变分方程

Those equations are dispersed in space by iso-parameter elementmethod and in time by using backward difference. A numerical simulator is established byFortran, the ideas of high part make the of structure program clear, maintain easy, calculationeffective.

在此基础上利用Fortran语言编制了有限元方法的油藏模拟器，采用等参元对渗流方程在空间上离散，采用向后差分在时间上离散，线性方程组的求解采用变带宽高斯消去法，该方法充分利用刚度矩阵呈条带状和其对称性的特点，大大减少了所需存储空间。

VOF equation use Lax-Wendroffgeshi scheme with precision of two steps. Pressure of host field is turned into initial-boundary value problem of variable coefficient parabolic equation on regular border. We utilize implicit difference method to solve it.

VOF方程的离散求解使用Lax-Wendroffgeshi格式，这种格式具有二阶精度；主场压力的求解转化为固定边界上变系数抛物型方程的初边值问题，采用隐式差分格式。

The grids can be densified locally where the flow is complicated for the sharp change of water depth.(5) 2-D hydrodynamic equations in the generalized curvilinear coordinates have been derived with the contravariant velocities as main variables. The new equations keep the original styles and physical meanings. Based on the water depth correction method, the 2-D flow numerical model has been established and validated by the measured data.

推导了广义曲线坐标系下以逆变流速张量作为主变量的二维水动力方程，新方程保持原有结构形式及物理含义，采用水位校正法建立了二维水流数学模型，经实测资料验证后的模型，模拟并分析了分流角度、宽深比等因素变化对分汊流平面二维水流结构的影响。

The paper consists of four chapters:In chaper 1, we introduce the background and signficance, research and actuality on oscillation of functional partial differential equations; we present research subject in this paper;In chaper 2, we discuss oscillatory property of systems of parabolic differential equations with delays and obtain necessary and sufficient conditions for the oscillation of their solutions; we show the difference between oscillatory property of systems of parabolic differential equations with delays and that of systems of partial differential equtions without delays; we explain the main results with examples;In chapter 3, we discuss oscillatory property of systems of functional parabolic differential equations of neutral type; we obtain some sufficient conditions for the oscillation or full oscillation of their solutions under some conditions; we explain the main results with examples;In chapter 4, we discuss oscillatory property of systems of functional hyperbolic differential equations of neutral type; we obtain sufficient conditions for the oscillation or full oscillation of their solutions under some conditions; we explain the main results with examples.

全文共分四章：第一章简要介绍了泛函偏微分方程的振动的背景和意义、对其研究的简单历史和现状，给出了本文的主要研究对象；第二章讨论了一类时滞抛物方程组解的振动性质，获得了判断其所有解振动的一个易于验证的充要条件；指出了这类具有时滞偏差变元的抛物方程组解的振动性质和不具有时滞偏差变元的抛物方程组解的振动性质的差异；并举例对主要结果进行阐明；第三章讨论了一类中立型抛物方程组解的振动性质，获得了在给定的条件下其所有解振动或全振动的若干充分条件；并举例对主要结果进行阐明；第四章讨论了一类中立型双曲方程组解的振动性质，获得了在给定的条件下其所有解振动或全振动的若干充分条件；并举例对主要结果进行阐明。

It adopts the variable step length scheme to evaluate at the connection point, and adopts the implicit difference scheme to evaluate in the same rod.

3运用在均质处采用隐式差分格式、节点处采用变步长的有限差分的混合方法求解抽油杆柱的波动方程。

In chapter 3,we extend the differece format in chapter 2 to two-dimensional changing coefficient parabolic equation.

在第三章，我们将第二章的差分格式推广到二维变系数抛物型方程中去。

The equations of the towed cable motion are based on Ablow and Schechter model and six degree-freedom ordinary differential equations are used in the analysis of the motion of a towed body. The partial differential equations are discretized by finite difference method and the transient values of towed body depth and cable tension are computed by Newton Iteration when the heave compensation system performs and the length of the cable varies.

拖缆动力学模型基于Ablow and Schechter模型，拖体采用水下运载体六自由度方程模拟，运用有限差分法离散偏微分方程组和牛顿迭代法计算变缆长情况下拖体深度与拖缆各点张力的动态取值。

The equation of states under high temperatures and high pressures, phase -transition and metalization for H_2 and its isotopes are one of the hot topics of scientific studies for a long time.

氢及其同位素的高温高压状态方程、相变与金属化等问题是长期以来科学研究的热点课题之一；氢、氦分别是结构最简单的双原子和单原子分子，在冲击加载条件下，氢，氦材料的热力学特性一直是从事凝聚态物理研究的理论和实验工作者非常关注的前沿研究课题之一。

A seven-node difference scheme of the diffusion equation was proposed to study the behaviors of transient electromagnetic field in complicated 3-D geoelectric body. Models of roadway and anomaly body were set up for simulating the transient field excited by a vertical magnetic dipole source. The result of numerical simulation shows that the presence of low resistive conductor leads to noticeable distortion of isolines for the "smoke ring" field, whereas the distortion is not so obvious where the roadway and the poor conductor are located.

为了探讨复杂三维地电体中瞬变电磁场的响应特征，推导了三维扩散方程的七点差分格式，建立了巷道和异常体模型，并对垂直磁偶源激发的瞬变场进行了数值模拟，观察到早期&烟圈&场在低阻体处等值线发生的明显畸变，在巷道和高阻体处的畸变较弱，随着时间的增加异常体的影响逐渐减弱。

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。