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Relevant bibliographies by topics / Homotopy analysis method

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Journal articles

Academic literature on the topic 'Homotopy analysis method'

Author: Grafiati

Published: 4 June 2021

Last updated: 11 June 2025

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Journal articles on the topic "Homotopy analysis method"

1

He, Ji-Huan. "Comparison of homotopy perturbation method and homotopy analysis method." Applied Mathematics and Computation 156, no. 2 (2004): 527–39. http://dx.doi.org/10.1016/j.amc.2003.08.008.

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2

Ahmad Soltani, L., E. Shivanian, and Reza Ezzati. "Shooting homotopy analysis method." Engineering Computations 34, no. 2 (2017): 471–98. http://dx.doi.org/10.1108/ec-10-2015-0329.

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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 used to predict multiplicity of solutions of NBVPs, is a time-consuming computation of high-order HAM-approximate solutions due to a symbolic variable namely “prescribed parameter”. The proposed new technique which is based on traditional shooting method, and the HAM cuts the dependency on the prescribed parameter. Findings To demonstrate the computational efficiency, the mentioned method is implemented on three important nonlinear exactly solvable differential equations, namely, the nonlinear MHD Jeffery–Hamel flow problem, the nonlinear boundary value problem arising in heat transfer and the strongly nonlinear Bratu problem. Originality/value The more high-order approximate solutions are computable, multiple solutions are easily searched and discovered and the more accurate solutions can be obtained depending on how nonhomogeneous boundary conditions are transcribed to the homogeneous boundary conditions.

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3

Liao, Shijun. "Comparison between the homotopy analysis method and homotopy perturbation method." Applied Mathematics and Computation 169, no. 2 (2005): 1186–94. http://dx.doi.org/10.1016/j.amc.2004.10.058.

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4

He, Ji-Huan. "Homotopy Perturbation Method with an Auxiliary Term." Abstract and Applied Analysis 2012 (2012): 1–7. http://dx.doi.org/10.1155/2012/857612.

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The two most important steps in application of the homotopy perturbation method are to construct a suitable homotopy equation and to choose a suitable initial guess. The homotopy equation should be such constructed that when the homotopy parameter is zero, it can approximately describe the solution property, and the initial solution can be chosen with an unknown parameter, which is determined after one or two iterations. This paper suggests an alternative approach to construction of the homotopy equation with an auxiliary term; Dufing equation is used as an example to illustrate the solution procedure.

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5

Nave, Ophir, Shlomo Hareli, and Vladimir Gol’dshtein. "Singularly perturbed homotopy analysis method." Applied Mathematical Modelling 38, no. 19-20 (2014): 4614–24. http://dx.doi.org/10.1016/j.apm.2014.03.013.

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6

Huseen, Shaheed N. "A Comparative Study of q-Homotopy Analysis Method and Liao’s Optimal Homotopy Analysis Method." Advances in Computer and Communication 1, no. 1 (2020): 36–45. http://dx.doi.org/10.26855/acc.2020.12.004.

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7

Liang, Songxin, and David J. Jeffrey. "Comparison of homotopy analysis method and homotopy perturbation method through an evolution equation." Communications in Nonlinear Science and Numerical Simulation 14, no. 12 (2009): 4057–64. http://dx.doi.org/10.1016/j.cnsns.2009.02.016.

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8

LIU, CHENG-SHI, and YANG LIU. "COMPARISON OF A GENERAL SERIES EXPANSION METHOD AND THE HOMOTOPY ANALYSIS METHOD." Modern Physics Letters B 24, no. 15 (2010): 1699–706. http://dx.doi.org/10.1142/s0217984910024079.

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A simple analytic tool, namely the general series expansion method, is proposed to find the solutions for nonlinear differential equations. A set of suitable basis functions [Formula: see text] is chosen such that the solution to the equation can be expressed by [Formula: see text]. In general, t0 can control and adjust the convergence region of the series solution such that our method has the same effect as the homotopy analysis method proposed by Liao, but our method is simpler and clearer. As a result, we show that the secret parameter h in the homotopy analysis methods can be explained by using our parameter t0. Therefore, our method reveals a key secret in the homotopy analysis method. For the purpose of comparison with the homotopy analysis method, a typical example is studied in detail.

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9

Das, S., and P. K. Gupta. "Application of homotopy perturbation method and homotopy analysis method to fractional vibration equation." International Journal of Computer Mathematics 88, no. 2 (2010): 430–41. http://dx.doi.org/10.1080/00207160903474214.

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10

Motsa, Sandile Sydney, Precious Sibanda, Gerald T. Marewo, and Stanford Shateyi. "A Note on Improved Homotopy Analysis Method for Solving the Jeffery-Hamel Flow." Mathematical Problems in Engineering 2010 (2010): 1–11. http://dx.doi.org/10.1155/2010/359297.

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This paper presents the solution of the nonlinear equation that governs the flow of a viscous, incompressible fluid between two converging-diverging rigid walls using an improved homotopy analysis method. The results obtained by this new technique show that the improved homotopy analysis method converges much faster than both the homotopy analysis method and the optimal homotopy asymptotic method. This improved technique is observed to be much more accurate than these traditional homotopy methods.

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