数值方程

Four bands Runge - Kutta method for ordinary differential equations, numerical algorithm of the function subroutine.

4阶龙格库塔方法求常微分方程的数值算法的函数子程序。

In this method, Maxwell's equations are approximated by a set of finite-dif

程的众多数值解法中，FDTD可能算是最流行的一种[41]。在这一方法中，麦克斯韦方程

This paper focuses on four important aspects as follows. The first one is the establishment of variational quations which provides the mathematics theories for the finite element method of HMT; the second one is for the study of scalar/node and vector/edge finite element method; the third one is about how to solve faster for the large-sacled matrix system of scalar/node and vector/edge finite element; and the last one is achieving the forward modeling with high precision of HMT method.

主要包括四部分：建立与高频大地电磁法边值问题相等价的变分问题，为有限元数值计算奠定数理基础；标量/矢量有限元方法的研究；加速标量/矢量有限元矩阵系统方程迭代求解技术的研究；实现高频大地电磁参数精确快速正演模拟的研究。

Next, the principle of PWTD algorithm used for solving scalar quantity fields is analyzed in details. The implementation and the numerical realization are also discussed.

最后，详细分析了利用两层时域平面波算法求解时域积分方程的原理和数值实现过程，在此基础上评估了该方法的计算量。

Results of analysis show that Generalized Paris Law can consider the complex crack propagation in the material of the pavement structure. The fatigue life of the pavement increases with increasing thickness of surface layer in a power function. Use of a thicker surface layer may extend the service life of the asphalt pavement. The fatigue life increases with decreasing modulus of surface layer in a power function with a negative exponent. However, since reduced modulus would scarify the structural strength and might cause rutting-related distress, caution should be taken when using low modulus materials for improving fatigue performance of asphalt pavements. The fatigue life increases with increasing modulus of base material in a power function. However, the fatigue life can not infinitely increases with increasing modulus of the base.

计算与分析表明：广义Paris公式可以考虑沥青路面结构内材料复杂的裂缝扩展：沥青面层的疲劳寿命随着面层厚度的增加以幂函数的形式增加，适当增加沥青面层厚度可以提高路面的使用寿命；沥青面层的疲劳寿命随着面层材料模量的降低以负指数的幂函数形式增加；由于材料模量的降低将牺牲路面的整体强度并可能引起路面车辙类损坏，以此提高疲劳寿命的方法应慎重对待；沥青面层的疲劳寿命随着基层材料模量的增加呈幂函数的形式增加，但由疲劳方程可以看出，寿命并不是随基层材料模量的增加而无限的增加，疲劳曲线在经过一个上升段后，逐渐趋于一个常数值，这说明，这时基层模量对寿命已不作关键性贡献；随着底基层厚度的增加，面层的疲劳寿命近似地呈线性函数增加，但效果并不很明显。

The inlet internal flow structure was well visu-alized by the schlieren photographs and pressure data.

采用纹影方法，结合压力测量对进气道内流结构进行诊断，同时用Yee的TVD有限差分格式通过求解二维N─S方程对相应实验状态下的进气道内流场进行了数值模拟。

The section curve graph of a singularity surface is drawn. A numerical example of singularity configuration analysis is given for illustration.

主进给机构的奇异位形的集合为参数空间的曲面片，得到了奇异曲面方程及奇异曲面的截面曲线图，给出了奇异位形分析计算的数值实例。

Three aspects have been studied theoretically in this paper which were based on an analysis of a compliant multleaf journal self-acting air bearing, which are as follows:(1) A set of theoretical analysis method which include the development of .physical and mathematical model, the solution of governing equations and theprediction of static and dynamic performance of the foil gas bearing is proposed.

本文在分析悬臂型弹性箔片径向动压气体轴承工作原理的基础上，做了以下几个方面的工作：(1)建立了悬臂型弹性箔片径向动压气体轴承的物理和数学模型，确立并求解了控制方程，得到了静、动态性能的稳定性分析方法，为数值分析悬臂型弹性箔片径向动压气体轴承奠定了基础。

It gets correct results with very few calculations and it is self-starting.

使用了一个特殊二阶微分方程的数值解法，该方法精度较高，计算量很小，而且可以自启动。

Stress intensity factor is obtained by solving singular integral equation. Numerical examples are given to show the effects of material properties, interlayer thickness, and especially the distribution parameter k on the stress intensity factor.

通过处理奇异积分方程得到了应力强度因子，数值结果给出了材料特性、界面层厚度、尤其是分布特征参数k对应力强度因子的影响。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。