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This thesis consists of two parts. The first one was that boundary value problem was discrete with five point difference method. Three kinds of memory formats were studied, which were full matrix, half band width and row compress sparse. Full matrix memory format and half band width memory format first was contrasted. The results show that half band width has efficiency in space. Then the algebraic system of finite element method was solved by Gauss-Seidel iteration method to popular row compress sparse memory format.

本论文由两部分组成,第1部分针对边值问题,用5点差分格式进行离散,并对离散矩阵这类大型稀疏矩阵,研究了系数矩阵的3种存储格式的优劣,即:满矩阵存储格式、半带宽存储格式和按行压缩稀疏存储格式,首先我们将满矩阵存储方式和半带宽存储格式进行了对比,迭代法的数值实验表明:利用半带宽存储的矩阵在空间运算方面具有高效性;然后针对目前数值实验中流行的按行压缩稀疏存储格式,实现了有限元离散代数系统的迭代法的求解。

The distributed parameter model is changed into variable coefficient nonlinear stiff ordinary differential equations by central difference method.

运用中心差分法将分布参数形式的系统模型转换为一变系数非线性的刚性常微分方程组。

Because the central difference method is conditional stable, the critical time step and damping were estimated by model analysis, which can guarantee the computation stability. In this paper, the mesh method was used to described the tool surface.

由于中心差分法的计算是有条件稳定,作者对确定系统临界时间步长和阻尼系数的方法进行了研究,采用模态分析理论估计临界时间步长和阻尼,保证了计算的稳定性。

In the second part, we make the study of the application of Z-transformation when we solve linear difference equation bearing constant coefficient and transmission function in pulsing system.

第2部分:"Z变换的应用",主要通过上1章研究的Z-变换的逆变换和10个性质定理,研究了Z-变换在求解具有常系数的线性差分方程和脉冲系统的传递函数方面的应用。

VOF equation use Lax-Wendroffgeshi scheme with precision of two steps. Pressure of host field is turned into initial-boundary value problem of variable coefficient parabolic equation on regular border. We utilize implicit difference method to solve it.

VOF方程的离散求解使用Lax-Wendroffgeshi格式,这种格式具有二阶精度;主场压力的求解转化为固定边界上变系数抛物型方程的初边值问题,采用隐式差分格式。

This paper gives several non-linear difference equations based on the orthogonality,regularity and standardity of the orthogonal wavelet with compact support.

从紧支撑正交小波滤波器的正交性、规范性及正则性条件出发,获得了求解滤波器系数的非线性差分方程组,并采用最优化方法求解。

This paper studies semi-discrete finite difference methods of constant coefficient heat equations .

本文主要研究了常系数热传导方程的半离散有限差分方法。

In the thesis, the fundamental formula of FFD method derives from the square root that is approximated by a continued fraction expansion in the one-way wave equation. Optimizations of the parameters of the finite-difference operator improve the validity of the method.

本论文用连分式近似单程波波动方程中的平方根导出FFD算法的基本公式,并对FFD算法中的有限差分算子进行了系数优化,进一步提高了计算的有效性。

Firstly, based on the wave equation, determining reasonably its initial boundary condition, the paper establishes a computer diagnostic model of oil pumping mechanical well, the damping factor in the model has been reasonably determined, the implicit difference solutionis conducted to the model by changing of step width expression difference solves, and the half analytical solution is explored to the model - fine integral method; and realizes the transformation from dot indicator diagram to indicator diagram of any section.

首先从抽油机井计算机诊断技术的理论基础入手,考虑多级抽油杆连续性,建立了粘滞阻尼波动方程,合理确定模型中的阻尼系数,采用无条件稳定的隐式差分法及半解析方法求解方程,获得抽油杆柱任意断面和抽油泵处的示功图。

A sufficient condition for the oscillation of bounded solutions of a kind of second order neutral differential difference equation s established.

建立了一类二阶中立型微分差分方程有界解振动的充分条件,且当变系数都是常数时,该条件也是必要的;同时,根据该方程的"极限"方程建立了它自身的一个有界振动准则。

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