共查询到16条相似文献,搜索用时 156 毫秒
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应用同伦分析法研究无限长柱体内角毛细流动解析近似解问题,给出了级数解的递推公式.不同于其他解析近似方法,该方法从根本上克服了摄动理论对小参数的过分依赖,其有效性与所研究的非线性问题是否含有小参数无关,适用范围广.同伦分析法提供了选取基函数的自由,可以选取较好的基函数,更有效地逼近问题的解,通过引入辅助参数和辅助函数来调节和控制级数解的收敛区域和收敛速度,同伦分析法为内角毛细流动问题的解析近似求解开辟了一个全新的途径.通过具体算例,将同伦分析法与四阶龙格库塔方法数值解做了比较,结果表明,该方法具有很高的计算精度. 相似文献
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以同伦近似对称法为理论依据研究了远场模型方程, 通过归纳各阶相似约化解和各阶相似约化方程的通式构造相应的同伦级数解. 各阶相似约化方程均为线性变系数常微分方程, 并且可以从零阶开始依次求解. 同伦模型中的辅助参数影响同伦级数解的收敛性.
关键词:
同伦近似对称法
远场模型方程
同伦级数解 相似文献
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本文研究了在满足Concus-Finn条件时,微重力环境下内角沿容器轴线变化时的毛细驱动流问题,建立了变内角的毛细流动控制方程,获得了变内角流动的近似解析解,并与FLOW-3D软件的数值模拟结果进行了对比验证. 计算结果表明,随着时间的增大,近似解析解与数值解的相对误差越来越小,在6 s以后,相对误差不超过5%. 论文研究了不同结构参数对内角毛细流动的影响规律,得出液体前缘位置和液面高度均随内角、接触角、内角斜率和内角幂指数的增大而减小的结论. 在不同时刻,液体的液面高度随着时间的增大而增大,但在初始时刻存在一个常高度,该高度不随时间的变化而变化. 在空间流体管理时,可以根据本文的工作进行容器设计和选择适合的溶液.
关键词:
变内角
毛细驱动流
近似解析解
前缘位置 相似文献
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利用同伦分析法求解了(2+1)维改进的 Zakharov-Kuznetsov方程, 得到了它的近似周期解,该解与精确解符合很好. 结果表明,同伦分析法在求解高维非线性演化方程时, 仍然是一种行之有效的方法. 同时,还对该方法进行了一定的扩展, 经过扩展后的方法能够更方便地求解更多非线性演化方程的高精度近似解析解.
关键词:
同伦分析法
改进的 Zakharov-Kuznetsov方程
周期解 相似文献
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Solutions of Heat-Like and Wave-Like Equations with Variable Coefficients by Means of the Homotopy Analysis Method 下载免费PDF全文
A. K. Alomari M. S. M. Noorani R. Nazar 《中国物理快报》2008,25(2):589-592
We employ the homotopy analysis method (HAM) to obtain approximate analytical solutions to the heat-like and wave-like equations. The HAM contains the auxiliary parameter h, which provides a convenient way of controlling the convergence region of series solutions. The analysis is accompanied by several linear and nonlinear heat-like and wave-like equations with initial boundary value problems. The results obtained prove that HAM is very effective and simple with less error than the Adomian decomposition method and the variational iteration method. 相似文献
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Application of Homotopy Analysis Method for Solving Systems of Volterra Integral Equations 下载免费PDF全文
In this paper, we prove the convergence of homotopy analysis method (HAM).
We also apply the homotopy analysis method to obtain approximate
analytical solutions of systems of the second kind Volterra integral equations.
The HAM solutions contain an auxiliary parameter
which provides a convenient way of controlling the convergence region
of series solutions. It is shown that the solutions obtained by the
homotopy-perturbation method (HPM) are only special cases of the HAM
solutions. Several examples are given to illustrate
the efficiency and implementation of the method. 相似文献
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《Physics letters. A》2006,360(1):109-113
Here, the homotopy analysis method (HAM), which is a powerful and easy-to-use analytic tool for nonlinear problems and dose not need small parameters in the equations, is compared with the perturbation and numerical and homotopy perturbation method (HPM) in the heat transfer filed. The homotopy analysis method contains the auxiliary parameter ℏ, which provides us with a simple way to adjust and control the convergence region of solution series. 相似文献
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Here, an analytic technique, namely the homotopy analysis method (HAM), is applied to solve a generalized Hirota–Satsuma coupled KdV equation. HAM is a strong and easy-to-use analytic tool for nonlinear problems and dose not need small parameters in the equations. Comparison of the results with those of Adomian's decomposition method (ADM) and homotopy perturbation method (HPM), has led us to significant consequences. The homotopy analysis method contains the auxiliary parameter ?, which provides us with a simple way to adjust and control the convergence region of solution series. 相似文献
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In this study,by means of homotopy perturbation method(HPM) an approximate solution of the magnetohydrodynamic(MHD) boundary layer flow is obtained.The main feature of the HPM is that it deforms a difficult problem into a set of problems which are easier to solve.HPM produces analytical expressions for the solution to nonlinear differential equations.The obtained analytic solution is in the form of an infinite power series.In this work,the analytical solution obtained by using only two terms from HPM soluti... 相似文献
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A. Sami Bataineh 《Physics letters. A》2008,372(5):613-618
In this Letter, the homotopy analysis method (HAM) is employed to obtain a family of series solutions of the time-dependent reaction-diffusion problems. HAM provides a convenient way of controlling the convergence region and rate of the series solution. 相似文献