理论和数值实验都表明同伦方法是一种收敛稳定的方法。
Theory and numerical simulation show that the method presented is a convergence and stable method.
运用同伦方法的基本思想研究飞机非线性平衡状态的求解。
In this paper, the method of solving nonlinear equilibrium state of aircraft is studied according to homotopy concept.
利用组合极大熵同伦方法，研究一般的非凸非线性规划问题。
We utilized the combined maximum entropy homotopy method to solve the general nonconvex nonlinear programming problems.
利用组合极大熵同伦方法，研究一般的非凸非线性规划问题。
In this paper, we present a new interior point method-combined homotopy interior point method.
用同伦方法分析了可分解映射的零点存在性，并获得它对一类非线性特征值问题的应用。
Using homotopy methods, this paper gives an analysis on the existence of zeros of the decomposable mapping, and finds its application to a class of nonlinear eigenvalue problems.
文章针对传统的声波阻抗反演方法的不足，将大范围收敛的同伦方法用于地震勘探声波阻抗的反演。
In consideration of the drawbacks in conventional acoustic impedance inversion method, the homotopy method with vast convergence was applied to the acoustic impedance inversion in seismic exploration.
本文利用连续同伦方法讨论非线性映射在有界区域内零点的存在性和零点数目，以及推广若干经典定理。
With homotopy methods, this paper discusses the existence and the number of zeroes of nonlinear mappings on bounded regions and extends some classical theorems.
本文用某种同伦方法，借助于一些适当的变换，讨论了有序的局部凸拓扑线性空间中集值凝聚映象方程的正解问题。
Under several suitable transformations, the problem of positive solutions for set-valued condensing mapping equation in an ordered locally convex topological space is studied by some homotopy method.
为改进网络学习效率及大范围收敛性，提出了网络权值学习的单调同伦方法，该方法具有与牛顿法相同的二阶收敛性。
To improve the learning efficiency and global convergence we present the monotone homotopy method, which has the same convergence as the Newton's method, to train the weights of the network.
证明了同伦映射为正则映射的条件下，选取合适的同伦方程，用此同伦方法得到的K-K-T点一定是问题局部最优解。
We prove that when the homotopy map is a regular map, the K-K-T point obtained from this homotopy method must be a local optimal solution by choosing proper homotopy equation.
本文的研究结果丰富了介质波动理论和同伦方法的应用范围，对促进正、反演在工程中的应用具有一定的理论意义与实际价值。
The results in this thesis enrich the application range of media wave theory and the homotopy methods application in inversion problems, which are of great theoretical and practical significance.
地球物理反问题大部分是非线性问题，基于路径跟踪的同伦法是求解该类问题的有效方法。
Most of geophysical inversion are non-linear problems, the homotopy method based on path tracking is effective method for solving this kind of problems.
利用同伦分析方法，得到了该模型的近似解。
Using the homotopy analysis method, the approximation solution is obtained.
阐述利用最新提出的同伦分析方法求解有正阻尼的强非线性振动方程，得到了该方程的六阶近似解析解。
In this paper, the sixth-order approximate analytical solutions of the strong nonlinear oscillation with positive damping are obtained by using newly developed homotopy analysis method.
利用同伦分析方法，得到了该模型解的近似展开式。
Using the homotopy analysis method, the approximation of the solution for the model was obtained.
本文一篇综述类文章，综述了同伦摄动方法及它在非线性微积分方程中的某些应用。
The paper reviews Some applications of the homotopy perturbation method to nonlinear differential and integral equations.
本文给出了几个应用实例，以说明“同伦分析方法”的有效性及巨大的潜力。
Examples are given in this paper to show the validity of this method.
利用精细积分技术对同伦摄动方法进行了改进，构造了一种求解非线性动力学方程的新的渐近数值方法。
A new asymptotic numerical method for nonlinear dynamic equations was proposed. In this method, the homotopy perturbation method was improved by using the precise integration technique.
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。
The results indicate that the HAM is still valid for solving a class of higher dimensional evolution equations.
同时在分析了同伦参数正则化效应的基础上，提出一种两段同伦参数修正方法。
Considering the regularization effect of homotopy parameter, we adopt a two-step update scheme of homotopy parameter.
为保证迭代稳定性，并同时削弱观测噪声的影响，同伦参数的修正采用了连续化修正方法。
Moreover, a continuous method is employed to modify the homotopy parameter during iteration in order to ensure the ability of the iteration and the capability of the noise resistance.
在第4章，同伦摄动的方法被成功应用到求解带有一个可动边条件的时间分数阶扩散方程并且得到了一个近似解。
In chapter 4, Homotopy perturbation method is successfully extended to solve time-fractional diffusion equation with a moving boundary condition and an approximate solution is obtained.
应用“同伦分析方法”成功求解了科学和工程中众多类型的非线性问题，证实了其有效性和普遍适用性。
The homotopy analysis method has been successfully applied to a lots of different types of nonlinear problems in science and engineering so as to prove its general validity in a wide region of fields.
应用“同伦分析方法”成功求解了科学和工程中众多类型的非线性问题，证实了其有效性和普遍适用性。
The homotopy analysis method has been successfully applied to a lots of different types of nonlinear problems in science and engineering so as to prove its general validity in a wide region of fields.
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