数值微分法

It is necessary to analyze the convergence of a special class of such step- parallel iteration methods for delay differential equations.

针对延迟微分方程分析了一类特殊的并行迭代法的收敛性，数值算例表明这种算法是有效的。

The scaled boundary finite-element method is a novel semi-analytical technique for solving the linear partial differential equation.

比例边界有限元法是线性偏微分方程的一种新的数值求解方法。

Proceeding by Bubnov-Galerkin method in combination with numerical method based on the quadrature formula the problem was reduced to a solution of a system of nonlinear integro-differential equations with singular kernel of relaxation.

根据Bubnov-Galerkin法，结合基于求积公式的数值方法，将问题简化为求解具有松弛奇异核的非线性积分－微分方程的问题。

The first part gives some basic introduction to the meshless methods of Partial Differential equation.

第一部分给出了偏微分方程数值解的无网格方法，特别介绍了以径向基函数插值为基础的配置点法。

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。

In the analysis, a nonlinear wave vibration equation of the thin cylindrical shell including damping and items due to geometric nonlinearities was established and then transformed by Galerkin's method. With different combinations of modes different nonlinear differential equations in modal coordinates were obtained. The Runge Kutta method was used to solve the equations numerically and some features of nonlinear wave vibration were discussed.

在研究过程中，首先，考虑阻尼并引入几何非线性项，建立薄壁圆柱壳的非线性波动方程，然后，采用Galerkin方法对波动方程进行转换，选取不同的模态组合，得到相应模态坐标下的非线性微分方程，最后用Runge-Kutta法进行数值计算并对圆柱壳的非线性波动振动特性进行了分析。

Taking into the feature of computer computing method, using Stress solution of elasticity theory and according to different method of solving of system of second order ordinary differential equations , this article provides two numerical value computing method as for the stress and deformation of the turbine impeller which is within the scope of elasticity .

从计算机计算的特点出发，采用应力法，根据二阶常微分方程组的不同解法，给出了透平机叶轮在弹性范围内应力和变形计算的两种数值计算方法。

In order to improve accuracy and intelligibility of error prediction for one novel target system based on six-intersected-screen, which was used to measure bullet flight vector, a method based on Taguchi and Monte Carlo simulation approach other than traditional differential approach was introduced.

为了解决多光幕交汇立靶测量精度分析过程中运用传统微分误差分析法所得结果偏大，且直观性差的问题，介绍了一种采用数值分析和田口试验方法相结合的改进方案。

A time domain differential equation model is established by using the axisymmetrical form of the Maxwell's equations,and the finite element time domain method is applied to solve the model.

使用麦克斯韦方程组的轴对称形式建立时域微分方程数学模型，应用时域有限元法求解，给出了数值算例，模拟了在不同缺陷参数下涂有电介质的导体对入射脉冲太赫兹波的响应，并归纳了响应在空间上和时间上的变化规律。

The bifurcation and chaos behavior of impact and rubbing fault rotor system caused by the parameters of nonlinear rigidity, rotor rotating speed, eccentric mass is analyzed, in the numerical value analysis method. The bifurcation diagrams, maximum Lyapunov exponent diagrams, Poincaré maps, phase plane portraits, trajectories of journal center, time-history curve, amplitude spectra diagrams of the rotor motion are used. The convert and evolution course of periodical response, quasi-periodical response, double-periodical bifurcation, chaos of the system response is analyzed.(3). It is deduced that the general differential equation of bending-torsional-pendular coupling vibration about rotor with the gyroscopic moment. On the basis of this equation, the general differential equations of coupled bending, torsional and pendular nonlinear vibration about rotor with unbalance character and rubbing character are deduced.

2建立了具有非线性刚度的转子系统在非稳态非线性油膜力作用下的径向碰摩动力学微分方程，并应用含高阶余项的非线性动力方程的线性化数值法研究了此类系统响应的复杂动力学行为，利用转子响应的分岔图、最大Lyapunov指数曲线、Poincaré截面映射、时域波形、相轨线、轴心轨迹、幅值谱等图形分析了系统响应的周期运动、拟周期运动、倍周期分岔、混沌等运动形式的转化与演变过程，重点研究了非线性刚度、转子转速、偏心质量等系统参数对碰摩故障转子系统的分岔和混沌行为的影响。

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。