数值方程

However, the refraction of plane wave in reaction-diffusion system obeys Snell's law only for proper diffusion coefficients and system parameters.

在二维复金兹堡-朗道方程描述的反应扩散振荡系统中，就扩散对平面波折射率的影响进行了数值研究，从Snell定律出发导出了折射率的解析表达式，数值和理论结果表明：在纯扩散情况下，平面波的折射满足Snell折射定律，扩散只影响着平面波折射率的大小；在同时存在反应扩散情况下，只有在适当的扩散系数和系统参数下，平面波的折射才满足Snell折射定律。

In this paper, a new numerical method, the coupling method of spherical harmonic function spectral and streamline diffusion finite element method for unsteady Boltzmann equation in the neutron logging field is discussed, and the convegrence and error estimations of this scheme are proved.

针对中子测井问题，研究非定常Boltamann中子输运方程的确定型数值求解方法，给出了求解Boltzmann方程的球谐函数展开和流线扩散有限元耦合方法，证明了这种耦合方法的收敛性和误差估计·实际算例表明此方法是有效

Applying the boundary condition in the interface between the uniaxial anisotropic medium and free space, the surface of the conducting sphere, the expansion coefficients of electromagnetic fields in terms of spherical vector wave function in uniaxial anisotropic medium are obtained, and then the expansion coefficients of scattering fields and radar cross sections can be obtained.

通过矩阵方程的求解和球B(来源：e3ABC论文网www.abclunwen.com)essel函数的大宗量渐进表达式，我们给出了各向异性单轴介质球结构对平面波电磁散射的数值计算结果，并和其他的数值计算结果进行了比较，其结果正如我们所预料的一样，达到了预期的结果。

Based on the N-S equation, standard κ-ε turbulence model, the FLUENT was used to simulate the kind of air inlet of solid ducted rocket.

基于RANS平均的N-S方程、标准κ-ε双方程湍流模型，利用FLUENT软件对某型固体火箭冲压发动机进气道内外流场进行了三维数值模拟。

In the aspect of the study of the application of HHT method, This dissertation has done three part of jobs: first, the Elcentro strong ground motion which is in common use in earhtquake engineering is analyzed by HHT method, getting its amplitude-frequency-time distribution and the comparison between the HHT marginal spectrum and Fourier spectrum is also made; second, the typical nonlinear system defined by the Duffing equation is analyzed by HHT method, getting its numerical value's amplitude-frequency-time distribution and the comparison between the HHT marginal spectrum and Fourier spectrum is also made; third, define the stationary degree of non-stationary signals making use of 3-D time-frequency spectrum and marginal spectrum, the stationary degree curve of Elcentro seismic recording is protracted according to its defining formula, the stationary degree curve of Elcentro seismic recording which change with time is protracted according to similiar definition.

在HHT方法的应用研究方面，本文做了三部分的工作：首先，利用HHT方法分析了地震工程中常用的Elcentro非平稳强震记录，得到了该记录的振幅－频率－时间分布特性，并将得到的边际谱与傅立叶谱做了比较；其次，应用HHT方法分析了典型的非线性系统－Duffing方程，得到了该方程数值解的振幅－频率－时间分布特性，并将得到的边际谱与傅立叶谱做了比较；最后，利用三维时频谱与边际谱定义了非平稳信号的平稳度，并依照其定义式绘制了Elcentro地震波记录的平稳度曲线，依照类似与依赖与频率变化的平稳度定义，初步尝试编程绘制了Elcentro地震波随时间变化的平稳度曲线。

In the present work, we educed the systematic energy functional of the binary lipid membrane model. And based on the phase kinetics of continuous systems, we established the governing equations for the phase separation in binary lipid membrane under stationary shear flow. Then, by means of the cell dynamical system approach, the equations were numerically solved, intuitively giving out the domain morphologies and membrane shapes.

在本论文工作中，我们导出了两组分磷脂膜模型的系统能量泛函，基于连续系统的相场动力学，建立了稳定剪切流场作用下的两组分磷脂膜的相分离动力学控制方程，进而利用元胞动力学系统方法对控制方程进行数值求解，直观地给出了微区域形态和膜形状。

The numerical calculation commonly used for the Delphi process more than 100, including solutions of linear algebraic equations, interpolation, numerical integration, special, function approximation, eigenvalue problems, data fitting equation Root and solve nonlinear equations, functions and the extreme optimization, statistical data description, Fourier transform spectra, solution of ordinary differential equations reconciliation partial differential equations.

本书共有数值计算中常用的Delphi子过程100多个，内容包括解线性代数方程组、插值、数值积分、特殊函数、函数逼近、特征值问题、数据拟合、方程求根和非线性方程组求解、函数的极值和最优化、数据的统计描述、傅里叶变换谱方法、解常微分方程组和解偏微分方程组。

And some computing methods of stochastic differential equation are given.

基于Monte Carlo方法，结合微分方程数值解的方法，采用多种随机过程产生策略和随机模拟方法，对原系统进行了仿真，提出了相应的数值计算格式。

By applying the H〓lder inequality, the Gronwall inequality, the Doob's inequality and the properties of the Ito stochastic integral to the integral form of the test equation, several important inequalities related to the analytical solution are proved, and the local order of the numerical solutions in mean square sense is obtained accordingly.

通过对试验方程的积分形式使用Holder不等式、Gronwall不等式、Doob不等式和Ito随机积分的性质，得出了试验方程解析解满足的几个重要不等式，进而得出了数值方法在均方意义下的局部误差阶。

In this paper, we give the method of solving the partial differential equations with the combine use of symbolic and numerical method, which is a new way of solving the extremely complicated partial differential equations.

本文作出了将符号计算方法和数值计算方法结合起来求解偏微分方程的研究工作，这是求解比较复杂的偏微分方程的新途径。

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。