微分方程的积分

Spectral element methods for partial differencial equation is introduced in this study from viewpoint of the collocation approximation of Chebyshev polynomial. Wave Equation and its space discretization are deduced. Two time integral methods, central difference method and implicit Newmark method, are introduced, and their stability and applicability are also discussed in some details. The significance of absorbing boundary conditions in spectral element methods for Aeroacoustics is explained, and Clayton-Engquist-Majda absorbing boundary conditions is emphasized and introduced, then the discrete scheme of this boundary conditions is deduced and applied to spectral element methods for wave equation.

本文从Chebyshev多项式逼近理论出发，详细介绍了谱元方法求解偏微分方程的过程；推导了流体中的声波动方程并在空间上对其进行了谱元离散；详细讨论了两种时间积分方法──中心差分法和Newmark方法，分析了它们的稳定性条件，并从理论上对比了两种方法的优缺点和适用范围；将吸收边界条件推广应用于谱元方法求解气动声学问题中，重点介绍了Clayton-Engquist-Majda吸收边界条件的原理和公式，推导了该吸收边界条件的变分形式，并将其引入波动方程的离散形式中。

On the one hand, Lagrange hit upon the new idea to redefine the complete integral when he was inspired by his study on the first-order partial differential equation with the method of variation of constants.

在分析、比较欧拉和拉格朗日完全积分定义的基础上，依据原始文献，重点考究了拉格朗日重新定义偏微分方程完全积分的原因和动机。

An approximate solution can be derived by using Crammer\'srule.Illustrative examples are given to show that the method in the present paper is simple and efficient.

第六章总结了前面讨论的用Taylor展开方法解Fredholm-Volterra积分方程以及线性常微分方程的两点边值问题。

In the solution of the problems in algebraic equation, differential equation and integral equation, we usually resort the sotution of equation to the fixed point of mapping in metric space. The contraction mapping principle can be used to solve many problems of the existence and uniqueness of equation solution.

在代数方程、微分方程和积分方程的求解问题中，通常把所求的解归结为度量空间中映射的不动点，然后应用压缩映象原理来统一处理许多方程解的存在性和唯一性问题。

Some sufficient criteria were obtained for oscillation of all solutions of such systems under first boundary value conditions by employing Gauss＇ divergence theorem, the integral inequalities and some results of the functional differential equations.

研究一类具非线性扩散系数的中立型双曲泛函偏微分方程组的振动性，利用Gauss散度定理、积分不等式和泛函微分方程的某些结果，获得了该类方程组在第一类边值条件下所有解振动的若干充分判据，结论充分表明振动是由时滞量引起的，同时也揭示该类方程组与普通双曲型偏微分方程组质的差异。

By using the theory of differential or integral equation, an explicit formula for the vaccine-dependent reproductive number R is first obtained.

运用微分方程和积分方程理论，得到一个与接种疫苗有关的再生数的表达式。

Making use of the fundamental solution of Laplace equation, we change the nonhomogeneous Helmholtz equation with veriable coeffients into integral equation.

利用Laplace方程的基本解，将变系数非齐次Helmholtz偏微分方程的边值问题化为积分方程问题。

The first is refered to the vibration model with retardation for the market equilibrium price, where the knowledge of the second order linear ordinary differential equation is used.

第一个是研究市场调节下平衡价格的阻尼振荡模型，使用了二阶线性常系数微分方程的课程知识；第二个是在引进社会福利因素时商品的最优定价模型，使用了定积分和微分法的课程知识。

The first is refered to the vibration model with retardation for the market equilibrium price, where the knowledge of the second order linear ordinary differential equation is used. The second is refered to the optimal pricing model of the price under the frame of the social welfare, where the concept of the definite integral is exploited.

第一个是研究市场调节下平衡价格的阻尼振荡模型，使用了二阶线性常系数微分方程的课程知识；第二个是在引进社会福利因素时商品的最优定价模型，使用了定积分和微分法的课程知识。

The details of Newmark method is given in this paper clearly and the stabilization of Newmark method is approved under specified conditions.

文中详细推导了应用Newmark隐式时间积分方法求解高阶偏微分方程的具体过程，并详细推导Newmark时间积分方法的稳定性要求，给出了该积分方法稳定性的详细证明过程。

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。