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Simplified Liénard Equation by Homotopy Analysis Method
Differential Equations and Dynamical Systems, 2017In this article the author used Homotopy analysis method (HAM) to solve a simplified Lienard's equation. (HAM) method is one of the easiest way to assure the convergence of solution to a series so that it is valid even if nonlinearity becomes quite strong.
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Homotopy Analysis Method for Stochastic Differential Equations with Maxima
2015The homotopy analysis method known from its successful applications to obtain quasi-analytical approximations of solutions of ordinary and partial differential equations is applied to stochastic differential equations with Gaussian stochastic forces. It has been found that the homotopy analysis method yields excellent agreement with exact results when ...
Maciej Janowicz +4 more
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Optimal Homotopy Analysis Method
2017Optimal homotopy analysis method is a powerful tool for nonlinear differential equations. In this method, the convergence of the series solutions is controlled by one or more parameters which can be determined by minimizing a certain function. There are several approaches to determine the optimal values of these parameters, which can be divided into ...
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Optimal Homotopy Analysis Method
2012In this chapter, we describe and compare the different optimal approaches of the homotopy analysis method (HAM). A generalized optimal HAM is proposed, which logically contains the basic optimal HAM with only one convergence-control parameter and also the optimal HAM with an infinite number of parameters.
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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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Comparison between Homotopy Analysis Method and Homotopy Renormalization Method
SSRN Electronic Journal, 2022Yu Yang, Shijun Liao
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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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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.
Kuppalapalle Vajravelu +1 more
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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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Homotopy Analysis Method for an Epidemic Model
20143, 11, Walailak Journal of Science and ...
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