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Comparison between Homotopy Analysis Method and Homotopy Renormalization Method
SSRN Electronic Journal, 2022Yu Yang, Shijun Liao
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Homotopy analysis method: A new analytic method for nonlinear problems
Applied Mathematics and Mechanics, 1998In 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
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General boundary element method: an application of homotopy analysis method
Communications in Nonlinear Science and Numerical Simulation, 1998zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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KBM method based on the homotopy analysis
Science China Physics, Mechanics and Astronomy, 2011The KBM method is effective in solving nonlinear problems. Unfortunately, the traditional KBM method strongly depends on a small parameter, which does not exist in most of the practice physical systems. Therefore this method is limited to dealing with the system with strong nonlinearity.
YanBin Liu, YuShu Chen
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On two new applications of the homotopy analysis method and the homotopy perturbation method
Physica Scripta, 2010We discuss two recent applications of the homotopy analysis method and the homotopy perturbation method and conclude that the results are of no physical or mathematical utility at all.
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Newton-homotopy analysis method for nonlinear equations
Applied Mathematics and Computation, 2007zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Abbasbandy, S., Tan, Y., Liao, S. J.
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Advances in the Homotopy Analysis Method
2013A Short Review of Homotopy Analysis Method: Change and Challenge Predictor Homotopy Analysis Method Spectral Homotopy Analysis Method Stability of Auxiliary Linear Operator and Convergence - Control Parameter On the Convergence of the Homotopy Analysis Method Homotopy Analysis Method for Some Boundary Layer Flows of Nanofluids Homotopy Analysis Method ...
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Homotopy analysis method applied to electrohydrodynamic flow
Communications in Nonlinear Science and Numerical Simulation, 2011zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Further Applications of the Homotopy Analysis Method
2012Here in this chapter, we present analytical solutions to additional problems of practical interest, using homotopy analysis method. Included are a fluid flow and heat transfer problem, as well as an ill-posed problem related to the flow of a thin fluid film.
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