非线性伪振子的高精度解析近似解

采用预估-校正牛顿谐波平衡方法构造恢复力与因变量成反比的非线性伪振子的解析近似解.先对非线性方程进行线性化,然后分预估和校正两步求解.在每个步骤中,使用谐波平衡法来获得一组线性代数方程.研究结果表明,只需一个简单的预估-校正牛顿迭代步骤,就可以推导出一个简洁且高度精确的显式解析近似解,所得近似解对伪振子的所有振幅都有效.     

一类“多项式型”初值问题的快速解法

对有解析解的偏微分方程定解问题 ,利用计算机系统有多种方法获得问题的数值 (近似 )解 ,但却无法给出解析解 (有限函数形式解 ) .经过深入研究 ,我们得出了“多项式型”初值问题解析解的计算机解法 ,并给出Mathematica语言源程序 .     

用迭代摄动法求解含立方项强非线性振动方程

采用迭代摄动法求解含有立方项的非线性振动微分方程,得到形式简单的近似解析解.通过讨论解析解在各种情况下的近似程度,说明所采用的方法及得到的简单公式在很大范围内是有效的.     

例析“精确度”和“精确到”的异同

利用二分法求方程近似解的题目中,"精确度…"和"精确到…"都是刻画方程近似解"近似程度"的量.但其意义不同,"精确度"(也称"精度")是指方程的准确解与近似解之差的绝对值的界,而"精确到…"指明近似解精确到的数位或保留多少位有效数字.因此,利用二分法求方程近似解的过程就有异同.下面举例解析.     

一类非线性偏微分方程的摄动解法

首先用行波变换将非线性偏微分方程转化为非线性常微分方程,然后采用摄动方法直接求解该非线性常微分方程,最后求得了非线性Klein-Gordon方程的二级近似解.这种方法也可进一步推广用于求其它非线性偏微分方程的近似解析解.     

求解定态薛定谔方程的有限差分法

特殊的定态薛定谔方程存在解析解,但大部分的定态薛定谔方程是很难找出解析解的,通过计算机可以得到其近似的数值解.利用有限差分法和matlab程序设计,可以求解定态薛定谔方程,并得到很好的数值解.     

双弹簧振子横向振动微分方程的近似解

在分析对称双弹簧振子横向振动特点的基础上,根据极限情况下方程解的性质,提出双弹簧振子横向振动微分方程的近似解析解,并得到了横向振动周期的具体表达式;通过与数值解结果的比较,说明近似解是有效的.     

线性分段连续型延迟微分方程的变分迭代解法

主要利用变分迭代法求解自变量分段连续型延迟微分方程的初值问题,由变分理论得到了拉格朗日乘子,进而构造了迭代关系式,在不同的区间上求得了各阶解析近似解,并且证明了收敛性,连续级数收敛结果和真实解的形式一致.通过具体的实例验证了该方法的有效性和可靠性.     

基于MATLAB的平方阻尼振动研究

摘用MATLAB研究了振动系统在与速度平方成正比的阻尼作用下的运动性质,采用平均法求出了平方阻尼情况下振动微分方程的近似解析解,讨论了解析解的使用条件并与数值解进行了比较．发现平方阻尼下,振动系统进行周期性的非指数型衰减振动,在一定条件下,采用近似解析式描写这种运动,有很高的精度．     

表面波问题的解析解

利用理想不可压缩流体的连续性方程和动量方程,推导了表面波基本方程,并应用线性近似理论求出了小振幅波情况下的解析解.     

旋转电机磁场计算的数值解析结合法

A numerical-analytical method is applied for the two-dimensional magnetic field computation in rotational electric machines in this paper. The analytical expressions for air gap magnetic field are derived. The pole pairs in the expressions are taken into account so that the solution region can be reduced within one periodic range. The numerical and analytical magnetic field equations are linked with equal vector magnetic potential boundary conditions. The magnetic field of a brushless permanent magnet machine is com-     

Numerical simulation of water mitigation effects on shock wave with SPH method

The water mitigation effect on the propagation of shock wave was investigated numerically. The traditional smoothed particle hydrodynamics (SPH) method was modified based on Riemann solution. The comparison of numerical results with the analytical solution indicated that the modified SPH method has more advantages than the traditional SPH method. Using the modified SPH algorithm, a series of one-dimensional planar wave propagation problems were investigated, focusing on the influence of the air-gap between the high-pressure air and water and the thickness of water. The numerical results showed that water mitigation effect is significant. Up to 60% shock wave pressure reduction could be achieved with the existence of water, and the shape of shock wave was also changed greatly. It is seemly that the small air-gap between the high-pressure air and water has more influence on water mitigation effect.     

变分法在渡江决策中的应用

本文在渡江者游速大小恒定、水流速度大小恒定或随水域均匀交化两种情况下。用交分法求得了最速渡江线路的解析解。并在此基础上求得了比参考文献[1]更优的数值解。     

花生仁水分测量结果的不确定度分析

对直接干燥法测定花生仁水分的不确定度进行评估。测量过程中的不确定度主要来源有称样皿质量、干燥前试样及称样皿质量、干燥后试样及称样皿质量和重复性。对各不确定度分量进行计算,最终合成标准不确定度和扩展不确定度。按95％置信区间,取包含因子k=2时,花生仁水分的扩展不确定度为0．10％。     

Computation of one-dimensional consolidation of double layered ground using differential quadrature method

The authors give the solution to the problem of one-dimensional consolidation of double-layered ground with the use of the differential quadrature method. Case studies showed that the computational results for pore-water pressure in soil layer agreed with those of analytical solution; and that in the computational results for the interface of soil layer also agreed with those of the analytical solution except for the small discrepancies during shortly after the start of computation. The advantages of the solution presented in this paper are that compared with the analytical solution, it avoids the cumbersome work in solving the transcendental equation for eigenvalues, and in the case of the Laplace transform solution, it can resolve the precision problem in the numerical solution of long time inverse Laplace transform. Because of the matrix form of the solution in this paper, it is convenient for formulating computational program for engineering practice. The formulas for calculating double-layered ground consolidation may be easily extended to the case of multi-layered soils. Project (No. RC9609) supported by the Zhejiang Provincial Natural Science Foundation of China     

FINITE VOLUME METHOD BASED ON THE CROUZEIX-RAVIART ELEMENT FOR THE STOKES EQUATION

ＩＮＴＲＯＤＵＣＴＩＯＮＷｅｃｏｎｓｉｄｅｒｔｈｅＳｔｏｋｅｓｅｑｕａｔｉｏｎ :-Δ ｕ ｐ = ｆ　ｉｎΩ ( 1 )ｄｉｖ ｕ =0　ｉｎΩ ( 2 ) ｕ =0　ｏｎ Ωｗｈｅｒｅ ｕ =(ｕ1 ,ｕ2 ) Ｔａｎｄｐｄｅｎｏｔｅｔｈｅｖｅｌｏｃｉｔｙａｎｄｔｈｅｐｒｅｓｓｕｒｅｏｆｔｈｅｆｌｕｉｄｒｅｓｐｅｃｔｉｖｅｌｙ . ｆｄｅ ｎｏｔｅｓｔｈｅｅｘｔｅｒｎａｌｂｏｄｙｆｏｒｃｉｎｇｄｅｎｓｉｔｙ.Ωｉｓａｎｏｐｅｎｂｏｕｎｄｅｄａｎｄｃｏｎｖｅｘｐｏｌｙｇｏｎａｌｄｏｍａｉｎ . Ωｄｅｎｏｔｅｓｔｈｅｂｏｕｎｄａｒｙｏｆ…     

X射线荧光光谱法在耐火材料分析中的应用

采用熔融法制样,应用经验系数法校正基体元素间的增强吸收效应,X荧光光谱法代替传统化学法进行高硅质、高铝质、粘土质等耐火材料中SiO2、Al2O3、CaO、MgO、FeO、TiO2等含量的快速分析方法,还研究了测定精度及制样精度,拓展了铝、硅质耐火材料的分析范围。     

Time Collocation Method for Structural Dynamic Problems

In order to achieve highly accurate and efficient numerical calculations of structural dynamics, time collocation method is presented. For a given time interval, the numerical solution of the method is approximated by a polynomial. The polynomial coefficients are evaluated by solving alge-braic equation. Once the polynomial coefficients are evaluated, the numerical solutions at any time in the interval can be easily calculated. New formulae are derived for the polynomial coefficients, which are more practical and succinct than those previously given. Two structural dynamic equations are calculated by the proposed method. The numerical solutions are compared with the traditional fourth-order Runge-Kutta method. The results show that the method proposed is highly accurate and computationally efficient. In addition, an important advantage of the method is the simplicity in software programming.     

“空军第一”——威廉·米切尔的空军思想

威廉·米切尔预见到空军将在未来的战争中起决定性作用,提出了空权论,据此阐述了空中国防论和战略轰炸的思想,论述了空军的战术以及美国空军在世界上的作用,提出了一系列有远见的空军战略设想,重视空军人员的教育和培养。他还在实战中显示了高超的空军指挥才能,并为建立一支独立的美国空军而不遗余力。     

一个求解非线性互补问题的光滑化全局收敛性算法

求解非线性互补问题的一种方法是将其转化为非光滑方程组。本文通过引进一个基于Fischer-Burmeister函数的光滑NCP函数[8],建立了求解P0函数非线性互补问题的一个新的光滑牛顿算法。这个算法在每步迭代中只需要解一个光滑方程且不要求给出具体光滑因子下降的过程。在一定的条件下,证明了该算法的全局收敛性。数值试验表明该算法是有效的.