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廖世俊

Bio: 廖世俊 is an academic researcher from Shanghai Jiao Tong University. The author has contributed to research in topics: Homotopy analysis method & Radius of convergence. The author has an hindex of 2, co-authored 2 publications receiving 168 citations.

Papers
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TL;DR: In this paper, the basic ideas of a new analytic technique, namely the Homotopy Analysis Method (HAM), are described, and the validity of the HAM is independent on whether or not there exist small parameters in considered nonlinear equations.
Abstract: In this paper, the basic ideas of a new analytic technique, namely the Homotopy Analysis Method (HAM), are described. Different from perturbation methods, the validity of the HAM is independent on whether or not there exist small parameters in considered nonlinear equations. Therefore, it provides us with a powerful analytic tool for strongly nonlinear problems. A typical nonlinear problem is used as an example to verify the validity and the great potential of the HAM.

186 citations

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TL;DR: A generalized Taylor series of a complex function was derived and related theorems about its convergence region were given in this paper, which can he applied to greatly enlarge convergence regions of approximation series given by other traditional techniques.
Abstract: A generalized Taylor series of a complex function was derived and some related theorems about its convergence region were given. The generalized Taylor theorem can he applied to greatly enlarge convergence regions of approximation series given by other traditional techniques. The rigorous proof of the generalized Taylor theorem also provides us with a rational base of the validity of a new kind of powerful analytic technique for nonlinear problems, namely the homotopy analysis method.

4 citations


Cited by
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Journal ArticleDOI
Ji-Huan He1
TL;DR: The homotopy perturbation method is applied to the nonlinear oscillators with discontinuities and only one iteration leads to high accuracy of the solutions.

871 citations

Journal ArticleDOI
Ji-Huan He1
TL;DR: Comparison of homotopy perturbation method (HPM) and Homotopy analysis method is made, revealing that the former is more powerful than the later.

613 citations

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TL;DR: 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.

231 citations

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TL;DR: The steady laminar flow and heat transfer of a second grade fluid over a radially stretching sheet is considered in this article, where axisymmetric flow is induced due to linear stretching of a sheet.

214 citations

Journal ArticleDOI
TL;DR: In this article, Adomian's decomposition method is proposed to solve the well-known Blasius equation, which is of high accuracy compared with homotopy perturbation method and Howarth's numerical solution.
Abstract: In this paper, Adomian’s decomposition method is proposed to solve the well-known Blasius equation. Comparison with homotopy perturbation method and Howarth’s numerical solution reveals that the Adomian’s decomposition method is of high accuracy.

161 citations