利用摄动方法求出了相应模式的渐近解。
Using the perturbative method the asymptotic solution of the corresponding model is obtained.
他把这些解叫作渐近解。
高斯束是波动方程在特定射线附近的高频渐近解。
Gaussian beam is the asymptotic solution of wave equation concentred at the central ray.
使问题的维数，对各级渐近解而言，降低了一维。
For every order of the asymptotic solution, the dimensionality of the problem has been decreased by one.
采用正则摄动法，求出了由有限项初等函数所构成的渐近解。
The asymptotic solutions composed of finite terms of elementary functions are obtained by regular perturbation method.
这些精确解为实验，数值以及渐近解的检验提供了借鉴和参考。
The exact solutions are analytical physical solutions and can be served as accuracy checks for experimental, numerical and asymptotic methods.
我们利用问题的渐近解证明了差分格式关于小参数的一致收敛性。
By means of the asymptotic solution of singular perturbation problem we proved the uniform convergence of this scheme with respect to the small parameter.
还举了一个椭圆形截面杆强化弹塑性扭转问题，获得了它的渐近解。
Another example on the torsion of a prismatic bar with elliptic section is presented here and its asymptotic analytical solution is also obtained.
利用微分不等式理论，得到了原初始边值问题解的一致有效的渐近解。
The uniformly valid asymptotic solution to the original initial boundary value problems was obtained by the theory of differential inequalities.
此外，还得到了导致破产的索赔额的分布满足的瑕疵更新方程和渐近解。
Furthermore, the renewal equation and asymptotic formula of the distribution of the amount of the claim causing ruin are obtained.
这是首次研究差分方程的双向渐近解的存在性并获得了满意的研究成果。
This is the first time to discuss homoclinic solutions for difference equations, some satisfactory results are obtained.
其次，一种数值阶验证技术证实求得的二阶渐近解对小参数都是一致有效的。
Secondly, a technique of numerical order verification was applied to verify that the asymptotic solutions were uniformly valid for small parameter.
文中给出了这一非线性振动模型的微分方程，并用奇异摄动法求得了渐近解。
This paper also gives the differential equation of the nonlinear vibration model, and obtains its asymptotic solution by means of singular perturbation methods.
依据牛顿算法及渐近解分析，本文提出了一种梯形明渠临界流方程的直接算法。
By Newton algorithm and the analysis for asymptotic solution, this paper presents a direct formula for calculating critical depths of trapezoidal open channels.
在比较的基础上指出了这两种方法各自的优缺点，检验了高频渐近解的准确性。
The comparison between the two methods shows that each of them has its advantages and shortcomings.
本文利用特征方程根的性质，研究了开口圆柱薄壳精确微分方程的特征方程的渐近解。
Using the root of the characteristic equation, this paper studies the asymptotic solution of the characteristic equation of the open circular cylindrical thin shells.
提出了用初始层校正法求解机电耦合系统状态方程组的方法，获得了问题的渐近解析解。
In this paper, a method of using initial layer correction to solve the electromechanical coupled systems is submitted, an asymptotic solution of analysis are obtained.
本文讨论了一个奇摄动催化反应问题，得到了问题的形式渐近解，证明了它的一致有效性。
In this paper, a singularly perturbed catalytic reaction problem is considered. The formal asymptotic solution is obtained and its uniform validity is proved.
给出了利用渐近解公式，由模有效折射率的测量值确定波导表面折射率和扩散深度的方法。
A method is given for determining the parameters of a diffused waveguide from the observable values of mode efficient index by using the asymptotic solution equations.
采用全量理论和幂级数形式的应力一应变曲线，导出了弹塑性强化材料旋转园盘的渐近解。
Based on the stress - strain curve uith Power series, the asymptotic nalytical solution of rotating disks uith strain-hardening is obtained from the total strain theory.
分析了影响组织隐性知识传播渐近解的主要参数控制，指出了一些改进隐性知识传播效率的途径。
Then the main parameters influencing the asymptotic solution of the transfer process are analyzed, and some new methods to improve the implicit knowledge transfer efficiency are put forward.
最后，通过在裂尖前方引人一快变化区，本文得到了一个在裂尖周围应力和速度全连续的渐近解。
Finally, with the introduction of a fast varying zone ahead of the crack tip, a solution with fully continuous stress and velocity fields is obtained.
本文证明了求解周期区域上的二阶线性偏微分方程的一致有效渐近解的正交条件是充分和必要的。
In this paper, We prove that the orthogonal condition to solve the uniform asymptotic solution of second order linear P. D. E in periodic region is the necessary and sufficient condition.
因此，研究非线性浅水波的高阶渐近解对丰富近海水波动力学理论和指导工程实践均具有重要意义。
Therefore, the study of higher-order nonlinear approximate to shallow water waves enriches the water wave dynamics and is crucial to engineering practice.
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。
The uniqueness of the solution is proved, and the asymptotic expansion of the solution and remainder estimation are also given.
然后，运用微分不等式理论，证明了形式渐近解的一致有效性，并得出了解得任意阶的一致有效展开式。
And then, the uniform validity of solution is proved and the uniform valid asymptotic expansions of arbitrary order are obtained by using the theories of differential inequalities.
在适当的条件下，得出了这类问题的渐近解及其可解性条件，推广了一类近乎圆膜的振动问题所得的结果。
Under the appropriate conditions, the asymptotic solution and its existence conditions are obtained, the results for a class of quasi-circular membrane oscillation problem is extended.
本文用适当的多项式函数近似扩散光波导的高斯折射率分布函数，推导了导模有效折射率的解析形式渐近解。
The Gaussian index profile of a diffused optical waveguide is approximated by an appropriate polynomial, and the asymptotic solutions of the mode efficient index is derived in a analytical form.
本文通过简洁而又直观的方法讨论了线性情形时的有限维接触无的渐近行为，特别地，给出了渐近解的表达式。
This paper deals with asymptotic behaviour of finite-dimensional contact elements of infinite-dimensional linear systems. In particular. the analytical expression of the asymptotic solutions is given.
本文通过简洁而又直观的方法讨论了线性情形时的有限维接触无的渐近行为，特别地，给出了渐近解的表达式。
This paper deals with asymptotic behaviour of finite-dimensional contact elements of infinite-dimensional linear systems. In particular. the analytical expression of the asymptotic solutions is given.
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