数值微分

Gridless methods and their applications for the solution of partial differential equations are studied in this thesis.

本文的主要目的是研究无网格方法，并将其应用于偏微分方程的数值解过程中。

Numerical results for perfectly conduction and homogeneous penetrable circular cylinder are presented and compared with the solutions by using second-order differential operator B2 type absorbing boundary condition.

本文使用这种边界条件对理想导电及均匀电磁可穿透材料圆柱散射体的表面场进行了数值计算，并与使用二阶微分算子B_2型的吸收边界条件的结果作了比较。

Numerical experiments were performed to demonstrate the efficiency and efficacy of the proposed methods, for both smooth and piecewise smooth domains with exact and noisy data.

文中给出了数值算例说明了基本解方法和边界节点法求解椭圆型偏微分方程反问题的有效性，分析了基本解方法的收敛性，考察了光滑和分片光滑的几何区域以及数据精确和含有噪音两种情形。

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。

The mathematical model of coal-bed methane seepage is established considering slipped effect, giving the weak form of the differential equation based on the principle of virtual displacement, hereby writing FEPG program. Using FEPG system's all the source program of the finite element which considers the mathematical model of coal-bed methane seepage of slip effect the numerical solution is sought.

建立考虑滑脱效应的煤层气渗流数学模型，给出了基于虚位移原理的微分方程的弱形式，据此编写了FEPG程序，利用FEPG系统生成了考虑滑脱效应的煤层气渗流数学模型有限元问题的全部Fortran源程序，并进行了数值求解。

The paper introduces a differential equation derived from Markov theory and probability generating function.

文章介绍用Markov理论与母函数方法建立相关微分方程，并导出近似解析解，着重对常数源在系统中的涨落作了数学描述，给出了数值例子。

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。

First and second order linear differential equations Path integral Numerical series Functions of the real variable: sequences and series of functions, entire series, applications to Fourier series.

第一，二阶线性微分方程路径积分数值系列在实变函数：序列和职能系列，整个系列，以傅里叶级数的应用。

The generalized magnetostatic field reciprocity theorem is deduced by the language of differential forms.

应用微分几何语言导出了广义静磁场互易定理，并应用该定理推导了漏磁无损检测数值分析中的富内德和蒙积分方程和线圈电感增量公

The boundary problem of differential equations is a problem of function regression.

求解偏微分方程边值问题的数值解是函数估计的一个方面。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。