微分方程的积分

In this paper the boundary value problem of integro-differential equation is discussed and several basic theories of it are proved.

利用上解和下解的概念讨论了积分微分方程的边值问题，给出了几个基本定理。

It is used to solve the discretized equation which is derived by EFGM.

精细积分法是求解常微分方程的一种成熟的数值算法。

Based on initial condition, during certain time span, numerical analysis method of differential equation, algebra iteration and optimization method are used to solve response of generalized system and to analyze stability of generalized system.

从初始条件出发，在一定时间长度上，采用微分方程数值积分法、代数迭代和优化方法来求解系统响应，获得非线性广义系统稳定性的数值分析方法。

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。

And control problems such as optimal import rate control, optimal harvesting control, optimal birth control are investigated. By means of nonlinear functional analysis, differential equations, integral equations, and modern control theory, a number of research results are obtained, which are theoretically valuable and provide a solid ground for the practical use of our models.

本文系统讨论了几类年龄依赖的单种群和多种群动力系统，综合应用非线性泛函分析、微分方程、积分方程以及分布参数系统控制论等理论与方法，深入地研究了这些系统的解的存在性、唯一性以及非负有界性；研究了这些种群动力系统的最优输入率、收获率和出生率控制问题，获得了一批重要的理论成果。

In this approach we have the freedom in the choice of step size during the integration of the ordinary differential equation.

在这种方法中，我们可以在对常微分方程进行积分的过程中自由选择步长。

However, the multi-time values before the initial time are required in solving the ordinary differential equation with linear multi-step method, the values at these time levels are still computed from the given initial value by one of above mentioned schemes.

在常微分方程的线性多步法中用到初始时次前若干时次的数值，但这些时次上的起动值仍然由初值运用方程计算得到的。这就是说，人们在预报问题中始终恪守只用一个初值的原则。在天气预报中，数值积分只用到一个起报场，即最后一个时次的观测场。

In this paper, we consider lumped mass metheds for parabolic type integro-differential equations.

本文讨论了抛物型积分微分方程的集中质量法。

First and second order linear differential equations Path integral Numerical series Functions of the real variable: sequences and series of functions, entire series, applications to Fourier series.

第一，二阶线性微分方程路径积分数值系列在实变函数：序列和职能系列，整个系列，以傅里叶级数的应用。

This method uses the generator model of constant transient voltage and the saliency of generator is included.

本文提出了一种基于特殊二阶微分方程数值积分的电力系统动态安全评价方法。

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。