Relevant bibliographies by topics / Homotopy analysis method

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Homotopy analysis method'

Author: Grafiati
Published: 4 June 2021
Last updated: 15 February 2022

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Journal articles on the topic "Homotopy analysis method"

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

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Ahmad Soltani, L., E. Shivanian, and Reza Ezzati. "Shooting homotopy analysis method." Engineering Computations 34, no. 2 (April 18, 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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Liao, Shijun. "Comparison between the homotopy analysis method and homotopy perturbation method." Applied Mathematics and Computation 169, no. 2 (October 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 procedure.
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Nave, Ophir, Shlomo Hareli, and Vladimir Gol’dshtein. "Singularly perturbed homotopy analysis method." Applied Mathematical Modelling 38, no. 19-20 (October 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 (December 15, 2020): 36–45. http://dx.doi.org/10.26855/acc.2020.12.004.

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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 (December 2009): 4057–64. http://dx.doi.org/10.1016/j.cnsns.2009.02.016.

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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 (June 20, 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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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 (November 28, 2010): 430–41. http://dx.doi.org/10.1080/00207160903474214.

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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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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 use several linear operators. The results are all purely analytical, meaning these are approximate solutions that we can evaluate at points and take their derivatives. Another main focus is error analysis, where we test how good our approximations are. The method will always produce approximations, but we use residual errors on the domain of the problem to find a measure of error. In the last two chapters, we apply similarity transforms to PDEs to transform them into ODEs. We then use the Homotopy Analysis Method on one, but are able to find exact solutions to both equations.
Ph.D.
Doctorate
Mathematics
Sciences
Mathematics
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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.
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 Elemente Raum von Crouzeix und Raviart und einem Postprocessing. Die Effizienz der garantierten Schranke des Eigenwertfehlers hängt von der globalen Gitterweite ab. Der dritte Teil betrachtet eine adaptive Finite Elemente Methode basierend auf Verfeinerungen von Knoten-Patchen. Dieser Algorithmus zeigt eine asymptotische Fehlerreduktion der adaptiven Sequenz von einfachen Eigenwerten und Eigenfunktionen des Laplace Operators. Die hier erstmals bewiesene Eigenschaft der Saturation des Eigenwertfehlers zeigt Zuverlässigkeit und Effizienz für eine Klasse von hierarchischen a posteriori Fehlerschätzern. Der vierte Teil betrachtet a posteriori Fehlerschätzer für Konvektion-Diffusion Eigenwertprobleme, wie sie von Heuveline und Rannacher (2001) im Kontext der dual-gewichteten residualen Methode (DWR) diskutiert wurden. Zwei neue dual-gewichtete a posteriori Fehlerschätzer werden vorgestellt. Der letzte Teil beschäftigt sich mit drei adaptiven Algorithmen für Eigenwertprobleme von nicht selbst-adjungierten Operatoren partieller Differentialgleichungen. Alle drei Algorithmen basieren auf einer Homotopie-Methode die vom einfacheren selbst-adjungierten Problem startet. Neben der Gitterverfeinerung wird der Prozess der Homotopie sowie die Anzahl der Iterationen des algebraischen Löser adaptiv gesteuert und die verschiedenen Anteile am gesamten Fehler ausbalanciert.
This thesis "on the numerical analysis of eigenvalue problems" consists of five major aspects of the numerical analysis of adaptive finite element methods for eigenvalue problems. The first part presents a combined adaptive finite element method with an iterative algebraic eigenvalue solver for a symmetric eigenvalue problem of asymptotic quasi-optimal computational complexity. The second part introduces fully computable two-sided bounds on the eigenvalues of the Laplace operator on arbitrarily coarse meshes based on some approximation of the corresponding eigenfunction in the nonconforming Crouzeix-Raviart finite element space plus some postprocessing. The efficiency of the guaranteed error bounds involves the global mesh-size and is proven for the large class of graded meshes. The third part presents an adaptive finite element method (AFEM) based on nodal-patch refinement that leads to an asymptotic error reduction property for the adaptive sequence of simple eigenvalues and eigenfunctions of the Laplace operator. The proven saturation property yields reliability and efficiency for a class of hierarchical a posteriori error estimators. The fourth part considers a posteriori error estimators for convection-diffusion eigenvalue problems as discussed by Heuveline and Rannacher (2001) in the context of the dual-weighted residual method (DWR). Two new dual-weighted a posteriori error estimators are presented. The last part presents three adaptive algorithms for eigenvalue problems associated with non-selfadjoint partial differential operators. The basis for the developed algorithms is a homotopy method which departs from a well-understood selfadjoint problem. Apart from the adaptive grid refinement, the progress of the homotopy as well as the solution of the iterative method are adapted to balance the contributions of the different error sources.
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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 predictability of the chaotic dynamics. Secondly, we provide the analytical solutions of the mentioned tumor growth model. We apply a method for solving strongly nonlinear systems - the Homotopy Analysis Method (HAM) - which allows us to obtain a one-parameter family of explicit series solutions. Due to the importance of chaos generating mechanisms, we analyze a mathematical ecological model mainly focusing on the impact of species rates of evolution in the dynamics. We analytically proof the boundedness of the trajectories of the attractor. The complexity of the coupling between the dynamical variables is quantified using observability indices. The topological entropy of existing one-dimensional iterated maps is characterized using symbolic dynamics. To extend the previous analysis, we study the predictability and the likeliness of finding chaos in a given region of the parameter space. We conclude our research work with the analysis of a HIV-1 cancer epidemiological model. We construct the explicit series solution of the model. An optimal homotopy analysis approach is used to improve the computational efficiency of HAM by means of appropriate values for the convergence control parameter. We end up this dissertation presenting some final considerations; RESUMO: Este trabalho constitui um contributo para a análise rigorosa da complexidade dinâmica de modelos epidemiológicos e ecológicos submetidos a diferentes tipos de interações Primeiramente, estudamos a dinâmica de um modelo de crescimento tumoral, representando a interacção de células tumorais com tecidos saudáveis e células efectoras do sistema imunitário. Usando a teoria da dinâmica simbólica, caracterizamos a entropia topológica de aplicações unidimensionais identificadas na dinâmica. Esta análise ´e complementada com o cálculo dos expoentes de Lyapunov, dimensão fractal e o cálculo da previsibilidade dos atractores caóticos. Seguidamente, apresentamos soluções analíticas do modelo de crescimento tumoral mencionado. Aplicamos um método para resolver sistemas fortemente não lineares - o Método de Análise Homotópica (HAM) - o qual nos permite obter uma família a um parâmetro de soluções explícitas em forma de série. Devido à importância dos mecanismos geradores de caos, analisamos um modelo matemático em ecologia, centrando-nos no impacto das taxas de evolução das espécies na dinâmica. Provamos analiticamente a compacticidade das trajectórias do atractor. A complexidade do acoplamento entre as variáveis dinâmicas é quantificada utilizando índices de observabilidade. A entropia topológica de aplicações unidimensionais é caracterizada usando a dinâmica simbólica. Para estender a análise anterior, estudamos a previsibilidade e a probabilidade de encontrar comportamento caótico numa determinada região do espaço de parâmetros. Concluímos o nosso trabalho de investigação com a análise de um modelo epidemiológico tumoral HIV-1. Construímos uma solução explícita do modelo. Usamos uma análise homotópica optimal para melhorar a eficiência computacional do HAM através de valores apropriados para o parâmetro de controlo da convergência. Terminamos esta dissertação com a apresentação de algumas considerações finais.
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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 for finding all isolated solutions of a complex coefficient polynomial system of equations by a probability-one homotopy method. The package is intended to be used in conjunction with HOMPACK90, and makes extensive use of Fortran 90 derived data types to support a partitioned linear product (PLP) polynomial system structure. PLP structure is a generalization of m-homogeneous structure, whereby each component of the system can have a different m-homogeneous structure. POLSYS_PLP employs a sophisticated power series end game for handling singular solutions, and provides support for problem definition both at a high level and via hand-crafted code. Different PLP structures and their corresponding Bezout numbers can be systematically explored before committing to root finding.
Master of Science
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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 solution of a phase stability analysis problem. In addition, predicting the liquid-liquid phase compositions reliably depends on robust phase stability analysis. A phase stability analysis problem has multiple feasible solutions, all of which have to be sought to ensure both the robust solving of the model and predictive process model. Finding all the solutions with a local solving method is difficult and generally inexact. Therefore, the modified bounded homotopy methods, a global solving method, were further developed to solve the problem robustly. Robust solving demanded the application of both variables and homotopy parameter bounding features and the usage of the trivial solution in the solving strategy. This was shown in multiple liquid-liquid equilibrium cases. In the context of membrane separation models, predictive capabilities are achieved with the application of a Maxwell-Stefan based model. With the Maxwell-Stefan approach, multicomponent separation can be predicted based on pure component permeation data alone. On the other hand, the solving of the model demands a robust solving strategy with application-dependent knowledge. These issues were illustrated in the separation of a H2/CO2 mixture with a high-silica MFI zeolite membrane at high pressure and low temperature. Similarly, the prediction of mixture adsorption based on pure component adsorption data alone was successfully demonstrated. In the context of membrane separation models, predictive capabilities are achieved with the application of a Maxwell-Stefan based model. With the Maxwell-Stefan approach, multicomponent separation can be predicted based on pure component permeation data alone. On the other hand, the solving of the model demands a robust solving strategy with application-dependent knowledge. These issues were illustrated in the separation of a H2/CO2 mixture with a high-silica MFI zeolite membrane at high pressure and low temperature. Similarly, the prediction of mixture adsorption based on pure component adsorption data alone was successfully demonstrated
Tiivistelmä Työn tavoitteena oli muotoilla prosessin käyttäytymisen ennustamiseen kykeneviä erotusprosessimalleja ja niiden ratkaisuun käytettäviä luotettavia strategioita. Vaikka kaikkien erotusprosessimallien tulisi olla ennustavia, on tällä hetkellä useita kohteita, joissa prosessin käyttäytymistä ei voida ennustaa siten, että käytettävissä olisi sekä ilmiöpohjainen malli että ratkaisuun soveltuva luotettava strategia. Tässä työssä erotusprosessimalleista kohteina tarkasteltiin neste-neste-erotuksen ja membraanierotuksen kuvaukseen käytettäviä malleja. Neste-neste-erotusmallien luotettava ratkaisu vaatii yleensä faasistabiilisuusongelman ratkaisua. Lisäksi faasien koostumusten luotettava ennustaminen pohjautuu faasistabiilisuusanalyysiin. Faasistabiilisuusongelmalla on useita mahdollisia ratkaisuja, jotka kaikki tulee löytää, jotta voitaisiin varmistaa luotettava mallin ratkaisu sekä prosessimallin ennustuskyvyn säilyminen. Kaikkien ratkaisujen löytäminen on sekä vaikeaa että epätarkkaa paikallisesti konvergoituvilla ratkaisumenetelmillä. Tämän vuoksi globaaleihin ratkaisumenetelmiin kuuluvia modifioituja rajoitettuja homotopiamenetelmiä kehitettiin edelleen, jotta faasistabiilisuusongelma saataisiin ratkaistua luotettavasti. Ratkaisun luotettavuus vaati sekä muuttujien että homotopiaparametrin rajoittamista ja ongelman triviaalin ratkaisun käyttöä ratkaisustrategiassa. Tämä käyttäytyminen todennettiin useissa neste-nestetasa-painoa kuvaavissa esimerkeissä. Membraanierotusta tarkasteltaessa ennustava malli voidaan muotoilla käyttämällä Maxwell-Stefan pohjaista mallia. Maxwell-Stefan lähestymistavalla voidaan ennustaa monikomponenttiseosten erotusta perustuen puhtaiden komponenttien membraanin läpäisystä saatuun mittausaineistoon. Toisaalta mallin ratkaisu vaatii luotettavan ratkaisustrategian, jossa hyötykäytetään kohteesta riippuvaa tietoa. Näitä kysymyksiä havainnollistettiin H2/CO2 seoksen erotuksessa MFI-zeoliitti-membraanilla korkeassa paineessa. Samoin seosten adsorboitumiskäyttäytymistä ennustettiin onnistuneesti pelkästään puhtaiden komponenttien adsorptiodatan pohjalta. Kokonaisuutena voidaan todeta, että tarkasteltujen erotusprosessimallien ennustavuutta voidaan parantaa yhdistämällä malli, jolla on selkeä ilmiöpohja ja luotettava ratkaisustrategia. Lisäksi mallien käytettävyys erotusprosessien suunnittelussa on parantunut työn tulosten pohjalta
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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-dimensional Abelian group formed by the symmetries, breaking of geometrical symmetries and ball lightning phenomenon. Next we review the recent work of Bogoyavlenskij [19] to present the derivation of exact plasma equilibria with axial and helical symmetries. Asymptotic and periodic nature of the obtained solutions has also been studied. The last chapter comprises of my own results and it deals with finding solution to unsteady thin film flow of a magnetohydrodynamic fluid. Governing equations of such flows are often very complex and nonlinear. So, we use Homotopy Analysis Method to find exact solution to such nonlinear equations.
Thesis (Master, Mathematics & Statistics) -- Queen's University, 2010-08-24 17:33:50.341
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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
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 spectral homotopy analysis method is more efficient and converges faster than the standard homotopy analysis method
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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
國立成功大學
機械工程學系碩博士班
101
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 thermal and mass diffusion. The non-dimensional velocity, temperature and concentration fields are well illustrated. And the impact of the Prandtl number, Schmidt number and the buoyancy parameter on the flow are widely discussed in detail. Next, heat transfer problem with four different shape of longitudinal fins (rectangular, triangular and parabolic profiles) is analyzed. Both the thermal conductivity and heat transfer coefficient are assumed to be functions of temperature. The obtained solution has high accuracy when comparing it with other-generated by the 4th-order Runge-Kutta method. The fin efficiency and the optimum fin length are also investigated in detail. The third research topic is about the transient heat transfer processes under periodical temperature variation condition occurring in a convective rectangular fin with variable thermal conductivity. The effects of the physical applicable parameters on the non-dimensional temperature distribution along the fin surface are widely discussed.
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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
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 ratio. The study further reveals that increase in the internal heat generation variable decreases the fin temperature gradient, which invariably decreases the heat transfer of the fin. The obtained results using HPM highlights the accuracy of the present method for the analysis of nonlinear heat transfer problems, as it agrees well with the established results of Runge–Kutta.
Supported in part by the Tertiary Education Trust Fund of Federal Government of Nigeria, and the European Union’s Horizon 2020 research and innovation programme under grant agreement H2020-MSCA-ITN-2016SECRET-722424.
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Books on the topic "Homotopy analysis method"

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

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

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Homotopy analysis method in nonlinear differential equations. Beijing: Higher Education Press, 2012.

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

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

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Kushkuley, Alexander. Geometric methods in degree theory for equivariant maps. Berlin: 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. Providence, Rhode Island: American Mathematical Society, 2013.

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Motives, quantum field theory, and pseudodifferential operators: Conference on Motives, Quantum Field Theory, and Pseudodifferential Operators, June 2-13, 2008, Boston University, Boston, Massachusetts. Providence, R.I: American Mathematical Society, 2010.

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Burgos Gil, José I. (José Ignacio), 1962- editor, ed. Feynman amplitudes, periods, and motives: International research conference on periods and motives : a modern perspective on renormalization : July 2-6, 2012, Institute de Ciencias Matematicas, Madris, Spain. Providence, Rhode Island: American Mathematical Society, 2015.

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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. Providence, Rhode Island: American Mathematical Society, 2014.

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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, 1–8. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-10-6963-5_271-1.

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Liao, Shijun. "Optimal Homotopy Analysis Method." In Homotopy Analysis Method in Nonlinear Differential Equations, 95–129. Berlin, Heidelberg: 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, 157–84. Berlin, Heidelberg: 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, 15–94. Berlin, Heidelberg: 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, 101–55. Berlin, Heidelberg: 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, 144–53. Berlin, Heidelberg: 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, 223–35. Berlin, Heidelberg: 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, 3–14. Berlin, Heidelberg: 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, 363–81. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-25132-0_10.

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Liao, Shijun. "Non-similarity Boundary-layer Flows." In Homotopy Analysis Method in Nonlinear Differential Equations, 383–401. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-25132-0_11.

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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. Reston, Virigina: 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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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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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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Ene, R. D., V. Marinca, and B. Cãruntu. "Optimal homotopy perturbation method for solving a nonlinear problem in elasticity." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756603.

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Barari, A., M. Omidvar, S. Gholitabar, D. D. Ganji, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Variational Iteration Method and Homotopy-Perturbation Method for Solving Second-Order Non-Linear Wave Equation." In Numerical Analysis and Applied Mathematics. AIP, 2007. http://dx.doi.org/10.1063/1.2790272.

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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. Fort Belvoir, VA: Defense Technical Information Center, April 1992. http://dx.doi.org/10.21236/ada251641.

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