在第一部分，我们提出了用于构建把有关质量的摄动展开到三阶的方法。
In the first part, we develop the method used for the construction of the third order perturbations with respect to the masses.
本文描述了一种新的、不依赖于小参数的非线性分析方法，并分析、比较了该方法与摄动展开方法的优缺点。
In this paper, a new kind of nonlinear analytical method which does not depend on small parameters is described and is compared with the perturbation techniques.
最后文章证明了对带松弛项的流波方程初值问题所作的奇异摄动展开的有效性，得出了有关解的存在性的一些有用的推论。
In the end, we prove the validity of the singular perturbation expansions and get some useful deductions about the existence of the classical solution to the flood wave equations.
运用分歧理论、固有值的解析摄动理论和渐近展开的方法，获得了共存时间周期解的存在性和稳定性。
The existence and stability of periodic solution are studied by using the bifurcation theory, linear stability theory and the method of asymptotic expansion.
本文利用奇异摄动理论的两时间变量展开法，研究了垂直强迫圆柱形容器中的单一水表面驻波模式。
The single standing wave mode in a circular cylinder subjected to a vertical oscillation was studied by employing two-time-scale perturbation expansions.
为此，考虑到高阶模态的影响，提出了基于改进一阶摄动法的模态高精度展开法，算例表明，此方法能显著地改善摄动特征解的精度。
Taking higher frequency modes into account, an accurate expansion method based on the improved first-order perturbation is put forward, which can improve the precise of modes obviously.
然后利用摄动方法证明了这个问题解的存在唯一性，同时给出了解的渐近展开和误差估计。
The existence and uniqueness theorem of its solution is proved by the perturbation method and the estimation of error for its approximate solution is given.
模态展开法是计算特征向量摄动量的常用方法之一，但当高阶模态被截断时。
The modal superposition method is often used for computing the Perturbation of eigenvectors in the modification for structural and correCtion for model.
该VSOP82方法是由考虑了所有行星质量的展开到三阶的摄动构成的。
The VSOP82 solution is made of the perturbations developed up to the third order of the masses for all the planets.
本文通过对油膜压力进行二阶泰勒级数展开得到油膜摄动压力方程组，采用指数膜假定求解油膜摄动压力方程组，得到推力轴承油膜刚度和阻尼的解析表达式。
In this article, author derives oil film perturbed pressure equation through expanding pressure using a Taylor Series. With exponential film assumption, analytical expression of OFSD is also derived.
通过摄动方法得到一系列关于水头展开式的偏微分方程，用有限差分法进行求解，获得了压力水头的随机描述，并计算其均值和方差。
The equations are solved by finite difference method and the mean and variance of pressure head are determined from its random expression.
研究了一类ENSO摄动模型。利用摄动理论和方法，构造了相应问题的渐近展开式。
A class of ENSO perturbed model is studied. Using the perturbation theory and method, the asymptotic expansions of solution of corresponding problem are constructed.
从基于小参数渐近展开和摄动方法的均匀化理论出发，给出了求解细观应力的数学表达式。
A homogenization method based on the perturbation theory is presented to deduce the mathematical expression of the (micro-stress).
从基于小参数渐近展开和摄动方法的均匀化理论出发，给出了求解细观应力的数学表达式。
A homogenization method based on the perturbation theory is presented to deduce the mathematical expression of the (micro-stress).
应用推荐