查询词典 simultaneous differential equations

In both the cases we provide necessary conditions for any linear multistep method applied to delay differential equations and neutral delay differential equations to be τ(0)-stable and Nτ(0)-stable respectively.

针对这两种情况，分别给出了线性多步方法关于延迟微分方程τ（0）-稳定及中立型延迟微分方程Nτ（0）-稳定的必要条件。

In this paper, we deal with the existence of periodic solutions of sublinear Liénard differential equations and Duffing differential equations with singularity.

本文研究次线性Liénard方程和具有奇异性Duffing方程周期解的存在性。

Aim at the shortage of vertically additive method by which we can't discuss forced oscillations of systems of partial functional differential equations,we directly use the oscillatory definition,Green's formula and boundary condition of homogeneous Neumann to change the oscillatory problem of solutions to a class of systems of quasilinear parabolic equations of neutral type into the problem of which functional differential inequality haven't eventually positive solution.

针对垂直相加法无法讨论泛函偏微分方程组的强迫振动性的不足，直接利用振动的定义、Green公式以及齐次Neumann边界条件把中立型抛物微分方程组的振动问题转化为泛函微分不等式不存在最终正解的问题，然后利用最终正解的定义及上下极限得到了在齐次Neumann边界条件下判别其所有解振动或全振动的充分条件。

In Chapter Ⅲ, by considering functions H k that may not have nonpositive partial derivative on s and employing integral averaging technique and Hardy inequality, the oscillation for a class of high order nonlinear differential equations and high order nonlinear damped differential equations is discussed, new oscillation criteria are established.

第二章利用广义Riccati技巧、积分平均技巧以及微分不等式理论，讨论了一类二阶非线性常微分方程的振动性，得到了若干新的振动准则，并讨论了该方程具有强迫项时解的渐近性态。

One of the primary methods to solve them is numerical method, and the other is Galerkin method, which change partial differential equations into normal differential equations, and then solve them with the traditional method.

小波分析已成为当前应用数学中迅速发展的新领域，它可以解决Fourier分析不能解决的许多困难问题，是近年来在研究工具及方法上的创新，已成为众多学科共同关注的热点。

This thesis is divided into six parts. The first chapter is preface, the current status of research in the inverse problems for parabolic partial differential equations is reported; the second chapter is "regularization methods for numerical differentiation and their applications ", in this chapter we investigate many regularization methods from a viewpoint of regularization theory and algorithm, some applications in the inverse problems for parabolic partial differential equations are given; the third chapter is "spectral regularization methods". Based on Fourier analysis, within the framework of regularization theory, we apply the spectral methods to some ill-posed problems. Many numerical experiments are done in order to show the validity of the methods; the fourth chapter is devoted to wavelet dual least squares method and a revised wavelet method; in the fifth chapter,we combine finite difference method with method of lines and apply it to the backward heat conduction problem in time; in the sixth chapter "identification problems for unknown source ", the essence and the degree of two problems related to source identification are pointed out, at the same time, some numerical methods are reported.

本文分为六个部分，第一章前言简要分析了国内外抛物型偏微分方程反问题的研究现状；第二章数值微分的正则化及其应用从正则化理论和算法的角度出发，考察了许多正则化方法，还给出了数值微分在抛物型偏微分方程反问题的一些应用；第三章谱正则化方法是在Fourier分析的基础上，在一般正则化理论的框架下，给出了这种方法在各种不适定问题中的应用，数值实验表明谱方法是有效的；第四章研究了小波对偶最小二乘方法和改进的小波方法；第五章主要研究了有限差分方法结合线方法在时间反向热传导问题中的应用；第六章是未知源识别问题，主要指出了两类未知源问题的不适定程度和不适定本质，同时报告了一些数值方法。

By adapting the existed numerical methods for ordinary and delay differential equations, and matching certain suitable numerical quadrature formulas, Rosenbrock methods are constructed for delay integro-differential equations, the stability criteria of the methods are derived.

通过改造现有常及离散型延迟微分方程的数值方法，并匹配以适当数值求积公式，构造了求解时滞积分微分方程的Rosenbrock方法，导出了其稳定性准则。

Firstly,using the method of concentrate mass this paper establish a non-linear dynamics model of a two-stage gear train with backlashe between the gear pair,and through analysed the dynamics model,the torsional motion differential equations are got , on this basis,then calculate the torsional motion differential equations using Runge—Kutta method ,and discuss how to influence the dynamics characteristic of system when these parameters chage such as mesh frequentcies、 stiffness of the intermediate shaft、the ration of mesh frequentcies.and discuss when the chaos will happen under the change of these parameters.

首先用集中质量法建立系统的含间隙的非线性动力学模型，并根据牛顿力学定理，得到系统的运动微分方程。然后对所建立的运动微分方程运用四阶变步长Runge—Kutta方法进行了求解，并对计算结果进行分析，研究了齿轮啮合频率、中间联接轴的刚度，一、二级齿轮的啮合频率比等参数变化时，对系统非线性动力学特性的影响规律，并讨论了当参数如何变化时会导致系统的混沌响应的出现。

In this paper, we give the method of solving the partial differential equations with the combine use of symbolic and numerical method, which is a new way of solving the extremely complicated partial differential equations.

本文作出了将符号计算方法和数值计算方法结合起来求解偏微分方程的研究工作，这是求解比较复杂的偏微分方程的新途径。

The finite difference method is applied to reduce the system of partial differential equations to ordinary differential equations.

采用有限差分方法，将由偏微分方程组描述的空间连续系统约化为由常微分方程组描述的空间离散高维动力系统。

Connectors are lines that can be anchored to particular places, called glue points , on the graphic object.

连接符，可固定在图形对象的特定的地方的线条。

Another way of putting it, too many agents have a say in each other's work, and bureaucratic rigor mortis sets in.

另一种表达是，太多的作用物在彼此的工作里都有话语权，官僚的僵尸开始抬头。