The uniformly valid asymptotic expansion in entire is obtained.
并得到了一致有效的渐近展开式。
The uniformly valid asymptotic expansion of solution for the problem is obtained.
得到了问题解的一致有效的渐近展开式。
The likelihood ratio criterion of sphericity test, its asymptotic expansion and limiting distribution are obtained.
论文得到了球形检验的似然比准则，它的渐近展开与极限分布。
Thus, the fully asymptotic expansion of the homogeneous solution within the accuracy of theory of thin shells is obtained.
这样，轴对称正交异性圆环壳的齐次解第一次有了达到薄壳理论精度的完全的渐近展开。
The uniqueness of the solution is proved, and the asymptotic expansion of the solution and remainder estimation are also given.
研究了一类含有迁移项的奇摄动抛物方程的周期解问题，给出了解的存在唯一性、渐近解及其余项估计。
Renormalization group method is an effective tool to obtain the uniformly valid asymptotic expansion exact solutions of this kind of problems.
重正化群方法已成为获得这类问题精确解的一致有效渐近展开式的有用工具。
The existence and stability of periodic solution are studied by using the bifurcation theory, linear stability theory and the method of asymptotic expansion.
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 matched-asymptotic expansion method is adopted to solve the problem of transmission and reflection of a planar soliton on a two-dimensional floating body.
本文应用渐近匹配方法探讨了孤立波遇到二维柱体时的透射与反射问题。
On the basis of the governing equations and the asymptotic expansion of the stress fields proposed by Gao and Hwang, a generally asymptotic analysis is performed.
基于基本方程组和高玉臣、黄克智提出的应力场的渐近展开式作了渐近分析。
The existence of co-exist periodic solution is investigated by using the bifurcation theory, the implicit function theorem and the method of asymptotic expansion.
运用分歧理论，隐函数定理，以及渐近展开的方法，获得了非平凡周期解的存在性。
In chapter two, the asymptotic expansion and superconvergence result of a class of second order quasilinear equation in generalized finite element space is presented.
第二章中，给出了一类二阶拟线性方程广义有限元解的渐近展式和超收敛结果。
When parameters of the input of a large scale system deviate, its approximate reduced order model can be obtained by using the asymptotic expansion of the input function.
当大系统的输入函数的初始参数发生偏离时，其最优简化模型的近似模型可以利用输入函数的渐近展开得到。
If a parameter in the inputs of the original large scale system deviates, the corresponding reduced order model can be changed by using the asymptotic expansion of the input functions.
本文最后给出，当角频率有偏离时，其最优简化模型可以利用正弦输入函数的渐近展开式作相应的改变的结论。而且这种方法也适用于其它输入函数的参数偏离时的情形。
The relation between the explicit difference solution and the implicit one is established. A correction difference solution with higher accuracy is constructed by the use of asymptotic expansion.
首先讨论了隐差分解与显差分解的关系，并利用差分解的渐近展开式构造差分校正解来提高精度。
The Rayleigh inverse-iteration method and boundary layer asymptotic expansion method are used to solve the blunt cone boundary layer stability equation to get reliable boundary layer transition data.
然后应用反迭代法与边界层渐近匹配的方法求解了钝锥边界层的稳定性方程，得到了钝锥边界层转捩数据。
The finite element method is combined with homogenization theory based on asymptotic expansion for predicting effective properties of polymer matrix composites toughened and strengthened by particles.
将数学上的均匀化方法与有限元法相结合，预测了颗粒增韧增强聚合物基复合材料的有效性能。
Our proof of the convergence is based on an asymptotic diffusion expansion and requires error estimates on a matched boundary layer approximation to the solution of the discrete-ordinate method.
其收敛性的证明是依据其渐近扩散展开式，在边界层上得到的误差估计逼近其离散纵标方法的解。
For this, we derive the weighted estimates for discreet Green function and the asymptotic error expansion inequalities, and then the proofs of the formulas are given.
为此先推导离散格林函数的权模估计和有限元解的渐近不等式展开，然后给出公式的证明。
By means of the Taylor expansion technique, the asymptotic expressions of the dispersion curves at the long wavelength region were derived for flexural and longitudinal vibration modes.
利用泰勒展开技术，给出了长波区域弯曲振动模式和伸缩振动模式的弥散曲线渐近表达式；
Special crack-tip SNQE includes the second term of the asymptotic series expansion of the displacement fields near the crack-tip.
特殊裂纹尖端单节点二次单元包括近裂纹尖端位移近似级数展开第二项。
Special crack-tip SNQE includes the second term of the asymptotic series expansion of the displacement fields near the crack-tip.
特殊裂纹尖端单节点二次单元包括近裂纹尖端位移近似级数展开第二项。
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