查询词典 geometric difference equation

In Chapter 2, starting from the basic fractional ordinary differential equations,weapply a high order approximation of fractional derivative advanced by Lubich to frac-tional differential equation, construct a high numerical difference scheme to solve thefractional differential equation, present error analysis of the algorithms theoretically,and prove the consistency ,convergency and stability.

接下来的第二章中，首先从基本的分数阶常微分方程出发，对Lubich提出的一个关于分数阶导数的高阶近似，将其应用于分数阶微分方程，构造高阶数值差分格式来进行分数阶微分方程的数值求解，并在理论上给出这一算法的误差分析，证明了它的相容性，收敛性和稳定性。

He difference between quantities equation and numerical value equation is analyzed in detail.

从定义、概念、应用以及相互关系等方面对量方程式和数值方程式进行了分析对比，指出了正确使用这两种方程式的重要性和方法。

Among used machine learning methods, the gradient descent method is widely used to train various classifiers, such as Back-propagation neural network and linear text classifier. However, the gradient descent method is easily trapped into a local minimum and slowly converges. Thus, this study presents a gradient forecasting search method based on prediction methods to enhance the performance of the gradient descent method in order to develop a more efficient and precise machine learning method for Web mining.However, a prediction method with few sample data items and precise forecasting ability is a key issue to the gradient forecasting search method. Applying statistic-based prediction methods to implement GFSM is unsuitable because they require a large number of data items to model a prediction model. In the contrast with statistic-based prediction methods, GM(1,1) grey prediction model does not need a large number of data items to build a prediction model, and it has low computational load. However, the original GM(1,1) grey prediction model uses a mathematical hypothesis and approximation to transform a continuous differential equation into a discrete difference equation in order to model a forecasting model.

其中梯度法是一个最常被使用来实现机器学习的方法之一，然而梯度法具有学习速度慢以及容易陷入局部最佳解的缺点，因此，本研究提出一个梯度预测搜寻法则(gradient forecasting search method， GFSM)来改善传统梯度法的缺点，用来提升一些以梯度学习法则为基础的分类器在资讯探勘上的效率与正确性；而一个所需资料量少、计算复杂度低且精确的预测模型是梯度预测搜寻法能否有效进行最佳解搜寻之关键因素，传统统计为基础之预测方法的缺点是需要较大量的数据进行预测，因此计算复杂度高，灰色预测模型具有建模资料少且计算复杂度低等优点，然而灰色预测理论以连续之微分方程式为基础，并且透过一些数学上的假设与近似，将连续之微分方程式转换成离散之差分方程式来对离散型资料进行建模及预测，这样的作法不尽合理，且缺乏数学理论上的完备性，因为在转换过程中已经造成建模上的误差，且建模过程仅考虑相邻的两个资料点关系，无法正确反应数列未来的变化趋势。

The finite difference method is employed to discretize the governing equations and the projection method is used to derive a pressure Poisson equation that can ensure the satisfaction of continuity equation.

控制方程式采用有限差分法求解，并利用投影法导出压力的波松方程，使得能自动满足连续方程式。

In the simplified model, the governing equation of heat conduction is discretized using implicit finite difference method, and the computational domain is discretized using cell centered scheme, and the solution of Maxwell equation is used to determine the distribution of the internal heating sources.

使用的简化模型中热传导方程的离散采用隐式差分法、区域的离散采用内节点法，并以Maxwell方程的解确定内热源分布。

And we show that random walk model converges to the stable law of Lévy-Feller advection-dispersion equation by use of a properly scaled transition to vanish-ing space and time steps,We propose an explicit finite difference approximation for Lévy-Feller advection-dispersion equation.

第三章讨论描述服从某种稳定分布反常扩散的非对称空间分数阶对流-扩散方程——Lévy-Feller对流-扩散方程，首先利用Fourier变换和Laplace变换给出方程的基本解，然后利用Grünwald-Letnikov分数阶导数移位离散算子离散方程中的Riesz-Feller分数阶导数得到离散格式，证明此格式可以解释为离散随机游走模型，并且证明了当时间和空间步长以一定的比率同时趋于0时，所提出的离散随机游走模型收敛到Lévy-Feller对流-扩散过程的稳定分布。

Use of the finite difference method for Volterra equation here as a variable element of the equation, As the same...

用差分方法求解沃尔泰拉方程，此处为一个变元的方程，由于该方程同时含有微分和积分，一般求解有一定的困难。

In the first part we consider the convergence and stability of finite difference scheme for Landau-Lifshitz equation in one dimensions space and 2d radial symmetric Landau-Lifshitz equation.

在第一部分，我们研究一维Landau-Lifshitz方程非齐次边值问题和二维柱对称Landau-Lifshitz方程Neumann边值问题的有限差分格式。

According to the properties of Wiener increments and the independent relation between the Wiener increments and the numerical solutions, the difference equation obtained by applying the numerical method to the general linear test equation is studied carefully in mean square sense and the conditions under which the numerical method is MS-stable and GMS-stable are determined.

依据维纳增量的性质以及维纳增量和数值解间的独立关系在均方意义下详细分析了数值方法应用到线性试验方程上得到的差分方程，并进一步确定了半隐式Milstein方法MS-稳定和GMS-稳定的条件。

Finite element discretization was carried out on the mathematical model to get a fully coupled finite element equation with the parameters of element nodal displacement and element nodal pore pressure as unknown variables. Finally, the transient nonlinear finite element equation in incremental form for reservoir fluid-solid coupling is obtained by means of time discretization in implicit difference scheme.

基于与微分方程等价的加权余量公式，在空间域采用有限元离散，对时间域进行隐式差分格式离散，导出了以单元节点位移和单元节点孔隙压力为未知量的储层流固耦合的非线性有限元增量方程。

When I started coding, I had problems with the ASF file writer.

当我开始编码，我曾与ASF文件作家的问题。

I know that in one of the schools the boys have risen up in the classroom and enlisted in a mass.

如果你们也和他们一样，是集体自愿的话，你们的老师将是多么地光荣啊。