数值方程

Especially, we give the embody expression of equation solution at unit square.

对于具体的单位矩形区域，给出了方程解在给定一点的表达式，并给出了数值算例。

First, we take the analysis of phase-plane on the invariant plane for the perturbed and unperturbed systems.

在第一章绪论中，我们简要介绍了近可积系统的相关内容，给出了具五次和导数项的非线性Schrodinger方程的物理背景，数值实验结果，研究状况以及本文所讨论的基本内容。

In the process of analytical solution, the divergent item can be give up according to the physical meaning of the solution. But there is no chance to give up the divergent item in the step-by-step integration method. This is why the numerical solution is unstable.

在比较了含有此发散项的该通解的数值结果与平均常加速度法的计算结果后，发现它们是一致的，从而找到了逐步积分法不稳定的原因，即逐步积分法不能避开方程解集中的不稳定子集（从而导致了一种发散性的不稳定）。

A conservative form for the flow equation is established by using upwind finite volume element method.

考察非饱和水流问题的模型方程，利用线性迎风有限体积元方法建立非饱和流动的守恒形式，并获得该方法形式为O的误差估计，最后给出数值模拟。

To avoid numerical diffusion caused by convection-dominated effect, the streamline upwind is introduced to modify the weighted function.

在有限元方程离散过程中，针对流动对流占优的问题，引入对权函数的流线迎风修正，有效地消除了高雷诺数流动计算中的数值震荡。

Based on the constrained variation principle, the penalty function suited to electromagnetic field calculation is proposed in this dissertation. Detailed research is conducted on some problems, such as the selection of penalisation parameters, the effect of penalisation parameters to the CPU time and the accuracy of solutions.

本文基于变分原理构造了适合电磁场数值计算的罚函数，得到了系统的控制方程，并对罚因子的选取原则及罚因子对计算精度和计算时间的影响进行了深入研究。

The approximation of meshless methods, the selection of weight function, the variational form and the discrete equation, and the numerical implementation are described.

描述了无网格法的近似方案、权函数的选择、变分形式和离散方程以及数值求解的实现。

Under the new boundary conditions related to viscous fluid, the variational equation of beam bundle fluid-solid coupling system related to viscous fluid is reached.

3在流体有粘的假设下，本文为随后的数值分析做了一些基础性的工作，在有粘流体相应的边界条件下，得到了粘性流体下管束流固耦合系统的变分方程。

In order to analyze the stiffness of 3D 4 directional braided composites, the homogenization theory based on the multi-scale perturbation theory was used as the basic theory. The virtual displacement principle was used to educe the homogenization formulation of effective elastic modulus and the schemes to solve the problem using finite element method. The effective elastic modulus of 3D braided composites were predicted by this method and the calculation results agree quite well with experiment results.

在对三维编织复合材料刚度性能的分析过程中，以基于小参数渐近展开和多尺度摄动方法的均匀化理论为理论基础，用虚位移原理导出了等效弹性模量的均匀化列式及其有限元求解方程，从而通过细观和宏观有限元的数值分析方法预测了三维四向编织复合材料的等效弹性模量，预测结果与实验结果较为吻合。

The author solved both unsteady and steady incompressible Navier-Stokes equations to simulate viscous flows and hydrodynamic force around a ship with free surface.

作者通过求解不可压缩Navier-Stokes方程数值计算水面船舶的粘性流场和水动力。

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。