Journal ArticleDOI
Optimal homotopy asymptotic method with application to thin film flow
TLDR
In this paper, the Optimal Homotopy Asymptotic Method (OHAM) has been applied to thin film flow of a fourth grade fluid down a vertical cylinder and the results reveal that the proposed method is very accurate, effective and easy to use.Abstract:
A new approximate analytical technique to address for non-linear problems, namely Optimal Homotopy Asymptotic Method (OHAM) is proposed and has been applied to thin film flow of a fourth grade fluid down a vertical cylinder. This approach however, does not depend upon any small/large parameters in comparison to other perturbation method. This method provides a convenient way to control the convergence of approximation series and allows adjustment of convergence regions where necessary. The series solution has been developed and the recurrence relations are given explicitly. The results reveal that the proposed method is very accurate, effective and easy to use.read more
Citations
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Journal ArticleDOI
An optimal homotopy-analysis approach for strongly nonlinear differential equations
TL;DR: In this paper, an optimal homotopy analysis approach is described by means of the nonlinear Blasius equation as an example, which can be used to get fast convergent series solutions of different types of equations with strong nonlinearity.
Journal ArticleDOI
Determination of periodic solutions for the motion of a particle on a rotating parabola by means of the optimal homotopy asymptotic method
TL;DR: In this article, an analytic approximate technique, namely optimal homotopy asymptotic method (OHAM), is employed to solve nonlinear oscillations of a particle which moves on a rotating parabola.
Journal ArticleDOI
Application of optimal homotopy asymptotic method for the analytic solution of singular Lane–Emden type equation
S. A. Iqbal,A. Javed +1 more
TL;DR: In this paper, an optimal homotopy asymptotic method is applied on singular initial value Lane-Emden type problems to check the effectiveness and performance of the method.
Journal ArticleDOI
MHD flow and heat transfer over a porous shrinking surface with velocity slip and temperature jump
TL;DR: A new technique is proposed to avoid the so called “secular” terms and to improve the computation efficiency of the HAM to arrive at the convergence results by a third order iterative, which is better than that of a twenty-fifth order iteratives in the literature obtained by classical HAM.
A new analytical approach to nonlinear vibration of an electrical machine
TL;DR: In this article, the nonlinear dynamic behavior of an electrical machine exhibiting nonlinear vibration is investigated using a new analytical technique, namely Optimal Homotopy Asymptotic Method.
References
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Book
Perturbation Methods
Ali H. Nayfeh,Vimal Singh +1 more
TL;DR: This website becomes a very available place to look for countless perturbation methods sources and sources about the books from countries in the world are provided.
Journal ArticleDOI
Homotopy perturbation technique
TL;DR: In this paper, the homotopy perturbation technique does not depend upon a small parameter in the equation and can be obtained uniformly valid not only for small parameters, but also for very large parameters.
Book
Introduction to perturbation techniques
TL;DR: In this paper, the authors introduce the notion of forced Oscillations of the Duffing Equation and the Mathieu Equation for weakly nonlinear systems with quadratic and cubic nonlinearities.
Book
Perturbation Methods in Applied Mathematics
TL;DR: In this paper, limit process expansions applied to Ordinary Differential Equations (ODE) are applied to partial differential equations (PDE) in the context of Fluid Mechanics.
Journal ArticleDOI
Some asymptotic methods for strongly nonlinear equations
TL;DR: In this paper, a survey of recent developments in asymptotic techniques, which are valid not only for weakly nonlinear equations, but also for strongly ones, is presented.