数值微分

Similar method may be applied in other types of partial differential equations.

类似的方法还可以用在其它类型的偏微分方程数值解中。

Fin ally, some numerical results to validate this method are presented for partial d ifferential equations with Dirichlet boundary condition.

最后 ，我们给出一些数值结果以验证这种针对 Dirichlet边界条件的偏微分程解法。

This book discusses the theory of elliptic differential equations and numerical processing.

本书论述了椭圆型微分方程的理论与数值处理。

Then the basic fundamental and method of the computation of thermal load of the heated parts of internal-combustion engine are elaborated, the deflective differential equation of heat conduction, basic equation and boundary condition of the theory of thermo elasticity and numerical computation by FEA are introduced.

接着阐述了求解内燃机受热零部件热负荷的基本原理和方法，介绍了热传导的偏微分方程、热弹性理论的基本方程和边界条件确定的原则以及用有限元法进行的数值求解。

The research of nonlinear ergodic theory began in the mid-seventies. Consequently, it got great development because it was widely used in many questions such as the numerical solution of differential equation, the existence theory of positive solution, control theory, optimization.

非线性算子半群的遍历理论的研究开始于二十世纪七十年代中期，随后由于被广泛应用于微分方程的数值解，正解的存在性理论，控制论，最优化等问题中而得到了很大发展。

Based on Crank-Nicoson's technique, and a new approach for the numerical simulation of the model is raised. The truncation error of the one step difference method reaches O (△t^2+△x^2) and of quite good stability condition.

基于Coriolis加速度和Lagrangian应力公式，利用Newton第二定律导出轴向加速度运动弦线横向振动的动力学模型；通过线性变换将方程化为一阶无量纲的非线性微分方程组；并利用Crank-Nicoson的中点离散技巧，给出运动方程的单步二阶差分方法；算法把对运动方程和本构方程分别离散，使之可以用于不同本构的运动弦线的数值仿真。

Yet, the number of instance the exact solution can be found byanalytical means is very limited.

因此，有必要用数值方法得到微分方程的近似解。

This is another novelty of this method. For a family of parameters, the analytical solutions of parabolic PDEs are given using the new method in this paper, the result schemes are posed.

给出了一类抛物型偏微分方程的解析解，并给出了其与差分数值解法所得到的解的比较，比较曲线表明了这种新解法的正确性。

A combustion simulation adopting the Reynolds stress model and the Laminar Flamelet model was performed to determine the effect of humidity in the combustion air on temperature, velocity and NO distributions of methane/air diffusion combustion in a swirl combustor.

采用湍流雷诺应力微分模型和层流小火焰模型，对湿空气透平带旋流器的燃烧室内甲烷扩散燃烧过进行了数值模拟。

After setting up the physical formulism, we compute the non-linear ODE based on single particle model using an explicit Runge–Kutta method.

我们建立了物理模型，以龙格—库塔显式格式作为具体的数值模拟方法，采用单粒子模型求解非线性微分方程组的初值问题。

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。