数值方程

The numerical simulation is based on the fundamental hydrodynamic conservation equations including viscous effects for compressible fluid, coupled with the equation of state for water.

数值计算是基于包括粘性影响的可压缩流体基本守恒方程，并耦合了水的状态方程。

Conditional stability.

反问题，边值问题，不适定问题，偏微分方程，积分方程，条件稳定性，数值分析

Based on the equilibrium equation of an arch element the cubic nonlinear dynamic model with second order is established and the nonlinear differential dynamic system without constant term is obtained through a transfer process of T=U+b. Hence three fixed points and the homoclinic orbits are found. The critical condition of the chaotic vibration of the elastic arch is given by using the method of Melnikov function. The numerical results of the stationary and chaotic motion are given and discussed.

首先利用拱的单元平衡方程建立了拱的二阶三次非线性动力学模型；然后通过变换使方程转化为不含常数项的非线性微分动力系统，并由此得到无扰动系统的3个不动点与同宿轨道；再用Melnikov函数法给出了发生混沌的临界条件；最后给出了该系统出现定常运动和混沌运动的数值结果。

On the basis of Navier-Stoks equation and continuity equation, the SOLA-VOF method was adapted to calculate the field of velocity and pressure in fluid in this program. According to the inertia and continuity of fluid, a new velocity boundary conditions of free surface for 3dimensional fluid flow simulation had been developed. By the new method, any velocity condition occupied on the free surface of the fliud flow could be treated reasonably.

以流体的动量守恒方程和连续性方程为基础，采用SOLA-VOF方法，结合首次提出的流体惯性原理与连续性原理相结合的自由表面速度边界条件处理方法，研制出了流场数值模拟程序。

For PDEs with small parameters, a scheme is AP if it possesses the discreteanalogy of the continuous asymptotic limit as the small parameter goes to zero.

对于含有小参数的偏微分方程，所谓一个算法是渐近保持的指的是，当相应的数值离散在小参数趋于零的时候，仍然是渐近极限的合理数值离散。

The PSE in the curve coordinate systems are solved by the numerical techniques developed efficiently in this paper. A normal transform is introduced, and there are enough much grids in the region between the critical layer and the wall, where the variation of the disturbance is the quickest. The finite-difference of governing equations with fourth-order accuracy in the normal direction is utilized in full regions including points close the wall, and is very important for accurately discreting equations.

对于曲线坐标系下的抛物化稳定性方程，文中发展了求解的高效数值方法：引进法向变换，使得在临界层与壁面之间的扰动量变化最快的区域有更多的法向网格点；导出包含边界邻域在内的完全四阶精度的法向有限差分格式，这对方程精确离散至关重要；采用全局法和局部法相结合的方法及其新的迭代公式，大大加速收敛并得到更精确的特征值。

Keywords: Delay differential equation;Numerical method;Numerical stability

中文关键词：延时微分方程；数值方法；数值稳定性

To research the propagation characteristics of travelling wave along transmission line in depth, the authors establish a mathematical model of travelling wave along lossless transmission line with the format of discrete time and space mesh lines, derive the stable condition and boundary condition of the wave equations using numerical solution of partial differential equation, and attempt the simplification of the boundary condition to realize full decoupling of voltage and current.

为深入研究行波在配电线路上的传播特性，建立了时间-空间网格线离散格式的无损传输线行波数学模型，采用偏微分方程的数值解法推导了波动方程的稳定条件和边界条件，并尝试对边界条件进行简化，以实现电压和电流的完全解耦。

Here the deriver' self-equilibrium velocity denotes the deriver' desired equilibrium velocity accompanying that the traffic flow is in the equilibrium state. Consequently the adaptive flux model like Navier-stokes traffic equation is derived from the extended Paveri-Fontana equation. Characteristics and the linear stability are analyzed. Numerical solution of the macroscopic traffic equations verifies rationality of our model.

把适应性公式和约化Paveri-Fontana等式结合得到扩展的Paveri-Fontana方程，通过使用Chapman – Enskog方法导出类Naveri-Stokes 方程的适应性交通流模型；通过线性稳定性分析，得到了适应性交通流模型的稳定条件；通过对算例的数值分析与其它连续性模型和交通实测数据的对比，验证了我们模型的合理性。

For nonlinear harmonic oscillators, we close the flow equations and acquired an explicit expression of energy-level. For nonlinear-coupled harmonic oscillators, we close the flow equations and diagonalize the Hamiltonian by numerical analysis methods.

对非线性谐振子系统，计算出系统参数随流参数变化的一组方程及系统的能级；对耦合的非线性谐振子系统，得出系统参数随流参数变化的一组非线性方程，数值分析对角化了系统。

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。