数值微分

In Chapter Five, we compare numerical integration of the reproducing kernel with the integral equation of complexified trapezoid through a detailed solution to the initial-value problem of ordinary differential equation to exemplify that the method of interpolation spline integrating and the reproducing kernel is not only feasible in theory but also significant in pratice.

在第五章，我们通过具体的求解一个常微分方程的初值问题，把再生核方法的数值积分和复化梯形积分公式相比较，说明样条插值和再生核相结合的方法不仅是理论上可行的，而且还具有重要的实际意义。

Because the workpiece is in dynamic balance, the resultant moment acting on it should be zero. Introducing the moment from lapping tool and press head a moving differential equation is built. In this equation only workpiece rotating speed is unknown. It means that workpiece rotating speed can be got by this equation. Since there is a transcendental function in integral function of the equation an analytic result can not be got, only digital result can be got by a computer. Thus a change rule of workpiece rotating speed with lapping parameters is known, e.g. the radius of press disc ball socket, radius of press head ball, the distance between the workpiece rotating axis and lapping tool rotating axis, workpiece radius, modulus of elasticity of the press head and press disc, friction coefficients between the lapping tool and workpiece, and between the head and disc, pressure between the lapping tool and workpiece and pressure between the press head and press disc.

因工件处于动态平衡状态，其上所受到的来自于磨具和压头的力矩应相等，将二力矩表达式联立，建立工件运动微分方程，该方程中只有工件的旋转角速度是未知量，因此可以求出工件旋转角速度，但该方程积分式中含有超越函数，得不出解析解，只能通过计算机求出数值解，得出工件旋转角速度随各研磨参数的变化规律，如压盖球座半径、压头的球头半径、工件回转中心相对磨具回转中心的偏心距、工件半径、压头和压盖材料的弹性模量、磨具与工件间的摩擦系数、压头压盖间的摩擦系数、磨具与工件间的压强、压头压盖间的压力等。

The stability of numerical methods for the linear Volterra delay integro differential equation was studied. A sufficient condition such that the implicit block θ-methods preserved the delay-independent stability of its exact solutions was obtained.

研究了线性中立型Volterra延迟积分微分方程数值方法的稳定性，给出了块隐式θ-方法保持系统解析解不依赖于延迟的稳定性质的一个充分条件。

The asymptote behavior of intermediate point in the Mean Value Theorem for integrals ;2. Based on numerical integrals , the model parameters are estimated from the differential equation without iterations, the method is very effective in overcoming large amounts of measurement noise in the output.

提出一种简单但鲁棒性强的传感器动态建模方法，该方法基于数值积分思想，能有效克服测量噪声，无需迭代即可直接从微分方程辨识出模型参数，所建模型阶次较低、准确度较高，且较易实现递推算法，为传感器改善动态特性、实现动态补偿提供一种有效方法。

This is the learning algorithm "Adams steps with four bands interpolation formula correction" of their times calculated for the numerical solution of differential equations procedures, they can modify the equation for the solution and the other equation, Hi!

这个算法是在学习"用Adams三步四阶内插公式校正"时自己遍的计算这个微分方程数值解的程序，可以修改里面的方程而用于求解其他的方程，请指正！

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。

Chapter 5 deals with the solvable theorem of adaptive inverse optimal control problems for a class of stochastic nonlinear systems driven by Wiener noises of unknown covariance. The systems are depicted by It〓 stochastic differential equations. By using an adaptive backstepping algorithm and stochastic control Lyapunov functions, the designing procedure of control laws of global asymptotic stability in probability and adaptive inverse optimal stabilization in probability are presented systematically. Adaptive control laws and parameter update laws can be obtained at the same time by this design scheme.

在第5章中，针对具有方差不确定Wiener噪声扰动和未知定常参数的随机非线性系统（假设方差的F—范数是一个常数或一个缓慢变化的量，对其进行在线辨识），给出并证明了自适应逆最优控制问题可解定理，基于随机Lyapunov定理和It〓微分规则，采用自适应Backstepping设计方法，系统地设计了全局依概率渐近稳定和自适应逆最优控制策略，这种设计方法可同时获得控制策略和自适应律，计算机数值仿真结果表明该控制算法是有效性的。

The forward finite difference and Newton iterance are used in the light of box model and other heavy gas dispersion models, such as IIT Heavy Gas Models and virtual point source model, to solve the differential equations of controlling heavy gas cl.

文中从控制重气云团扩散行为的微分方程入手，根据箱模型及其他一些重气扩散模型，如IITHeavyGasModels模型和虚点源模型，采用向前插分和牛顿迭代的方法，针对ThorneyIslandTrialNo 。0 0 8试验进行了数值模拟，得到了重气云团外形尺寸和空气卷吸量随时间的变化关系以及下风向固定点处地面最大浓度值。

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。

Secondly three kinds of approaches of function approximation are discussed which are the interpolation with radial basis function, moving least squares and approximate approximation. And the correlative theories are proved.

在此之后介绍了求解偏微分方程数值解的两种无网格方法：无网格伽辽金方法和无网格局部Petrov-Galerkin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。