差分法

MGM is introduced to solve field distributions in 3-D electron optical systems. The difference equation, the discrete form of Laplace's equation, is deduced in 3-D Cartesian coordinates. In view of the smooth effect, MGM combines Gauss-Seidel iteration with a technique known as coarse grid correction. Formulae for restriction and prolongation are deduced and expressed in terms of tensors.

将多重网格法引入电子光学系统中三维静电场的计算，对三维笛卡尔坐标系中的差分方程，采用高斯-赛德尔迭代法求解差分方程组，并结合迭代过程讨论了粗网格的误差校正技术；在不同网格层之间进行场值的限制和延拓，推导了三维静电场中的限制、延拓公式并以张量的形式表示。

Some known results are generalized.Second,the global asymptotic stability for a higher order rational difference equation was investigated by using "Subsequence Analysis Method " in Chapter 3,and the "Semi-cycle Analysis Method" is a extension and supplement of "Semi-cycle Analysis Method".

因此，本文第三章应用"子序列分析法"研究了一类高阶的有理差分方程解的全局动力行为，进一步得到了此类高阶有理差分程解得全局渐近稳定的一些充分条件，一些已知的结果被推广。

A new differential operator suitable for extracting leaves'texture was studied, and the percent histogram on base of the differential operator was used in extracting texture feature of leaves.

进行了基于差分算子的相对差值百分率直方图法提取缺素叶片上颜色差形成的纹理特征研究，并且提出了适合于本研究的最大化差分算子。

Compared with standard Crank-Nicholsonscheme in the same computational time and resource, the method has two characteristics: small truncation error of in the transverse direction and high accuracy. It is a useful tool for designing optical waveguide devices.

与标准格式的有限差分光束传播法相比，该算法在几乎不增加计算时间和计算机内存资源的情况下，结合了道(来源：122eA22BC论文网www.abclunwen.com)格拉斯格式的有限差分光束传播法截断误差小和宽角多步法所具有较高精度的优点，是光波导器件理想的数值模拟工具。

Firstly,the differential equation with parameters is given,at the same time,in order to let the truncation error of differential equation reach O(Δt~2+Δx~4) as high as possible,the method of undetermined coefficent is used to appropriately select the expression of these parameters.Secondly,the stability condition of the scheme derived is given by using the Fourier method of stability analysi...

首先给出了含参变量的差分方程，并用待定系数法适当地选取了这些参数的表示式，以使差分方程的截断误差阶尽可能高地达到了O(Δt2+Δx4)；其次用稳定性分析的Fourier方法给出了所得格式的稳定性条件；然后给出了确定差分格式中参数的两种方法，得到了一个稳定性条件为r/3的分支稳定的高精度显式差分格式；最后给出了数值例子，数值结果表明了本文格式较现有同类格式的优越性和理论分析的正确性。

In the two-dimensional simulation, the fully implicit difference scheme is used for the continuity equations to ensure numerical stability; Jacobian iteration is used to solve the difference equations, and only nonzero elements in the coefficient matrixes of these equations are dealt with, which reduce the requirement for memory and shorten the calculation time.

在两维模拟计算中，对连续性方程采用全隐式差分方案以保证数值稳定性；运用雅可比迭代法求解差分方程组，并且在求解过程中，只对差分方程组系数矩阵中的非零元素进行处理，因此减少了对内存的需求量，而且缩短了计算时间。

In this paper,the variable space finite difference method of lines is presented on the basis of equal space finite difference method of lines.

在等步长有限差分线法的理论基础上，构造出变步长的有限差分线法格式，并对其进行了误差分析。

Data pre-processing technologies such as singular points elimination, registration and radius compensation are studied. Base on chord high difference algorithm, a new one called chord high difference-ratio algorithm is proposed to improve veracity and robusticity of singular points elimination. Then, a registration algorithm based on local surface reconstruction is proposed, which avoids infaust influence coming from single reference point error.

在弦高差法的基础上，提出了全新的弦高差—比法，提高了异常点剔除的准确性和柔韧性；提出了一种基于局部图形重构的重定位方法，该方法通过对特征球的最小二乘拟合，消除了单一参考点的精度对重定位的影响；在此基础上对重定位的误差进行了详细的分析，给出了精确的误差值，从数学的角度保证了重定位的精度；在三角网格法的基础上提出了基于Delaunay三角剖分的半径补偿新方法，有效改善了补偿矢量的计算效率和准确性。

Specially,at lower power density of laser,quasi static model is used to simulate the radial heat dissipation from irradiated region to nonirradiated regions.

在数值计算中，应用部分线性法处理非线性非齐次热传导方程，得到相应的隐格式差分方程，再用追赶法求解隐格式差分方程，得出绝热边界条件下的温度的时间和空间分布，从而得出激光退火的再结晶厚度。

To improve the conventional difference threshold algorithm.

该文对QRS波群的检测算法进行了研究，对传统差分阈值法在R波检测中存在的一些问题加以改进，将正向和倒置R波分开检测，提出了在自适应差分阈值法检测正向R波的基础上，用幅值基线比较法检测倒置R波的检测方法。

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。