Journal ArticleDOI
Homotopy analysis method: a new analytic method for nonlinear problems
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TLDR
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.read more
Citations
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Journal ArticleDOI
The homotopy perturbation method for nonlinear oscillators with discontinuities
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.
Journal ArticleDOI
Comparison of homotopy perturbation method and homotopy analysis method
TL;DR: Comparison of homotopy perturbation method (HPM) and Homotopy analysis method is made, revealing that the former is more powerful than the later.
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Optimal homotopy asymptotic method with application to thin film flow
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.
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A numerical solution of Blasius equation by Adomian’s decomposition method and comparison with homotopy perturbation method
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.
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New numerical surfaces to the mathematical model of cancer chemotherapy effect in Caputo fractional derivatives.
TL;DR: The q-homotopy analysis transform method is applied to the mathematical model of the cancer chemotherapy effect in the sense of Caputo fractional to find some new approximate numerical results for different values of parameters of alpha.
References
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Journal ArticleDOI
An approximate solution technique not depending on small parameters: A special example
TL;DR: In this paper, a simple non-linear equation is used to describe a kind of analytical technique for nonlinear problems, which is based on both homotopy in topology and the Maclaurin series.
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On the Solution of the Laminar Boundary Layer Equations
TL;DR: In this paper, it was shown that Pohlhausen's method agrees reasonably with the observed one up to a point about five-sevenths of the way between the pressure minimum and the observed point of separation.
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A kind of approximate solution technique which does not depend upon small parameters — II. An application in fluid mechanics
TL;DR: In this paper, the homotopy analysis method was further improved by introducing a non-zero parameter into the traditional way of constructing a homhotopy, which can converge even in the whole region η ϵ [0, + ∞].