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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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Journal of Applied Mathematics and Computing, 2008
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Alomari, A. K. +2 more
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Alomari, A. K. +2 more
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2017
In this chapter, the analytic solution of nonlinear partial differential equations arising in heat transfer is obtained using the newly developed analytic method, namely the Homotopy Analysis Method (HAM). The homotopy analysis method provides us with a new way to obtain series solutions of such problems.
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In this chapter, the analytic solution of nonlinear partial differential equations arising in heat transfer is obtained using the newly developed analytic method, namely the Homotopy Analysis Method (HAM). The homotopy analysis method provides us with a new way to obtain series solutions of such problems.
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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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Comparison between Homotopy Analysis Method and Homotopy Renormalization Method
SSRN Electronic Journal, 2022Yu Yang, Shijun Liao
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On the homotopy analysis method for nonlinear problems
Applied Mathematics and Computation, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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