共查询到20条相似文献,搜索用时 78 毫秒
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张愉何和平田叶 《数学的实践与认识》2022,(11):150-158
威布尔(Weibull)分布极其广泛地被应用于生存分析和可靠性分析中,其形状参数和尺度参数在应用中通常用极大似然法及其相关数值方法来估计.在统计学文献中,首次利用同伦分析法方便地找到了Weibull分布中参数极大似然估计的近似解析表达式,从而对繁琐且不太可靠的数值方法提供了一个重要补充;特别地,由于利用了同伦分析法中的收敛控制参数,从而可保证得到的近似解析表达式的收敛性.蒙特卡洛模拟表明,所提出的近似解析方法具有相当高的可行性和精确性.从模拟结果可以得出,在统计学中同伦分析法可避开摄动法过分依赖小参数的缺点,且其近似解析解非常精确;利用同伦分析法,统计学中很多其它情形下的极大似然估计的近似解析表达式也可求得. 相似文献
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应用同伦分析方法,提出了一种求解非线性方程改进的试位法.给出的一些数值例证显示了该运算法则的有效性. 相似文献
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同伦分析方法:一种新的求解非线性问题的近似解析方法 总被引:9,自引:0,他引:9
本文描述了一种称为“同伦分析方法”(HAM)的新的求解非线性问题的近似解析方法之基本思想·不同于摄动展开方法,“同伦分析方法”的有效性不依赖于所研究的非线性方程中是否含有小参数·因此,该方法提供了一个强有力的分析非线性问题的新工具·作为示例,我们应用一个典型的非线性问题来说明该方法的有效性及其巨大潜力· 相似文献
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Duffing简谐振子同伦分析法求解 总被引:1,自引:1,他引:0
利用同伦分析方法求解了Duffing简谐振子,数值确定了变形方程中的辅助参数,得到了一族响应和频率的近似周期解,该解与精确解符合很好,结果表明,同伦分析法在求解强非线性振子时,仍然是一种行之有效的方法. 相似文献
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罗炯兴 《数学的实践与认识》2019,(9)
研究了结合变量替换应用同伦分析方法,去求解二阶非线性微分方程的两点边值问题,并得到了逼近解析解的函数级数形式.给出了应用同伦分析方法求解二阶非线性问题的三个实例,显示了同伦分析方法可以比较有效地求解非线性问题. 相似文献
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关于同伦满态与覆叠空间 总被引:5,自引:0,他引:5
本文在点标道路连通CW空间的同伦范畴中,利用同伦推出示性了同伦满态,得出了若f:X-Y是同伦满态,则对π1Y的任一正规子群H,升腾映射f:X(f-1#(H))→■(H)也是同伦满态. 相似文献
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《Communications in Nonlinear Science & Numerical Simulation》2010,15(8):2017-2025
This paper presents a study of the relationship between the homotopy analysis method (HAM) and harmonic balance (HB) method. The HAM is employed to obtain periodic solutions of conservative oscillators and limit cycles of self-excited systems, respectively. Different from the usual procedures in the existing literature, the HAM is modified by retaining a given number of harmonics in higher-order approximations. It is proved that as long as the solution given by the modified HAM is convergent, it converges to one HB solution. The Duffing equation, the van der Pol equation and the flutter equation of a two-dimensional airfoil are taken as illustrations to validate the attained results. 相似文献
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A. Sami Bataineh M.S.M. Noorani I. Hashim 《Communications in Nonlinear Science & Numerical Simulation》2009,14(2):430-442
In this paper, a new modification of the homotopy analysis method (HAM) is presented for solving systems of second-order boundary-value problems (BVPs). The main advantage of the modified HAM (MHAM) is that one can avoid the uncontrollability problems of the nonzero endpoint conditions encountered in the standard HAM. Numerical comparisons show that the MHAM is more efficient than the standard HAM. 相似文献
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A. Sami Bataineh M.S.M. Noorani I. Hashim 《Communications in Nonlinear Science & Numerical Simulation》2009,14(2):409-423
In this paper, a new modification of the homotopy analysis method (HAM) is presented and applied to homogeneous or non-homogeneous differential equations with constant or variable coefficients. A comparative study between the new modified homotopy analysis method (MHAM) and the classical HAM is conducted. The main advantage of MHAM is that one can avoid the uncontrollability problems of the non-zero endpoint conditions encountered in the traditional HAM. Several illustrative examples are given to demonstrate the effectiveness and reliability of MHAM. 相似文献
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《Communications in Nonlinear Science & Numerical Simulation》2010,15(9):2424-2430
In this article, a powerful analytical method, called the Homotopy Analysis Method (HAM) is introduced to obtain the exact solutions of heat transfer equation of a non-Newtonian fluid flow in an axisymmetric channel with a porous wall for turbine cooling applications. The HAM is employed to obtain the expressions for velocity and temperature fields. Tables are presented for various parameters on the velocity and temperature fields. These results are compared with the solutions which are obtained by Numerical Methods (NM). Also the convergence of the obtained HAM solution is discussed explicitly. These comparisons show that this analytical method is strongly powerful to solve nonlinear problems arising in heat transfer. 相似文献
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A. S. Bataineh A. K. Alomari M. S. M. Noorani I. Hashim R. Nazar 《Acta Appl Math》2009,105(2):189-198
Differential equations of fractional order appear in many applications in physics, chemistry and engineering. An effective
and easy-to-use method for solving such equations is needed. In this paper, series solutions of the FDEs are presented using
the homotopy analysis method (HAM). The HAM provides a convenient way of controlling the convergence region and rate of the
series solution. It is confirmed that the HAM series solutions contain the Adomian decomposition method (ADM) solution as
special cases.
相似文献
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《Communications in Nonlinear Science & Numerical Simulation》2010,15(3):590-601
A homotopy analysis method (HAM) is used to develop analytical solution for the thermal performance of a straight fin of trapezoidal profile when both the thermal conductivity and the heat transfer coefficient are temperature dependent. Results are presented for the temperature distribution, heat transfer rate, and fin efficiency for a range of values of parameters appearing in the mathematical model. Since the HAM algorithm contains a parameter that controls the convergence and accuracy of the solution, its results can be verified internally by calculating the residual error. The HAM results were also found to be accurate to at least three places of decimal compared with the direct numerical solution of the mathematical model generated using a fourth–fifth-order Runge–Kutta–Fehlberg method. The HAM solution appears in terms of algebraic expressions which are not only easy to compute but also give highly accurate results covering a wide range of values of the parameters rather than the small values dictated by the perturbation solution. 相似文献
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Esmail Hesameddini Habibolla Latifizadeh 《Mathematical Methods in the Applied Sciences》2012,35(12):1423-1433
In this paper, the homotopy analysis method (HAM) is presented to obtain the numerical solutions for the two kinds of the Painlevé equations with a number of initial conditions. Then, a numerical evaluation and comparison with the results obtained via the HAM are included. It illustrates the validity and the great potential of the HAM in solving Painlevé equations. Although the HAM contains the auxiliary parameter, the convergence region of the series solution can be controlled in a simple way. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
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《Communications in Nonlinear Science & Numerical Simulation》2010,15(6):1565-1574
The homotopy analysis method (HAM) is used to develop an analytical solution for the thermal performance of a radial fin of rectangular and various convex parabolic profiles mounted on a rotating shaft and losing heat by convection to its surroundings. The convection heat transfer coefficient is assumed to be a function of both the radial coordinate and the angular speed of the shaft. Results are presented for the temperature distribution, heat transfer rate, and the fin efficiency illustrating the effect of thickness profile, the ratio of outer to inner radius, and the angular speed of the shaft. Comparison of HAM results with the direct numerical solutions shows that the analytic results produced by HAM are highly accurate over a wide range of parameters that are likely to be encountered in practice. 相似文献
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A. Hassani M.H. Hojjati G.H. Farrahi R.A. Alashti 《Communications in Nonlinear Science & Numerical Simulation》2012,17(9):3747-3762
In this paper, distributions of stress and strain components of rotating disks with non-uniform thickness and material properties subjected to thermo-elasto-plastic loading are obtained by semi-exact method of Liao’s homotopy analysis method (HAM) and finite element method (FEM). The materials are assumed to be elastic-linear strain hardening and isotropic. The analysis of rotating disk is based on Von Mises’ yield criterion. A two dimensional plane stress analysis is used. The distribution of temperature is assumed to have power forms with the hotter point located at the outer surface of the disk. A mathematical technique of transformation has been proposed to solve the homotopy equations which are originally hard to be handled. The domain of the solution has been substituted by a new domain through which the unknown variable has been taken out from the argument of the function. This makes the solution much easier. A numerical solution of the governing differential equations is also presented based on the Runge–Kutta’s method. The results of three methods are presented and compared which shows good agreements. This verifies the implementation of the HAM and demonstrates its applicability to provide accurate solution for a very complicated case of strongly high nonlinear differential equations with no exact solution. It is important to notice that compared with other methods, HAM needs significant more computation time and computer hardware requirements which limit its application for those problems that other methods can easily handle them. 相似文献
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In this paper, we applied relatively new analytical techniques, the homotopy analysis method (HAM) and the Adomian’s decomposition method (ADM) for solving time-fractional Fornberg–Whitham equation. 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. The fractional derivatives are described in the Caputo sense. A comparison is made the between HAM and ADM results. The present methods performs extremely well in terms of efficiency and simplicity. Numerical results for different particular cases of the problem are presented. 相似文献