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Beyond Perturbation: Introduction to the Homotopy Analysis Method
Shijun Liao,SA Sherif +1 more
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TLDR
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 BIBLIOGRAbstract:
PART I BASIC IDEAS Introduction Illustrative Description Systematic Description Relations to Some Previous Analytic Methods Advantages, Limitations, and Open Questions PART II APPLICATIONS 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 Oscillation Systems with Quadratic Nonlinearity Limit Cycle in a Multidimensional System Blasius' viscous Flow Boundary-layer Flow with Exponential Property Boundary-layer Flow with Algebraic Property Von Karman Swirling Flow Nonlinear Progressive Waves in Deep Water BIBLIOGRAPHY INDEXread more
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Journal ArticleDOI
Homotopy Perturbation Method for Bifurcation of Nonlinear Problems
TL;DR: In this article, a simple homotopy is constructed by the modified Lindstedt-Poincare method, by the solution and the coefficient of linear term are expanded into series of the embedding parameter.
Book
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
Notes on the homotopy analysis method: Some definitions and theorems
TL;DR: 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.
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
The application of homotopy analysis method to nonlinear equations arising in heat transfer
TL;DR: In this paper, the homotopy analysis method (HAM) is compared with the numerical and HPM in the heat transfer file and the auxiliary parameter ℏ, which provides a simple way to adjust and control the convergence region of solution series.