微分方程的积分

These have been developed by the numerical integration of the differential equations of gas motion for a spherical blast wave in air.

这些都是根据空中球形爆震波气体运动的微分方程的数值积分得到的。

And the general thoughts in which we can deal with the nonlinear integro-differential equations in Banach space.

全文共分为三章，在第一章中，我们对具有凹凸性的非线性算子的研究现状及我们在本文中将要做的工作进行了阐述；同时给出了我们处理本文所讨论的非线性积分-微分方程的总体思路。

In order to get the exact value of the Hopf bifurcation point, we discuss the discrete version of the integro-differential equation, and use the approximation parameter as the initial value of the Newton iteration method.

为了得到Hopf参数的精确值，进一步讨论了延迟积分－微分方程的离散形式，利用Newton迭代法，得到了参数的逼近值。

This paper studies a class of cubic system with planar polynomial.We use the qualitative theory of ordinary differential equations method of analysis, reached the following conclusions of four parts: First, we analyze the quality of all critical points of the system,and draw the conditions of existence of singular integrals for the system , in front based on the analysis, using Pioncare form series method to calculate the focal value of o(0,0). Finally, we also study the behavior of critical points at infinity.

中文摘要：本文研究了一类平面三次多项式系统，我们采用常微分方程的定性理论的分析方法，得出如下四个部分结论：第一部分，分析系统所有奇点的性态，并得出系统存在奇异积分直线的条件；在前面分析的基础上，用Pioncare形式级数法，计算出了系统在奇点o(0，0)的三个焦点量；最后，研究了系统无穷远奇点的性态。

The introduction of displacement operator, derivation operator, integral operator and the operator, such as differential calculus operator and the definition of the form of computing, will be applied to similar derivation formula gives Newton a Kete Si formula and Bernstein theorem Law said the operator, and form is derived; linear differential equations is the operator solution.

有没有高手可以帮我翻译下这段话啊？？？引入位移算子、求导算子、积分算子和差分算子等微积分算子的定义及其形式运算，将其应用于近似求导公式；给出牛顿一柯特斯公式和伯恩斯坦定理的算子法表示，并进行形式推导；给出线性常微分方程的算子解法。

Based on the simplification of differential equation of driving function and the amendment of control law with error integral, the problems of controller design for a class of position serve system are discussed from the angle of practical use in engineering.

基于对驱动函数微分方程的简化和对控制律的误差积分修正，从工程实用角度讨论一类位置伺服系统控制器的设计问题。

The purpose of the paper is to investigate the convergence of the mixed finite element method for the initial-boundary value problem for the Hyperbolic type integro-differential equation and Hyperbolic type equation.

本文讨论了双曲型和双曲型积分微分方程的标准混合有限元和H~1-Galerkin混合有限元方法的L~2模和H~1模的误差估计。

This data visualization system in this thesis has an extensive function, including calculus operation, solving the algebraic equation and differential equation, the operation of series and the transform of integral and so on.

本设计开发的数据可视化系统具有强大的运算功能，包括微积分运算、代数方程与微分方程的求解、级数运算、积分变换等。

In chapter two,we consider a lumped mass generalized difference scheme for linear integro-differential equation in two dimensions.Lp and error estimates of the generalized Ritz-Volterra projection u ? V and and -norm error estimates of Dk = 1,2 are made,then we obtain and -norm error estimates of u?

第二章考虑二维线性积分微分方程的广义差分集中质量法，建立了广义Ritz-Volterra投影，得到u-V_h~*u的W~(1，p)和L~p(2≤p≤∞)模误差估计和D_t~k，k=1，2的V~p和W~(1，p)(2≤p≤∞)模误差估计，从而得到u-u_h的最优W~(1，p)和L~p(2≤p≤∞)模误差估计。

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。

Plunder melds and run with this jewel!

掠夺melds和运行与此宝石！

My dream is to be a crazy growing tree and extend at the edge between the city and the forest.

此刻，也许正是在通往天国的路上，我体验着这白色的晕旋。