所以我匆忙地写了篇论文，给出一阶近似解并指出至少在这个精确度下，理论和实验结构都相符合。
So I hastily wrote up a paper giving the first order of approximation and showing that to that accuracy, at any rate, we had agreement between the theory and observation.
如果高阶近似解不符合实验结果，也许这整个思想的基础都将被抛弃，而我只是无法面对这个结果。
Perhaps the whole basis of the idea would have to be abandoned if it should turn out that it was not right to the higher orders and I just could not face that prospect.
近似解的计算是极其繁重的工作。
The computation of approximate solutions was an extremely laborious task.
对于求近似解来说，它们却好用得多。
要利用这种近似解来模拟大爆炸在以前是不可能实现的。
The kinds of approximations needed to, for example, simulate a firestorm, were in the past computationally intractable.
在适当的条件下，较简捷地得出了这两类非线性波方程的近似解。
Under appropriate conditions, the approximate solutions for two nonlinear wave equations are obtained simply and conveniently.
从精确解出发，推导出最近文献中提出的“解析近似解”，并指出该近似解的适用条件。
The recently proposed "analytic approximation solution" is proved to be a good approximation to the corresponding analytic solution under some conditions.
借助于型参数，通过变换动量积分方程，得出动量损失厚度近似解的表达式。
By type factors and transitional momentum integral equation, the approximate expression of momentum thickness is presented as well.
并证明了如下结论：用这个方法得出的近似解，当阶梯数趋于无穷时趋于真解。
The following result is proved. The approximate solution by this method approaches the true solution if the number of the steps approaches the infinity.
本文就机床主轴箱的瞬态温度分布提供一个近似解。
This paper presents an approximate solution of instantaneous temperature distribution of the headstock.
我们可以利用这个结果求出近似解的界限。
We can use this result to establish bounds on approximate solutions.
处理孔缝边界时，用级数展开和积分方程得到金属拐角处电磁场的近似解。
For dealing with the electromagnetic fields near edges, an approximate scheme is developed using the series expansions and integral equations.
对带色散项非线性控制方程进行了研究，用“参数微分法”，得到其近似解。
This paper studies nonlinear wave equation with dispersion items, reaching an approximate Solution in the method of Parameter differentiation.
根据光波导理论，推算出弱导条件下光沿光纤传输场的标量近似解，给出场的各分量表达式，以便分析讨论。
Using wave guide theory, we deduce scalar approximate solution about transmissive light through a fiber weak-guide and give the expressions of field in each component.
本文主要就模糊目标规划问题的模型和近似解进行了探讨和研究。
In this paper, the models and approximate solutions of fuzzy goal programming problem were discussed.
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.
二次近似解达到薄壳理论所具有的精度，一次近似解也具有足够精度。
The second approximation of the solution is of the same accuracy as theory of thin shells, and the first approximation is also sufficiently precise for engineering computation.
本文给出有限长径向轴承雷诺方程的一种近似解。
This article brings forward an approximate analytical solution to Reynolds equation for finite journal bearings.
根据板材塑性成形过程中的拉应力与剪应力关系的假设，可以得到力学方程的近似解。
According to the hypothesis between tensile stress and shear stress relationship during sheet metal forming, a similar solution of the equations can be obtained.
针对梯度功能压电复合材料球壳热弹性响应提出了简单而精确的近似解。
A simple and accurate approximate solutions of thermoelastic responses of functionally gradient piezoelectric composite spheres is developed.
通过合理控制计算量，得到了微分方程近似解的局部截断误差的估计。
The local truncated error estimation of the approximately solution could be obtained with reasonable computational cost.
本文试图在时域范围内寻找一种近似解耦方法，称之为输入-输出能量解耦方法。
This paper tries to seek an approximate decoupling method in the time-domain framework. It is called as an energy decoupling method.
进一步指出了高斯光束作为波动方程傍轴近似解的条件。
Furthermore, the conditions have been given that Gaussian beam is a paraxial approximation solution of the wave equation.
求得了速度和温度的耦合非线性方程组的近似解。
Approximate solutions for the coupled non-linear equations are obtained for the velocity and the temperature.
只有在极特殊的情况下超定方程组才有精确解，一般情况下都是求超定方程组在某种意义下的近似解。
Only in under very special circumstance, an overdetermined systems have accurate solutions and general an approximated solution is often found in some determination of the overdetermined system.
并建议了一种新的流动法则，对应用定理求极限荷载的近似解给出了新的解题思路。
A new flow rule was recommended, and it offered a new way for obtaining the approximate solution of the ultimate load with the theorem.
并建议了一种新的流动法则，对应用定理求极限荷载的近似解给出了新的解题思路。
A new flow rule was recommended, and it offered a new way for obtaining the approximate solution of the ultimate load with the theorem.
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