymptotic Method ◽  
Optimal Homotopy Asymptotic Method

scholarly journals Optimal homotopy asymptotic method to large post-buckling deformation of MEMS

2018 ◽  
Vol 148 ◽  
pp. 13003 ◽  
Author(s):  
Nicolae Herisanu ◽  
Vasile Marinca
Keyword(s):  
Differential Equation ◽  
Numerical Solution ◽  
Approximate Method ◽  
Excellent Agreement ◽  
Electrostatic Field ◽  
Asymptotic Method ◽  
Integro Differential Equation ◽  
Analytical Results ◽  
Post Buckling ◽  
Optimal Homotopy Asymptotic Method

In the present paper, the post-buckling response of an axially stressed clamped-clamped actuator, modeled as a beam and subjected to a symmetric electrostatic field is analyzed. An analytical approximate method, namely the Optimal Homotopy Asymptotic Method (OHAM) is applied to the governing nonlinear integro-differential equation. The analytical results obtained through the proposed procedure show excellent agreement with numerical solution, proving the validity of the proposed procedure, which is simple and easy to use.

scholarly journals Systematic Review of Geometrical Approaches and Analytical Integration for Chen’s System

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1530
Author(s):  
Remus-Daniel Ene ◽  
Camelia Pop ◽  
Camelia Petrişor
Keyword(s):  
Systematic Review ◽  
Approximate Solution ◽  
Numerical Simulations ◽  
Numerical Solution ◽  
Asymptotic Method ◽  
Analytical Integration ◽  
Optimal Homotopy Asymptotic Method ◽  
Special Case

The main goal of this paper is to present an analytical integration in connection with the geometrical frame given by the Hamilton–Poisson formulation of a specific case of Chen’s system. In this special case we construct an analytic approximate solution using the Multistage Optimal Homotopy Asymptotic Method (MOHAM). Numerical simulations are also presented in order to make a comparison between the analytic approximate solution and the corresponding numerical solution.

scholarly journals Numerical solution of 2D-fuzzy Fredholm integral equations using optimal homotopy asymptotic method

2021 ◽  
Vol 60 (2) ◽  
pp. 2483-2490
Author(s):  
Sumbal Ahsan ◽  
Rashid Nawaz ◽  
Muhammad Akbar ◽  
Kottakkaran Sooppy Nisar ◽  
Emad E. Mahmoud ◽  
...  
Keyword(s):  
Numerical Solution ◽  
Integral Equations ◽  
Asymptotic Method ◽  
Fredholm Integral Equations ◽  
Optimal Homotopy Asymptotic Method

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.

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