Journal ArticleDOI
Notes on the homotopy analysis method: Some definitions and theorems
TLDR
In this article, the basic ideas and current developments of the homotopy analysis method, an analytic approach to get convergent series solutions of strongly nonlinear problems, which recently attracts interests of more and more researchers, are described.About:
This article is published in Communications in Nonlinear Science and Numerical Simulation.The article was published on 2009-04-01. It has received 835 citations till now. The article focuses on the topics: Homotopy analysis method & n-connected.read more
Citations
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Homotopy Analysis Method in Nonlinear Differential Equations
TL;DR: In this paper, a convergence series for Divergent Taylor Series is proposed to solve nonlinear initial value problems and nonlinear Eigenvalue problems with free or moving boundary in heat transfer.
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
Shape effects of nanosize particles in Cu-H2O nanofluid on entropy generation
TL;DR: In this article, a mathematical model is analyzed in order to study the natural convection boundary layer flow along an inverted cone, where the shape of nanosize particles on entropy generation with based fluid is considered.
Journal ArticleDOI
Stagnation-point flow of a nanofluid towards a stretching sheet
TL;DR: In this article, the authors reported the flow of a nanofluid near a stagnation point towards a stretching surface and the effects of Brownian motion and thermophoresis are further taken into account.
Journal ArticleDOI
Cattaneo-Christov heat flux model for rotating flow and heat transfer of upper-convected Maxwell fluid
TL;DR: In this article, the Cattaneo-Christov heat flux model is used to investigate the rotating flow of viscoelastic fluid bounded by a stretching surface and the boundary layer equations are first modeled and then reduced to self-similar forms via similarity approach.
References
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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.
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
Beyond Perturbation: Introduction to the Homotopy Analysis Method
Shijun Liao,SA Sherif +1 more
TL;DR: In this paper, a simple bifurcation of a nonlinear problem multiple solutions of a Nonlinear Problem Nonlinear Eigenvalue Problem Thomas-Fermi Atom Model Volterra's Population Model Free Oscillation Systems with Odd Nonlinearity Free oscillations with Quadratic nonlinearity Limit Cycle in a Multidimensional System Blasius' viscous flow Boundary-layer Flow Boundarylayer Flow with Exponential Property Boundary Layer Flow with Algebraic Property Von Karman Swirling Flow Nonlinear Progressive Waves in Deep Water BIBLIOGR
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.