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homotopy analysis method for Solving Biological Population Model

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Communications in Theoretical Physics 2011年第11期56卷 797-800页

作者： A.A.M.Arafa S.Z.Rida H.Mohamed Department of Mathematics Faculty of ScienceSouth Valley University

In this paper,the homotopy analysis method (HAM) is applied to solve generalized biological *** fractional derivatives are described by Caputo's *** method introduces a significant improvementin this field over existing *** obtained using the scheme presented here agree well with the analyticalsolutions and the numerical results presented in Ref.[6].However,the fundamental solutions of these equations stillexhibit useful scaling properties that make them attractive for applications.

关键词： biological populations model fractional calculus homotopy analysis method Mittag-Leffier function

Improving convergence of incremental harmonic balance method using homotopy analysis method

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Acta Mechanica Sinica 2009年第5期25卷 707-712页

作者： Yanmao Chen Jike Liu State Key Laboratory of Mechanical System and Vibration Shanghai Jiao Tong University 800 Dongchuan Road 200240 Shanghai China Department of Mechanics Sun Yat-sen University 510275 Guangzhou China

We have deduced incremental harmonic balance an iteration scheme in the （IHB） method using the harmonic balance plus the Newton-Raphson method. Since the convergence of the iteration is dependent upon the initial values in the iteration, the convergent region is greatly restricted for some cases. In this contribution, in order to enlarge the convergent region of the IHB method, we constructed the zeroth-order deformation equation using the homotopy analysis method, in which the IHB method is employed to solve the deformation equation with an embedding parameter as the active increment. Taking the Duffing and the van der Pol equations as examples, we obtained the highly accurate solutions. Importantly, the presented approach renders a convenient way to control and adjust the convergence.

关键词： Incremental harmonic balance method homotopy analysis method Initial value Convergence

Vertical Sediment Concentration Distribution in High-Concentrated Flows:An Analytical Solution Using homotopy analysis method

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Communications in Theoretical Physics 2018年第9期69卷 367-378页

作者： Manotosh Kumbhakar Jitraj Saha Koeli Ghoshal Jitendra Kumar Vijay P.Singh Department of Mathematics Indian Institute of Technology KharagpurKharagpur 721302India Department of Mathematics National Institute of TechnologyTiruchirappalliTamil Nadu 620015India Department of Biological and Agricultural Engineering&Zachry Department of Civil Engineering Texas A~M UniversityCollege StationTX 77843USA

Transport of suspended sediment in open channel flow has an enormous impact on real life situations,*** and management of reservoir sedimentation,geomorphic evolution such as dunes,rivers,and coastlines *** entails advection and *** diffusion is governed by the concept of Fick’s law,which is based on the molecular diffusion theory,and the equation that represents the distribution of sediment concentration is the advection-diffusion *** study uses the existing governing equation which considers different phases for solid and fluid,and then couples the two *** deal with high-concentrated flow,sediment and turbulent diffusion coefficients are taken to be different from each *** effect of hindered settling on sediment particles is incorporated in the governing equation,which makes the equation highly *** study derives an explicit closed-form analytical solution to the generalized one-dimensional diffusion equation representing the vertical sediment concentration distribution with an arbitrary turbulent diffusion coefficient *** solution is obtained by homotopy analysis method,which does not rely on the small parameters present in the ***,the solution is validated by comparing it with the implicit solution and the numerical solution.A relevant set of laboratory data is selected to check the applicability of the model,and a close agreement shows the potential of the model in the context of application to high-concentrated sediment-laden open channel flow.

关键词： open channel flow diffusion equation hunt equation homotopy analysis method

homotopy analysis method for Solving (2+1)-dimensional Navier-Stokes Equations with Perturbation Terms

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Communications in Mathematical Research 2018年第1期34卷 1-14页

作者： Ji Juan-juan Zhang Lan-fang School of Physics and Electrical Engineering Anqing Normal University

In this paper homotopy analysis method(HAM) is implemented for obtaining approximate solutions of(2+1)-dimensional Navier-Stokes equations with perturbation terms. The initial approximations are obtained using linear systems of the Navier-Stokes equations; by the iterations formula of HAM, the first approximation solutions and the second approximation solutions are successively obtained and homotopy Perturbation method(HPM) is also used to solve these equations; finally,approximate solutions by HAM of(2+1)-dimensional Navier-Stokes equations without perturbation terms and with perturbation terms are compared. Because of the freedom of choice the auxiliary parameter of HAM, the results demonstrate that the rapid convergence and the high accuracy of the HAM in solving Navier-Stokes equations; due to the effects of perturbation terms, the 3 rd-order approximation solutions by HAM and HPM have great fluctuation.

关键词： Navier-Stokes equation homotopy analysis method homotopy perturbation method perturbation term

Application of the homotopy analysis method for the Gross-Pitaevskii equation with a harmonic trap

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Chinese Physics B 2012年第12期21卷 88-93页

作者：石玉仁刘丛波王光辉周志刚 College of Physics and Electronic Engineering Northwest Normal University

The homotopy analysis method （HAM） is adopted to find the approximate analytical solutions of the Gross- Pitaevskii equation, a nonlinear Schrodinger equation is used in simulation of Bose-Einstein condensates trapped in a harmonic potential. Comparisons between the analytical solutions and the numerical solutions have been made. The results indicate that they fit very well with each other when the atomic interaction is weak.

关键词： Gross-Pitaevskii equation homotopy analysis method analytical solution

SOLUTION OF THE ENSO DELAYED OSCILLATOR WITH homotopy analysis method

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Journal of Hydrodynamics 2009年第1期21卷 131-135页

作者： WU Zi-ku School of Science Qingdao Agriculture University Qingdao 266109 China

An ENSO delayed oscillator is considered. The E1 Nino atmospheric physics oscillation is an abnormal phenomenon involved in the tropical Pacific ocean-atmosphere interactions. The conceptual oscillator model should consider the variations of both the eastern and western Pacific anomaly patterns. Using the homotopy analysis method, the approximate expansions of the solution of corresponding problem are constructed. The method is based on a continuous variation from an initial trial to the exact solution. A Maclaurin series expansion provides a successive approximation of the solution through repeated application of a differential operator with the initial trial as the first term. This approach does not require the use of perturbation parameters and the solution series converges rapidly with the number of terms. Comparing the approximate analytical solution by homotopy analysis method with the exact solution, we can find that the homotopy analysis method is valid for solving the strong nonlinear ENSO delayed oscillator model.

关键词： ENSO delayed oscillator homotopy analysis method strong nonlinear

Consideration of transient heat conduction in a semi-infinite medium using homotopy analysis method

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Applied Mathematics and Mechanics(English Edition) 2008年第12期29卷 1625-1632页

作者： A. Rezania A. Ghorbali G. Domairry H. Bararnia Department of Mechanical Engineering Babol Industrial University

In the current work, transient heat conduction in a semi-infinite medium is considered for its many applications in various heat fields. Here, the homotopy analysis method （HAM） is applied to solve this problem and analytical results are compared with those of the exact and integral methods results. The results show that the HAM can give much better approximations than the other approximate methods： Changes in heat fluxes and profiles of temperature are obtained at different times and positions for copper, iron and aluminum.

关键词： homotopy analysis method semi-infinite medium conduction transient heat transfer integral methods temperature profile

Nonlinear oscillations with parametric excitation solved by homotopy analysis method

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Acta Mechanica Sinica 2008年第3期24卷 325-329页

作者： Jianmin Wen Zhengcai Cao School of Shipbuilding Engineering Harbin Institute of Technology at WeihaiWeihai 264209 China CIMS Research Center Tongji University Shanghai 200092 China

An analytical technique, namely the homotopy analysis method （HAM）, is used to solve problems of nonlinear oscillations with parametric excitation. Unlike perturbation methods, HAM is not dependent on any small physical parameters at all, and thus valid for both weakly and strongly nonlinear problems. In addition, HAM is different from all other analytic techniques in providing a simple way to adjust and control convergence region of the series solution by means of an auxiliary parameter h. In the present paper, a periodic analytic approximations for nonlinear oscillations with parametric excitation are obtained by using HAM, and the results are validated by numerical simulations.

关键词： Nonlinear oscillation Parametric excitation Series solutions homotopy analysis method

A new modification of false position method based on homotopy analysis method

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Applied Mathematics and Mechanics(English Edition) 2008年第2期29卷 223-228页

作者： Saeid Abbasbandy 廖世俊 Department of Mathematics Imam Khomeini International University Ghazvin34149-16818Iran State Key Lab of Ocean Engineering School of Naval ArchitectureOcean and Civil Engineering Shanghai Jiaotong University

A new modification of false position method for solving nonlinear equations is presented by applying homotopy analysis method （HAM）. Some numerical illustrations are given to show the efficiency of algorithm.

关键词： false position method regula falsi method homotopy analysis method