共查询到19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微重力环境下圆管毛细流动解析近似解问题, 给出了级数解的表达公式. 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, 同伦分析法为圆管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.
关键词:
圆管
微重力
毛细流动
同伦分析法 相似文献
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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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研究了一类非线性燃烧模型.利用同伦分析方法,得到了该模型的近似解.
关键词:
非线性方程
燃烧模型
同伦分析法
近似解 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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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
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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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In this paper we consider the homotopy analysis transform method (HATM) to solve the time fractional order Korteweg-de Vries (KdV) and Korteweg-de Vries-Burger’s (KdVB) equations. The HATM is a combination of the Laplace decomposition method (LDM) and the homotopy analysis method (HAM). The fractional derivatives are defined in the Caputo sense. This method gives the solution in the form of a rapidly convergent series with h-curves are used to determine the intervals of convergent. Averaged residual errors are used to find the optimal values of h. It is found that the optimal h accelerates the convergence of the HATM, with the rate of convergence depending on the parameters in the KdV and KdVB equations. The HATM solutions are compared with exact solutions and excellent agreement is found. 相似文献
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Mustafa Inc 《Physics letters. A》2008,372(4):356-360
In this Letter, we present the Homotopy Analysis Method (shortly HAM) for obtaining the numerical solution of the one-dimensional nonlinear Burgers' equation. The initial approximation can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. Convergence of the solution and effects for the method is discussed. The comparison of the HAM results with the Homotopy Perturbation Method (HPM) and the results of [E.N. Aksan, Appl. Math. Comput. 174 (2006) 884; S. Kutluay, A. Esen, Int. J. Comput. Math. 81 (2004) 1433; S. Abbasbandy, M.T. Darvishi, Appl. Math. Comput. 163 (2005) 1265] are made. The results reveal that HAM is very simple and effective. The HAM contains the auxiliary parameter ?, which provides us with a simple way to adjust and control the convergence region of solution series. The numerical solutions are compared with the known analytical and some numerical solutions. 相似文献
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This article reports the homotopy solution for stagnation point flow of a non-Newtonian fluid.An incompressible second grade fluid impinges on the wall either orthogonally or obliquely.The resulting nonlinear problems have been solved by a homotopy analysis method(HAM).Convergence of the series solutions is checked.Such solutions are compared with the numerical solutions presented in a study [Int.J.Non-Linear Mech.43(2008) 941].Excellent agreement is noted between the numerical and series solutions. 相似文献
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Impact of Linear Operator on the Convergence of HAM Solution: A Modified Operator Approach 下载免费PDF全文
S. T. Hussain S. Nadeem & M. Qasim 《advances in applied mathematics and mechanics.》2016,8(3):499-516
The linear operator plays an important role in the computational process of
Homotopy Analysis Method (HAM). In HAM frame any kind of linear operator can
be chosen to develop a solution. Hence, it is easy to introduce the modified/physical
parameter dependent linear operators. The effective use of these operators has been
judged through solving fluid flow problems. Modification in linear operators affects
the solution and improves the computational efficiency of HAM for larger values of
parameters. The convergence rate of the solution is rapid and several times higher
resulting in less computational time. 相似文献
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In this Letter, we present the homotopy perturbation method (shortly HPM) for obtaining the numerical solution of the RLW equation. We obtain the exact and numerical solutions of the Regularized Long Wave (RLW) equation for certain initial condition. The initial approximation can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. Comparison of the results with those of other methods have led us to significant consequences. The numerical solutions are compared with the known analytical solutions. 相似文献