数值微分

Four bands Runge - Kutta method for ordinary differential equations, numerical algorithm of the function subroutine.

4阶龙格库塔方法求常微分方程的数值算法的函数子程序。

In the analysis, a nonlinear wave vibration equation of the thin cylindrical shell including damping and items due to geometric nonlinearities was established and then transformed by Galerkin's method. With different combinations of modes different nonlinear differential equations in modal coordinates were obtained. The Runge Kutta method was used to solve the equations numerically and some features of nonlinear wave vibration were discussed.

在研究过程中，首先，考虑阻尼并引入几何非线性项，建立薄壁圆柱壳的非线性波动方程，然后，采用Galerkin方法对波动方程进行转换，选取不同的模态组合，得到相应模态坐标下的非线性微分方程，最后用Runge-Kutta法进行数值计算并对圆柱壳的非线性波动振动特性进行了分析。

We reproduce the well-established and self-generated magnetic field equations, which are nonlinear partial differential equations.

我们证明该非线性偏微分方程具有塌缩波解，并用标准的数值方法解此方程来验证分析结果。

It gets correct results with very few calculations and it is self-starting.

使用了一个特殊二阶微分方程的数值解法，该方法精度较高，计算量很小，而且可以自启动。

A variational method with differential forms gives better precision for numerical solution of transport critical problem based on spherical geometry, and its computation seems simple than other approximate methods.

对于球几何问题，讨论了一种基于微分方程的变分形式求解方法，数值计算显示达到了较满意的精度，而且计算过程比起其他近似方法要简单

Some applications of spline functions in numerical solutions of differential equations are discussed in this dissertation.

本文讨论样条函数在微分方程数值解中的一些应用。

The paper have two parts, one is numerical solution of partial di?erential equation,another is submanifold.

本文分两部分，第一部分是偏微分方程数值解内容，第二部分是子流形几何内容。

Taking into the feature of computer computing method, using Stress solution of elasticity theory and according to different method of solving of system of second order ordinary differential equations , this article provides two numerical value computing method as for the stress and deformation of the turbine impeller which is within the scope of elasticity .

从计算机计算的特点出发，采用应力法，根据二阶常微分方程组的不同解法，给出了透平机叶轮在弹性范围内应力和变形计算的两种数值计算方法。

The threshold of lithium tantalite under single-shot is found to be 1.84J /cm 2 and the avalanche rate was determined to be 1.01 cm 2 /J by calculation. We found that avalanche dominates the ablation process, while photoionization serves as a free electron provider.

在800nm飞秒激光脉冲作用下，钽酸锂晶体单脉冲烧蚀阈值为1.84 J /cm 2；在此基础上，我们通过建立钽酸锂晶体中导带电子密度演化微分方程，并数值求解，得到了钽酸锂的碰撞电离速率系数为1.01 cm 2 /J ，并得出在钽酸锂表面烧蚀中，光致电离提供种子电子，雪崩电离起主导作用的结论。

Poincaré inequalities play an important role in the research of many fields such as in harmonic analysis and in theory and numerical method of differential equations.

Poincar 不等式在调和分析、微分方程理论及其数值方法等领域的研究中具有极其重要的作用。

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新