Relevant bibliographies by topics / Homotopy analysis method

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  2. Dissertations / Theses
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Academic literature on the topic 'Homotopy analysis method'

Author: Grafiati
Published: 4 June 2021
Last updated: 25 July 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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S, Naghshband. "Solving the cubic complex Ginzburg-Laundau equation by Homotopy analysis method." Indian Journal of Science and Technology 13, no. 24 (2020): 2387–403. https://doi.org/10.17485/IJST/v13i24.54557.90477.

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Abstract <strong>Objectives:</strong>&nbsp;This paper obtains the series solution of the cubic complex Ginzburg-Laundau equation, by means of homotopy analysis method(HAM).&nbsp;<strong>Methods:</strong>&nbsp;In addition to the homotopy analysis method, homotopy perturbation and Adomian decomposition methods are applied to determine approximation solution of the cubic complex Ginzburg-Laundau equation and advantage of using HAM. Also a theorem is proved to guarantee the convergence of the HAM to solve this equation.&nbsp;<strong>Findings:&nbsp;</strong>Three examples are solved to illustrate t
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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 meth
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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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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 p
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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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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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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
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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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Khawlah, H. Hussain. "New reliable modifications of the homotopy methods." Indonesian Journal of Electrical Engineering and Computer Science (IJEECS) 19, no. 1 (2020): 371–79. https://doi.org/10.11591/ijeecs.v19i1.pp371-379.

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In this article, new modifications of the homotopy methods are presented and applied to non-homogeneous fractional Volterra integro-differential equations with boundary conditions. A comparative study between the new modified homotopy perturbation method (MHPM) and the new modified homotopy analysis method (MHAM). Several illustrative examples are given to demonstrate the effectiveness and reliability of the methods.
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Dissertations / Theses on the topic "Homotopy analysis method"

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Baxter, Mathew. "Analytical solutions to nonlinear differential equations arising in physical problems." Doctoral diss., University of Central Florida, 2014. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/6247.

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Nonlinear partial differential equations are difficult to solve, with many of the approximate solutions in the literature being numerical in nature. In this work, we apply the Homotopy Analysis Method to give approximate analytical solutions to nonlinear ordinary and partial differential equations. The main goal is to apply different linear operators, which can be chosen, to solve nonlinear problems. In the first three chapters, we study ordinary differential equations (ODEs) with one or two linear operators. As we progress, we apply the method to partial differential equations (PDEs) and
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Jain, Divyanshu. "MVHAM an extension of the homotopy analysis method for improving convergence of the multivariate solution of nonlinear algebraic equations as typically encountered in analog circuits /." Cincinnati, Ohio : University of Cincinnati, 2007. http://www.ohiolink.edu/etd/view.cgi?acc%5Fnum=ucin1194974755.

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Thesis (M.S.)--University of Cincinnati, 2007.<br>Advisor: Harold W. Carter. Title from electronic thesis title page (viewed Feb. 18, 2008). Includes abstract. Keywords: Homotopy Analysis Method; Solution of Nonlinear Algebraic Equations; Convergence. Includes bibliographical references.
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Gedicke, Joscha Micha. "On the numerical analysis of eigenvalue problems." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2013. http://dx.doi.org/10.18452/16841.

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Die vorliegende Arbeit zum Thema der numerischen Analysis von Eigenwertproblemen befasst sich mit fünf wesentlichen Aspekten der numerischen Analysis von Eigenwertproblemen. Der erste Teil präsentiert einen Algorithmus von asymptotisch quasi-optimaler Rechenlaufzeit, der die adaptive Finite Elemente Methode mit einem iterativen algebraischen Eigenwertlöser kombiniert. Der zweite Teil präsentiert explizite beidseitige Schranken für die Eigenwerte des Laplace Operators auf beliebig groben Gittern basierend auf einer Approximation der zugehörigen Eigenfunktion in dem nicht konformen Finite Elem
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Rodrigues, Carla Cristina Morbey. "Topological and dynamical complexity in epidemiological and ecological systems." Doctoral thesis, Universidade de Évora, 2017. http://hdl.handle.net/10174/21241.

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In this work, we address a contribution for the rigorous analysis of the dynamical complexity arising in epidemiological and ecological models under different types of interactions. Firstly, we study the dynamics of a tumor growth model, governing tumor cells interacting with healthy tissue cells and effector cells of the immune system. By using the theory of symbolic dynamics, we characterize the topological entropy from one-dimensional iterated maps identified in the dynamics. This analysis is complemented with the computation of the Lyapunov exponents, the fractal dimension and the predicta
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Wise, Steven M. "POLSYS_PLP: A Partitioned Linear Product Homotopy Code for Solving Polynomial Systems of Equations." Thesis, Virginia Tech, 1998. http://hdl.handle.net/10919/36933.

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Globally convergent, probability-one homotopy methods have proven to be very effective for finding all the isolated solutions to polynomial systems of equations. After many years of development, homotopy path trackers based on probability-one homotopy methods are reliable and fast. Now, theoretical advances reducing the number of homotopy paths that must be tracked, and in the handling of singular solutions, have made probability-one homotopy methods even more practical. This thesis describes the theory behind and performance of the new code POLSYS_PLP, which consists of Fortran 90 modules f
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Kangas, J. (Jani). "Separation process modelling:highlighting the predictive capabilities of the models and the robustness of the solving strategies." Doctoral thesis, Oulun yliopisto, 2014. http://urn.fi/urn:isbn:9789526203768.

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Abstract The aim of this work was to formulate separation process models with both predictive capabilities and robust solution strategies. Although all separation process models should have predictive capabilities, the current literature still has multiple applications in which predictive models having the combination of a clear phenomenon base and robust solving strategy are not available. The separation process models investigated in this work were liquid-liquid phase separation and membrane separation models. The robust solving of a liquid-liquid phase separation model typically demands the
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Awais, Muhammad. "Symmetry Transforms, Global Plasma Equilibria and Homotopy Analysis Method." Thesis, 2010. http://hdl.handle.net/1974/5987.

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Magnetohydrodynamics (MHD) flows and equations have been the focus of a large number of researchers. Here a study of such flows and equations is presented. The first chapter contains a brief introduction to Homotopy Analysis Method (HAM) along with some other definitions. A detailed example on the application of HAM is also included to further clarify the scheme of the method. Second chapter deals with a study of symmetry transforms for ideal MHD equations which comes from the work of Bogoyavlenskij [18]. Different properties of such transforms are also discussed which include the infinite-di
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Moghtadaei, Mohsen. "Spectral-Homotopy analysis method for solving a nonlinear second order BVP." Master's thesis, 2013. http://hdl.handle.net/10316/94880.

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Documentos apresentados no âmbito do reconhecimento de graus e diplomas estrangeiros<br>A modification of the homotopy analysis method(HAM)for solving nonlinear second order boundary value problem(BVP) is proposed.the implementation of new approach is demonstrate by solving the Darcy-Brinkman-Forchheimer equation for steady fully developed fluid flow in a horizontal channel filled with a prous medium.The model equation is solved concurrently using the standard HAM approach and numerically using a shooting method based on the fourth order Rang-Kutta scheme.The results demonstrate that the new s
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Wei-ChungTien and 田偉中. "Application of Homotopy Analysis Method for Non-linear Heat Transfer Problems." Thesis, 2013. http://ndltd.ncl.edu.tw/handle/57842771834640598049.

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博士<br>國立成功大學<br>機械工程學系碩博士班<br>101<br>In this research, the homotopy analysis method is applied to investigate the non-linear heat transfer problems. Unlike all other analytic methods, this approximate analytical method is a powerful and easy-to-use tool for non-linear problems and it provides us with a simple way to adjust and control the convergence region of solution series. Without the need of iteration, the obtained solution is in the form of an infinite power series. This study contains three themes. The first topic is about the natural convection boundary layer flow with effects of ther
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Oguntala, George A., G. Sobamowo, Y. Ahmed, and Raed A. Abd-Alhameed. "Application of approximate analytical technique using the homotopy perturbation method to study the inclination effect on the thermal behavior of porous fin heat sink." 2018. http://hdl.handle.net/10454/16637.

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Yes<br>This article presents the homotopy perturbation method (HPM) employed to investigate the effects of inclination on the thermal behavior of a porous fin heat sink. The study aims to review the thermal characterization of heat sink with the inclined porous fin of rectangular geometry. The study establishes that heat sink of an inclined porous fin shows a higher thermal performance compared to a heat sink of equal dimension with a vertical porous fin. In addition, the study also shows that the performance of inclined or tilted fin increases with decrease in length–thickness aspect rat
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Books on the topic "Homotopy analysis method"

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Liao, Shijun. Homotopy Analysis Method in Nonlinear Differential Equations. Springer Berlin Heidelberg, 2012.

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Liao, Shijun. Homotopy Analysis Method in Nonlinear Differential Equations. Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-25132-0.

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Liao, Shijun. Beyond perturbation: Introduction to homotopy analysis method. Chapman & Hall/CRC Press, 2004.

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United States. National Aeronautics and Space Administration. Scientific and Technical Information Division., ed. An algebraic homotopy method for generating quasi-three-dimensional grids for high-speed configurations. National Aeronautics and Space Administration, Office of Management, Scientific and Technical Information Division, 1989.

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Kazimierz, Gęba, Rabinowitz Paul H, and NATO Advanced Study Institute, eds. Topological methods in bifurcation theory. Presses de l'Université de Montréal, 1985.

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Kushkuley, Alexander. Geometric methods in degree theory for equivariant maps. Springer, 1996.

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Spain) UIMP-RSME Lluis Santaló Summer (2012 Santander. Recent advances in real complexity and computation: UIMP-RSME Lluis A. Santaló Summer School, Recent advances in real complexity and computation, July 16-20, 2012, Universidad Internacional Menéndez Pelayo, Santander, Spain. Edited by Montaña, Jose Luis, 1961- editor of compilation and Pardo, L. M. (Luis M.), editor of compilation. American Mathematical Society, 2013.

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Litvinov, G. L. (Grigoriĭ Lazarevich), 1944- editor of compilation and Sergeev, S. N., 1981- editor of compilation, eds. Tropical and idempotent mathematics and applications: International Workshop on Tropical and Idempotent Mathematics, August 26-31, 2012, Independent University, Moscow, Russia. American Mathematical Society, 2014.

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Beyond perturbation: Introduction to the homotopy analysis method. Chapman & Hall/CRC Press, 2004.

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Liao, Shijun. Beyond Perturbation: Introduction to the Homotopy Analysis Method. Taylor & Francis Group, 2003.

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Book chapters on the topic "Homotopy analysis method"

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Yang, Xiaoyan, and Zhiliang Lin. "Homotopy Analysis Method." In Encyclopedia of Ocean Engineering. Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-10-6963-5_271-1.

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Yang, Xiaoyan, and Zhiliang Lin. "Homotopy Analysis Method." In Encyclopedia of Ocean Engineering. Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-10-6946-8_271.

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Liao, Shijun. "Optimal Homotopy Analysis Method." In Homotopy Analysis Method in Nonlinear Differential Equations. Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-25132-0_3.

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Vajravelu, Kuppalapalle, and Robert A. van Gorder. "Further Applications of the Homotopy Analysis Method." In Nonlinear Flow Phenomena and Homotopy Analysis. Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-32102-3_6.

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Liao, Shijun. "Basic Ideas of the Homotopy Analysis Method." In Homotopy Analysis Method in Nonlinear Differential Equations. Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-25132-0_2.

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Vajravelu, Kuppalapalle, and Robert A. van Gorder. "Application of the Homotopy Analysis Method to Fluid Flow Problems." In Nonlinear Flow Phenomena and Homotopy Analysis. Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-32102-3_5.

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Wang, Qi, and Fenglian Fu. "Solving Delay Differential Equations with Homotopy Analysis Method." In Communications in Computer and Information Science. Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-15853-7_18.

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Liao, Shijun. "Some Methods Based on the HAM." In Homotopy Analysis Method in Nonlinear Differential Equations. Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-25132-0_6.

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Liao, Shijun. "Introduction." In Homotopy Analysis Method in Nonlinear Differential Equations. Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-25132-0_1.

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Liao, Shijun. "A Boundary-layer Flow with an Infinite Number of Solutions." In Homotopy Analysis Method in Nonlinear Differential Equations. Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-25132-0_10.

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Conference papers on the topic "Homotopy analysis method"

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Biazar, Jafar, Zainab Ayati, and Hamideh Ebrahimi. "Comparing Homotopy Perturbation Method and Adomian Decomposition Method." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2008. American Institute of Physics, 2008. http://dx.doi.org/10.1063/1.2991054.

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Gupta, Neelam, and Neel Kanth. "Study of heat flow in a rod using homotopy analysis method and homotopy perturbation method." In EMERGING TRENDS IN MATHEMATICAL SCIENCES AND ITS APPLICATIONS: Proceedings of the 3rd International Conference on Recent Advances in Mathematical Sciences and its Applications (RAMSA-2019). Author(s), 2019. http://dx.doi.org/10.1063/1.5086635.

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Bai, Xiaoli, James Turner, and John Junkins. "A Robust Homotopy Method for Equality Constrained Nonlinear Optimization." In 12th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference. American Institute of Aeronautics and Astronautics, 2008. http://dx.doi.org/10.2514/6.2008-5845.

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Hajji, Mohamed A., and Fathi M. Allan. "Solving nonlinear boundary value problems using the homotopy analysis method." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756537.

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Zou, Li, Wang Zhen, Zong Zhi, and Tian Shoufu. "A study of the initial guess in Homotopy analysis method." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756543.

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Pınar, Zehra. "Modified multi-frequency homotopy analysis method for evolution equations." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2016). Author(s), 2017. http://dx.doi.org/10.1063/1.4992704.

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Sachit, Sahib Abdulkadhim, and Hassan Kamil Jassim. "Solving fractional PDEs by Elzaki homotopy analysis method." In INTERNATIONAL CONFERENCE OF COMPUTATIONAL METHODS IN SCIENCES AND ENGINEERING ICCMSE 2021. AIP Publishing, 2023. http://dx.doi.org/10.1063/5.0115742.

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Liu, Yuliang, Jinshu Lu, Hua Zhang, and Lin Li. "Homotopy Analysis Method of Internet Congestion Control Model." In 2010 International Conference on Communications and Mobile Computing (CMC). IEEE, 2010. http://dx.doi.org/10.1109/cmc.2010.224.

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E. De Gaston, Raymond, and Michael Safonov. "A homotopy method for nonconservative stability robustness analysis." In 1985 24th IEEE Conference on Decision and Control. IEEE, 1985. http://dx.doi.org/10.1109/cdc.1985.268717.

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Zhang, W., Y. H. Qian, M. H. Yao, and S. K. Lai. "Homotopy Analysis Method for Multi-Degree-of-Freedom Nonlinear Dynamical Systems." In ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/detc2010-28089.

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In reality, the behavior and nature of nonlinear dynamical systems are ubiquitous in many practical engineering problems. The mathematical models of such problems are often governed by a set of coupled second-order differential equations to form multi-degree-of-freedom (MDOF) nonlinear dynamical systems. It is extremely difficult to find the exact and analytical solutions in general. In this paper, the homotopy analysis method is presented to derive the analytical approximation solutions for MDOF dynamical systems. Four illustrative examples are used to show the validity and accuracy of the ho
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Reports on the topic "Homotopy analysis method"

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Watson, Layne T. Homotopy Methods in Control System Design and Analysis. Defense Technical Information Center, 1992. http://dx.doi.org/10.21236/ada251641.

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