Results 141 to 150 of about 33,166 (180)

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 ...
S. Das, P. K. Gupta
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A study on homotopy analysis method and clique polynomial method

2021
Summary: This paper generated the novel approach called the Clique polynomial method (CPM) using the clique polynomials raised in graph theory. Nonlinear initial value problems are converted into nonlinear algebraic equations by discretion with suitable grid points in the current approach.
S, Kumbinarasaiah, M. P, Preetham
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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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Homotopy Analysis Method for Solving Biological Population Model

Communications in Theoretical Physics, 2011
Summary: In this paper, the homotopy analysis method (HAM) is applied to solve generalized biological population models. The fractional derivatives are described in Caputo's sense. The method introduces a significant improvement in this field over existing techniques.
Arafa, A. A. M., Rida, S. Z., Mohamed, H.   +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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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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Comparison between the homotopy analysis method and homotopy perturbation method to solve coupled Schrodinger-KdV equation

Journal of Applied Mathematics and Computing, 2008
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Alomari, A. K., Noorani, M. S. M., Nazar, R.   +2 more
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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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Optimal Homotopy Analysis Method

2017
Optimal 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

2012
In 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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