差分法

Inverse M-matrices often occur in relation to systems of linear or non-linear equations or eigenvalues problems in a wide variety of areas including finite difference methods for partial differential equations, input-output production and growth model in economics, iterative methods in numerical analysis, and Markov processes in probability and statistics.

其中包括偏微分方程的有限差分法、经济中的投入产出和增长模型、数值分析中的迭代法以及概率论和数理统计中的马尔可夫过程。

The comparison study with the Laplace transform method of solving the transient temperature distribution and the finite difference method have discussed.

尤其对温度场的边界元求法、模腔的瞬态温度场分析进行了数学推导，对制品瞬态温度场的拉普拉斯变换法求解和有限差分法的求解进行了对比。

In Chapter 4, a symmetric triangular partitioned secant method for solving large scale sparse unconstrained optimization problems is constructed, which is a combination of a secant method and a finite difference method, and depends on a consistent partition of the columns of the lower triangular part of the Hessian matrix; it reduces the number of gradient evaluations required by Powell and Toints algorithm (the indirect lower triangular substitution algorithm) by one at every iterative step.

此算法是基于稀疏Hesse阵的下三角部分的列的相容分划的基础上建立起来的，把割线法和有限差分法有机的结合在了一起，在每次迭代中，把由Powell和Toint的算法所需要的梯度赋值次数减少了一。

Magnetic field method is used to analysis the distribution of multi-medium, complex boundary, large difference in dimension, non-linear and forced axial symmetry magnetic field in magnetic fluid seal, the data is derived by unequally spaced net finite difference, and the results of different structure are showed by magnetogram.

利用变步长有限差分法对磁场法描述的磁流体密封中磁介质多、边界复杂、尺寸差别大、非线性的强磁场进行求解，得到了多种形式密封结构磁力线和磁感应强度等值线的分析结果。

In the numerical computation, a two-dimensional numerical method integrating finite element method and difference method was employed, where the finite element method is used to calculate the magnetic field of the permanent magnetic guideway and the difference method is used to calculate the induced current in the superconductor, then the levitation force and the lateral force were calculated by Lorentz formula.

在数值计算部分，实现了一种集有限元法与差分法为一体的数值计算方法。

Meshless method is a kind of method with good prospection, it can deal with many problems which can not be resolved by traditional method (finite element method, finite difference method).

无网格法是一种前景广阔的方法，能够解决许多其他传统方法（如有限元方法、有限差分法等）所不能解决的问题。

By combination of the finite differential technique with the upper bound elemental technique, simulation for the technology of extrusion directly following liquid infiltration which involves infiltration, solidification, and large plastic deformation in one process has been realized and the essences of various technical processes have been revealed by their corresponding simulation results showing the variation of the infiltrated depth and the temperature field with time during infiltration, the punch position, the solidification development of the matrix alloy, the state of the composite within the deforming zone, and the forming load required at different times during extrusion.

采用有限差分法和上限元法相结合，对融浸渗、凝固和大塑性变形为一体的液态浸渗后直接挤压工艺过程进行了数值模拟，从浸渗时浸渗深度与坯料温度场随时间的变化以及挤压过程不同时刻的冲头压下位置、坯料凝固情况、变形区坯料状态、成形载荷大小等方面揭示了不同工艺条件下的各种挤压过程的实质。

The result of this method is accurate solution of differential equation because it is on the basis of analytic method. Compared with the value solutions, it has a lot of characteristics such as clear concepts, simple steps, quick convergence rate, etc.

此方法是建立在解析方法的基础上，得到的结构内力和位移具有足够的精度，它和目前应用广泛的有限元法、差分法等数值解法相比，具有概念清晰、步骤简单、收敛速度快等特点。

Gas insulated switchgear ; partial discharge ; ultra high frequency method ; finite-difference time-domain ; high voltage insulation technology

气体绝缘组合电器；局部放电；超高频法；时域有限差分法；高电压绝缘技术

Based upon a vectorial identity, an integral equation system concerning electromagnetic field in inhomogeneous medium is derived.

计算三维不均匀介质中测井响应的最常用的方法是有限元素法和有限差分法。

Cynanchum Lingtai apricot production in the average weight 65 grams, the brightly-colored fruit, juicy rich, sweet-sour taste, sweet from the nucleolus, when the late Qing Dynasty famous Shaanxi, Gansu provinces, the Qing imperial court Tongzhi tribute for years.

灵台生产的牛心杏平均单果重65克，果实色泽鲜艳，汁多味浓，甜酸适口，离核仁甜，清末时就驰名陕、甘两省，清同治年间曾为朝廷贡品。

Chenopodium album,Solanum nigrum, and Amaranthus retroflexus were very susceptible to the herbicides. Polygonum persicaria and Abutilon theophrasti were relatively less susceptible to the herbicides, and Lycopersicon esculentum was not susceptible to it. The relationship between reduction rates of weed biomass and PPM values of weed leaves 2,4, and 6 days after treatment was established.

供试的6种杂草对该混剂的敏感性存在显著差异：红心藜Chenopodium album、龙葵Solanum nigrum和反枝苋Amaranthus retroflexus对该混剂最敏感，ED90值分别为47.65、71.67和29.17g/hm2；春蓼Polygonum persicaria和苘麻Abutilon theophrasti敏感，ED90值分别为96.91、114.20g/hm2；而番茄不敏感。