Results 141 to 150 of about 2,716 (179)

Application of homotopy perturbation method and homotopy analysis method to fractional vibration equation

International Journal of Computer Mathematics, 2010
In this paper, the approximate analytical solutions of the mathematical model of vibration equation with fractional-order time derivative β ...
Subir Das, Praveen Kumar Gupta
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Shooting homotopy analysis method

Engineering Computations, 2017
Purpose The purpose of this paper is to present a new method based on the homotopy analysis method (HAM) with the aim of fast searching and calculating multiple solutions of nonlinear boundary value problems (NBVPs). Design/methodology/approach A major problem with the previously modified HAM, namely, predictor homotopy analysis method, which is ...
L. Ahmad Soltani, E. Shivanian, Reza Ezzati   +2 more
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Application of Homotopy Analysis Method in Nonlinear Oscillations

Journal of Applied Mechanics, 1998
In this paper, we apply a new analytical technique for nonlinear problems, namely the Homotopy Analysis Method (Liao 1992a), to give two-period formulas for oscillations of conservative single-degree-of-freedom systems with odd nonlinearity. These two formulas are uniformly valid for any possible amplitudes of oscillation.
Chwang, AT, Liao, SJ
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A study on the convergence of homotopy analysis method

Applied Mathematics and Computation, 2010
The author first briefly reviews the homotopy analysis method of [\textit{S. J. Liao}, Beyond perturbation: Introduction to the homotopy analysis method. CRC Series: Modern Mechanics and Mathematics. Boca Raton, FL: Chapman and Hall/CRC. (2004; Zbl 1051.76001)].
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Comparison of homotopy analysis method and homotopy perturbation method through an evolution equation

Communications in Nonlinear Science and Numerical Simulation, 2009
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Liang, Songxin, Jeffrey, David J.
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The improved homotopy analysis method for the Thomas–Fermi equation

Applied Mathematics and Computation, 2012
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yinlong Zhao, Zhiliang Lin, Zeng Liu, Shijun Liao   +3 more
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On two new applications of the homotopy analysis method and the homotopy perturbation method

Physica Scripta, 2010
We 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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Homotopy Analysis Method

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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Simplified Liénard Equation by Homotopy Analysis Method

Differential Equations and Dynamical Systems, 2017
In 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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KBM method based on the homotopy analysis

Science China Physics, Mechanics and Astronomy, 2011
The 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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