数值方程

For the long composite cylindrical panels, including the influences of the transverse shear deformation, rotatory inertia and initial geometric imperfections, the nonlinear dynamic equations of the long composite cylindrical panels were derived from Hamilton's philosophy. The nonlinear partial differential equations were transformed to ordinary differential equations by expansion in series and solved numerically by fourthorder Runge-Kutta method.

针对含初始几何缺陷的复合材料圆柱曲板，考虑横向剪切变形、转动惯量、初始几何缺陷以及非扁壳等诸多因素，利用Hamilton原理导出复合材料长圆柱曲板的非线性动力方程；用级数展开把非线性偏微分方程组转化为二阶常微分方程组，并由四阶Runge-Kutta方法数值求解。

The one-dimensional time-dependent Schrdinger equation was numerically solved with the symmetric splitting of the short-time exponential propagator and the fast Fourier transformation, and influence of intensity and pulse with on ionization of linear multi-ation molecular ion in two-color laser fields was researched.

利用短时指数传播子对称分割法和快速傅里叶变换技术，数值求解了一维含时Schrodinger方程，探讨了双色激光场中激光的基波和谐波强度之间的不同配比以及脉宽对线性多原子分子离子电离的影响。

The solution to the dual integral equations with exponential function can be discussed,too.

最后给出了含余弦函数对偶积分方程的数值算例。

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。

The two numerical methods to solve PRISM integral equations are introduced based on the Discrete Fourier Transformation and Fast Fourier Transformation.

详细介绍了用离散Fourier变换和快速Fourier变换求解PRISM积分方程的两种数值计算方法。

Firstly, according to electromagnetic field theory, the 2-dimensional (2-D) mathematical model of a three phase squirrel-cage Y802-2 induction motor is developed. Then general equations can be deduced from finite element discrete and functional analysis. The motor's 2D solving region of electromagnetic field is given based on the boundary conditions and assumption conditions of the squirrel-cage induction motor. Through finite element mothod and inner–outer convergence method, magnetic field distributions and magnetic forces of bars can be calculated in following rotor conditions: health rotor, one single broken bar, two adjacent broken bars, two broken bars with one good interval, two broken bars with two good interval and four adjacent broken bars.

本文首先根据电磁场理论建立Y802-2型三相笼型感应电动机二维电磁场的数学模型，并对其进行了有限元离散以及泛函分析，推导出总体方程；在基本假设和边界条件基础上，给出笼型感应电动机二维电磁场的求解区域，然后应用有限元并结合内外双收敛方法，对样机稳态运行进行数值计算，得出电机在转子完好、一根导条断裂、连续两根导条断裂、间隔一根两根导条断裂、间隔两根两根导条断裂及连续四根导条断裂六种情况下的磁场分布和导条所受电磁力的变化情况。

A new scheme for approximating the solution of 2D Maxwell's equations-the high order symplectic scheme is proposed to overcome the shortcoming of the conventional finite difference time domain. The scheme is obtained by discretizing the Maxwell's equations in time domain based on symplectic scheme with high order, and then evaluating the equation in spatial domain with second or fourth order finite difference approximation.

为克服标准时域有限差分方法的缺陷，引入一种新的数值计算方法－高阶辛算法求解Maxwell方程，即在时间上用高阶辛差分格式离散，空间分别采用二阶及四阶精度的差分格式离散。

Wave equation ; finite difference ; numerical modeling ; forward modeling

波动方程；有限差分；数值模拟；正演

Physical parameter substitutes for phase-changing latent heat, then critical temperature of thermal conductivity welding is determined, so finite difference equation can be solved by MATLAB software.

改变热物性参数替代相变潜热确定了热传导焊接的临界温度值，利用自编的MATLAB程序对有限差分方程进行求解，数值模拟了焊件的温度场。

Using the method of finite difference to discrete the governing equation,the elastic-plastic dynamic response of a simply-supported steel beam subjected to stepped loading and fire loading was investigated.

利用有限差分离散控制方程进行数值分析，研究了火侵袭时简支钢梁在阶跃载荷作用下的弹塑性动力响应。

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