scholarly journals Dual Approximate Solutions of the Unsteady Viscous Flow over a Shrinking Cylinder with Optimal Homotopy Asymptotic Method

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Vasile Marinca ◽  
Remus-Daniel Ene
Keyword(s):  
Viscous Flow ◽  
Asymptotic Method ◽  
Numerical Solutions ◽  
Similarity Transformation ◽  
Approximate Solutions ◽  
Rapid Convergence ◽  
Unsteady Viscous Flow ◽  
Optimal Homotopy Asymptotic Method ◽  
Shrinking Surface ◽  
Good Agreement

The unsteady viscous flow over a continuously shrinking surface with mass suction is investigated using the optimal homotopy asymptotic method (OHAM). The nonlinear differential equation is obtained by means of the similarity transformation. The dual solutions exist for a certain range of mass suction and unsteadiness parameters. A very good agreement was found between our approximate results and numerical solutions, which prove that OHAM is very efficient in practice, ensuring a very rapid convergence after only one iteration.

Analytical approximate solutions to the Thomas-Fermi equation

Open Physics ◽  
2014 ◽  
Vol 12 (7) ◽  
Author(s):  
Vasile Marinca ◽  
Remus-Daniel Ene
Keyword(s):  
Excellent Agreement ◽  
Asymptotic Method ◽  
Numerical Solutions ◽  
Approximate Solutions ◽  
Rapid Convergence ◽  
Thomas Fermi ◽  
Small Parameters ◽  
Optimal Homotopy Asymptotic Method

AbstractThe purpose of this paper is to show how to use the Optimal Homotopy Asymptotic Method (OHAM) to solve the nonlinear differential Thomas-Fermi equation. Our procedure does not depend upon small parameters and provides us with a convenient way to optimally control the convergence of the approximate solutions. An excellent agreement was found between our approximate results and numerical solutions, which prove that OHAM is very efficient in practice, ensuring a very rapid convergence after only one iteration.

scholarly journals Analytic Approximate Solution for Falkner-Skan Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-22 ◽  
Author(s):  
Vasile Marinca ◽  
Remus-Daniel Ene ◽  
Bogdan Marinca
Keyword(s):  
Differential Equation ◽  
Boundary Layer ◽  
Numerical Solutions ◽  
Approximate Solutions ◽  
Rapid Convergence ◽  
Boundary Layer Problem ◽  
Small Parameters ◽  
Optimal Homotopy Asymptotic Method ◽  
Good Agreement ◽  
Layer Problem

This paper deals with the Falkner-Skan nonlinear differential equation. An analytic approximate technique, namely, optimal homotopy asymptotic method (OHAM), is employed to propose a procedure to solve a boundary-layer problem. Our method does not depend upon small parameters and provides us with a convenient way to optimally control the convergence of the approximate solutions. The obtained results reveal that this procedure is very effective, simple, and accurate. A very good agreement was found between our approximate results and numerical solutions, which prove that OHAM is very efficient in practice, ensuring a very rapid convergence after only one iteration.

scholarly journals Different Approximations to the Solution of Upper-Convected Maxwell Fluid over a Porous Stretching Plate

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Vasile Marinca ◽  
Remus-Daniel Ene ◽  
Bogdan Marinca ◽  
Romeo Negrea
Keyword(s):  
Numerical Solutions ◽  
Nonlinear Partial Differential Equations ◽  
Maxwell Fluid ◽  
Approximate Solutions ◽  
Two Dimensional ◽  
Rapid Convergence ◽  
Similarity Transformations ◽  
Optimal Homotopy Asymptotic Method ◽  
Stretching Plate ◽  
Good Agreement

In the present paper, we consider an incompressible magnetohydrodynamic flow of two-dimensional upper-convected Maxwell fluid over a porous stretching plate with suction and injection. The nonlinear partial differential equations are reduced to an ordinary differential equation by the similarity transformations and taking into account the boundary layer approximations. This equation is solved approximately by means of the optimal homotopy asymptotic method (OHAM). This approach is highly efficient and it controls the convergence of the approximate solutions. Different approximations to the solution are given, showing the exceptionally good agreement between the analytical and numerical solutions of the nonlinear problem. OHAM is very efficient in practice, ensuring a very rapid convergence of the solutions after only one iteration even though it does not need small or large parameters in the governing equation.

scholarly journals Application of the optimal homotopy asymptotic method to nonlinear Bingham fluid dampers

Open Physics ◽  
2017 ◽  
Vol 15 (1) ◽  
pp. 620-626 ◽  
Author(s):  
Vasile Marinca ◽  
Remus-Daniel Ene ◽  
Liviu Bereteu
Keyword(s):  
Asymptotic Method ◽  
Approximate Solutions ◽  
Bingham Fluid ◽  
Rapid Convergence ◽  
Bingham Model ◽  
Mr Dampers ◽  
Approximate Analytical Solutions ◽  
Small Parameters ◽  
Optimal Homotopy Asymptotic Method ◽  
Fluid Dampers

AbstractDynamic response time is an important feature for determining the performance of magnetorheological (MR) dampers in practical civil engineering applications. The objective of this paper is to show how to use the Optimal Homotopy Asymptotic Method (OHAM) to give approximate analytical solutions of the nonlinear differential equation of a modified Bingham model with non-viscous exponential damping. Our procedure does not depend upon small parameters and provides us with a convenient way to optimally control the convergence of the approximate solutions. OHAM is very efficient in practice for ensuring very rapid convergence of the solution after only one iteration and with a small number of steps.

scholarly journals Optimal Auxiliary Functions Method for viscous flow due to a stretching surface with partial slip

2018 ◽  
Vol 8 (1) ◽  
pp. 261-274
Author(s):  
Vasile Marinca ◽  
Remus-Daniel Ene ◽  
Valentin Bogdan Marinca
Keyword(s):  
Differential Equation ◽  
Viscous Flow ◽  
Numerical Solutions ◽  
Equation Of Motion ◽  
Partial Slip ◽  
Stretching Surface ◽  
Rapid Convergence ◽  
Third Order ◽  
Auxiliary Functions ◽  
Good Agreement

Abstract The viscous flow induced by a stretching surface with partial slip is investigated. The flow is governed by a third-order nonlinear differential equation, corresponding to the planar and axisymmetric stretching. The derived equation of motion is solved analytically by Optimal Auxiliary Functions Method (OAFM). This procedure is highly efficient and it controls the convergence of the approximate solution. A few examples are given, showing the exceptionally good agreement between the analytical and numerical solutions of the nonlinear problem. OAFM is very efficient in practice, ensuring a very rapid convergence after only one iteration.

Free and Forced Vibrations of the Strongly Nonlinear Cubic-Quintic Duffing Oscillators

2017 ◽  
Vol 72 (1) ◽  
pp. 59-69 ◽  
Author(s):  
M.M. Fatih Karahan ◽  
Mehmet Pakdemirli
Keyword(s):  
Numerical Simulations ◽  
Numerical Solutions ◽  
Multiple Scales ◽  
Approximate Solutions ◽  
Response Curves ◽  
Strongly Nonlinear ◽  
Free And Forced Vibrations ◽  
Approximate Analytical Solutions ◽  
Strongly Nonlinear Oscillators ◽  
Good Agreement

AbstractStrongly nonlinear cubic-quintic Duffing oscillatoris considered. Approximate solutions are derived using the multiple scales Lindstedt Poincare method (MSLP), a relatively new method developed for strongly nonlinear oscillators. The free undamped oscillator is considered first. Approximate analytical solutions of the MSLP are contrasted with the classical multiple scales (MS) method and numerical simulations. It is found that contrary to the classical MS method, the MSLP can provide acceptable solutions for the case of strong nonlinearities. Next, the forced and damped case is treated. Frequency response curves of both the MS and MSLP methods are obtained and contrasted with the numerical solutions. The MSLP method and numerical simulations are in good agreement while there are discrepancies between the MS and numerical solutions.

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.

Mathematical study of fractional-order biological population model using optimal homotopy asymptotic method

2016 ◽  
Vol 09 (06) ◽  
pp. 1650081 ◽  
Author(s):  
S. Sarwar ◽  
M. A. Zahid ◽  
S. Iqbal
Keyword(s):  
Fractional Order ◽  
Asymptotic Method ◽  
Population Model ◽  
Approximate Solutions ◽  
High Accuracy ◽  
Population Models ◽  
Mathematical Study ◽  
Third Order ◽  
Biological Population ◽  
Optimal Homotopy Asymptotic Method

In this paper, we study the fractional-order biological population models (FBPMs) with Malthusian, Verhulst, and porous media laws. The fractional derivative is defined in Caputo sense. The optimal homotopy asymptotic method (OHAM) for partial differential equations (PDEs) is extended and successfully implemented to solve FBPMs. Third-order approximate solutions are obtained and compared with the exact solutions. The numerical results unveil that the proposed extension in the OHAM for fractional-order differential problems is very effective and simple in computation. The results reveal the effectiveness with high accuracy and extremely efficient to handle most complicated biological population models.

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