Results 151 to 160 of about 2,716 (179)

Comparison between Homotopy Analysis Method and Homotopy Renormalization Method

SSRN Electronic Journal, 2022
Yu Yang, Shijun Liao
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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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Homotopy analysis method for the Kawahara equation

Nonlinear Analysis: Real World Applications, 2010
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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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Homotopy analysis method: A new analytic method for nonlinear problems

Applied Mathematics and Mechanics, 1998
In 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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Advances in the Homotopy Analysis Method

2013
A 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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Comparison between the homotopy analysis method and homotopy perturbation method to solve coupled Schrodinger-KdV equation

Journal of Applied Mathematics and Computing, 2008
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Alomari, A. K., Noorani, M. S. M., Nazar, R.   +2 more
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Further Applications of the Homotopy Analysis Method

2012
Here 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, Robert A. van Gorder   +1 more
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Derivation of the Adomian decomposition method using the homotopy analysis method

Applied Mathematics and Computation, 2007
The solution of a nonlinear equation \( L(y(x)) + N(y(x)) = 0 \), where \(L\) and \(N\) are linear and nonlinear operators, respectively, is represented in the form \[ y =\sum_{n=0}^{\infty} y_{n} . \] The terms \(y_{n}\) can be calculated by recurrent relations using the decomposition \[ N(y)=\sum_{n=0}^{\infty} A_{n}, \] where \(A_{n}\) are the ...
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General boundary element method: an application of homotopy analysis method

Communications in Nonlinear Science and Numerical Simulation, 1998
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