数值方程

The essence idea of restoration based on Total Variation is that translate the problem into minimum of energy functional with TV regularization, then the Partial Differential Equations are got from the principle of variation, finally after discretization the optimal resolution with the numerical methods is obtained.

基于整体变分的图像恢复概括的说就是把图像恢复问题形式化为带有整体变分正则化项的图像能量泛函极值问题，采用变分原理将其中的最小化问题转为所要求解的偏微分方程，即Euler-Lagrange方程，利用数字图像本身的离散特征使用适当的数值方法来求它的最优解，最后达到逼近原始图像的目的。

In the second chapter, generalizing the contractilities and asymptotical stabilities for multi-delay integro-differential equations. Under proper stepsize, we obtain the discretization schemes of Runge-Kutta methods with the compound quadrature formula and the Pouzet quadrature formula, and besides, derive the global and asymptotical stabilities. Moreover, the numerical experiments show that the presented methods are highly effective.

第二章，考虑了多延迟情形下的积分微分方程，推广理论解的收缩性与渐近稳定性结果，在适当的步长下，利用复合求积公式与Pouzet求积公式扩展Runge-Kutta方法，获得离散的计算格式，并且证明了方法是数值稳定的，此外，数值试验表明此计算方法在实际应用中是非常有效的。

The qualitative theory of ordinary differential equations and numerical simulation method are employed to investigate the kink waves of a nonlinear quartic equation.

用微分方程定性理论结合数值模拟方法研究了一类非线性4阶Boussinesq方程的扭结波。

In order to study the numerical method to solve the viscous incompressible flow with free surface, the 3-D mathematical model for steady and unsteady hydrodynamic problem had been established and closed by k-εbuoyant turbulence model. The algebraic coordinate transformation method was used to fit the free surface, the Runge-Kutta method of three step and second precision was devised to simulate the time step. A high precision up-winding compact scheme was studied for the convection term, and the generalized conjugate residual method was set to solve the Poisson equation.

为了研究粘性不可压缩三维问题的数值求解方法，本文从基本的Navier-Stokes方程出发，采用代数拟合方法处理自由表面，用三级二阶Runge-Kutta方法对时间步进过程进行了模拟，并且对对流项的高精度迎风格式进行了研究，给出了求解压力Poisson方程的广义共轭剩余法，从而建立了能够模拟有自由表面的粘性不可压缩问题的定常、非定常三维水动力学模型，并采用k—ε浮湍流模型对其进行封闭。

The value solution adopts "the step-type" format to solve separate lights for the approximate value. The Euler method and the Runge—Kutta method are the most typical commonly value method to solve the differential equation.

数值解法采取"步进式"的方式求解离散点上的近似值，欧拉方法和龙格——库塔方法是求解微分方程最典型常用的数值方法。

The viscoelastic modeling in 2-D SEG/EAGE salt dome model is carried out by using the simplified viscoelastic equations. A comparison of the viscoelastic single-shot records derived from acoustic equations, Carcione's equations and the simplified viscoelastic equations is made.

并利用该简化方程对SEG/EAGE二维盐丘模型进行了正演数值模拟，将模拟得到的单炮记录和声波、Carcione黏弹性波方程模拟得到的单炮记录进行了对比分析。

In order to investigate and develop numerical calculation method for Schr odinger equation, we apply the finite difference method to eigenvalue problems in quantum mechanics.

为研究和发展薛定谔方程的数值计算方法，本文将有限差分法应用到量子力学求解薛定谔方程本征值问题。

These methods and models are based on solving the Schrodinger equation.

已经提出来的理论方法和建立的理论模型基本上都是基于求解含时薛定谔方程，这就要求理论工作者开展一些数值计算，即基于势能面的量子波包的数值模拟也越来越显得重要。

We reproduce the well-established and self-generated magnetic field equations, which are nonlinear partial differential equations.

我们证明该非线性偏微分方程具有塌缩波解，并用标准的数值方法解此方程来验证分析结果。

C Taking the short-fiber reinforced and inhomogeneity spreaded composite materials as engineering background, singular integal equations of plane problem of interaction between line inclusion and circular inclusion are deduced, and some particular cases are analysed.

以短纤维和颗粒弥散体复合材料为背景，导出了线夹杂与圆夹杂相互作用平面问题的奇异积分方程，并对一些特殊情形作了退化分析，建立了数值法，给出了圆夹杂和线夹杂两侧的界面应力及线夹杂端点的应力强度因子表达式，同时作了具体的数值计算。

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。