混合型微分求积法对求解联立的二维不可压Navier-Stokes方程和热方程的应用

1　Introduction　Variousnumericaltechniques,suchasthefinitedifferencemethodandfiniteelementsmethod ,havebeenusedinthepasttosolvetheincompressibleflowproblemnumerically .Usually ,thesemethodsrequirealargenumberofdiscretizedpointsinthecomputa tionaldomainforaccurateresults .Becausetheinfor mationonallgridpointsisusedtofitderivativesatgrid pointsinthedifferential quadrature (DQ )method ,itisenoughtouseonlyfewgridpointstoob tainhigh accuracynumericalsolutions .Therefore ,thenumberofgridpointscanb…     

二阶变系数线性齐次方程的三个可积充分条件

利用变量代换和凑项的方法,给出了二阶变系数线性齐次方程的三个可积充分条件,并得出求解方程的通解公式.     

Analysis of dynamical response to large deformation of piles with initial displacements

In this paper, a nonlinear mathematical model for analyzing dynamical response to the large deformation of piles with initial displacements is firstly established with the arc-coordinate, and it is a set of nonlinear integral-differential equations, in which, the Winkeler model is used to simulate the resistance of the soil to the pile. Secondly, a set of new auxiliary functions are introduced. The differential-integral equations are transformed into a set of nonlinear differential equations,and the differential quadrature method (DQM) and the finite difference method (FDM) are applied to discretize the set of nonlinear equations in the spatial and time domains, respectively. Then, the Newton-Raphson method is used to solve the set of discretization algebraic equations at each time step. Finally, numerical examples are presented, and the dynamical responses to the deformation of piles, including configuration, bending moment and shear force, are graphically illuminated. In calculation, two types of initial displacements and dynamical loads are applied, and the effects of parameters on the dynamical responses of piles are analyzed in detail.     

二阶变系数齐次线性微分方程两个非零解的关系

探讨了二阶变系数齐次线性微分方程两个非零解的关系,得到求二阶变系数齐次线性微分方程的一个解和通解的公式,介绍了二阶变系数线性微分方程的解法。     

轴向运动梁横向振动固有频率微分求积法研究

根据动力学分析和边界条件推导出轴向运动梁的系统特征方程,利用微分求积法对本征方程离散,计算出梁横向振动的固有频率,并数值模拟了梁运动速度和刚度对固有频率的影响。     

浅谈二阶变系数齐次微分方程的求解问题

在科学研究、工程技术中,常常需要将某些实际问题转化为二阶变系数线性微分方程。然而,对此类方程的一般形式,目前还尚未有通用的求解方法,但一些特殊类型是可以求解的。那么,对特殊的二阶变系数齐次微分方程又应该如何求解呢?这便是本文所要讨论的内容。本文主要利用构造法与常数变易法来求解二阶变系数齐次微分方程,希望能给读者一些启发与帮助。在实际问题中,二阶变系数齐次微分方程有着广泛的应用。本文给出了一类特殊二阶变系数齐次微分方程的求解方法。     

木材干燥过程中一个非线性模型的二阶收敛差分格式

针对描述木材干燥过程中的一个非线性微分方程模型,用降阶法对其建立了一个差分格式.此模型是由一个非线性常微分方程和一个非线性抛物方程组成的耦合微分方程组.首先引进一个新变量把原问题转化为一阶微分方程组问题,然后对此一阶微分方程组建立了一个线性化差分格式,应用能量方法证明了差分格式的可解性、稳定性和收敛性,并给出了误差估计式.差分格式关于时间步长和空间步长均为二阶.在实际计算时,将引入的新变量分离开,得到仅含原变量的差分格式,降低了计算量.数值计算结果验证了理论结果的可靠性.     

时间尺度上二阶非线性时滞动力方程的振动性定理

利用广义Riccati变换和不等式技巧,给出了一类时间尺度上二阶非线性时滞动力方程解的一个新的振动准则.该结果不仅推广和改进了已有文献的有关结果,而且在时间尺度上统一了二阶非线性时滞微分方程和二阶非线性时滞差分方程的振动性.     

试射法解二阶线性常微分方程模拟反应动力学过程

试射法可用于解二阶线性常微分方程，其原理在于把边值问题化为初值问题处理。该文采用龙格-库塔法求解，给出了模拟电化学二阶线性常微分方程求解方法及VB6．0程序源代码，可直观地看到该反应动力学曲线，并打印、输出结果。     

求解微分方程初值问题的高精度显式单步法

通过推导，得到求解线性或非线性常微分方程初值问题的具有3阶精度的显式单步法，此方法不同解离散方程组，计算简单且精度高，数值实验表明此方法求解常微分方程的7初值问题非常有效。     

微分求积法求解不可压二阶粘弹性流体和热迁移模型中的稳态流动

1IntroductionAlthoughthe computation of the fluid mechanics hasgreat development during the last decades,due to themodel in nonlinear fluid mechanics is very complicat-ed,the more efficient techniques for solvingthis prob-lemstill attract the interest of many researchers.Thedifferential quadrature method(DQM)introduced byBell man,et al.[1,2]is an efficient numerical methodfor solving partial differential equations.In recentyears,the DQMhas been widely used for solving theproblems of enginee…     

The condition of nonoscillation for a second-order differential equation

In this paper,by proving a differential identity,we obtain a necessary and sufficient condition of nonoscillation for a second-order differential equation.We also improve the known results of nonoscillation for a second-order differential equation.     

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     

Computation of one-dimensional consolidation of doublelayered ground using differential quadrature method

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二阶延迟微分方程Runge-Kutta方法的稳定性

研究二阶延迟微分方程Runge-Kutta方法的稳定性.首先,引入新变量,将二阶延迟微分方程化为一阶方程组.然后,应用Runge-Kuta 方法于一阶方程组,给出了Runge-Kutta稳定的充分条件,进而得到了二阶延迟微分方程Runge-Kutta方法稳定的充分条件.最后,通过数值试验验证所得结论的正确性.     

一类含有概周期强迫项的二阶非线性系统的概周期解

主要研究一类含有概周期强迫项的二阶非线性系统,即二阶非线性方程x″＋cx′＋g（t,x）=p（t,x（t-τ））的概周期解.在参考有关文献资料的基础上,将文献[9]研究的二阶非线性方程x″＋cx′＋g（x）=p（t）进行适当的推广.利用文献[10]中给出的证明方程概周期解存在性的方法,即指数型二分性和压缩映射原理研究二阶时滞微分方程x″＋cx′＋g（t,x）=p（t,x（t-τ））概周期的存在性,得到了某些充分条件,这些条件直接与方程的系数建立联系,推广了某些已有的结果。     

一类二阶非线性脉冲常微分方程解的振动性

讨论了二阶非线性脉冲常微分方程的振动性，得到了该方程所有解振动的充分条件。     

三阶变系数方程许可单参群的一个性质

在“初始”的三阶变系数线性方程许可某单参群的条件下，考察并获得另一三阶变系数方程许可同一单参群的条件。证明了如果一辅助的二阶线性方程有精确解，则这两个三阶方程在许可同一单参群时也可积。给出了一些例子。     

变时间分数阶扩散方程的数值模拟

考虑变时间分数阶扩散方程。首先利用分段线性插值法结合对一阶时间导数的一个二阶近似离散Coimbra变时间分数阶导数,然后利用Richardson外推法改进精度,最后用数值例子来验证提出的数值方法,从而说明数值方法的有效性。     

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.