数值稳定性

Firstly,the differential equation with parameters is given,at the same time,in order to let the truncation error of differential equation reach O(Δt~2+Δx~4) as high as possible,the method of undetermined coefficent is used to appropriately select the expression of these parameters.Secondly,the stability condition of the scheme derived is given by using the Fourier method of stability analysi...

首先给出了含参变量的差分方程，并用待定系数法适当地选取了这些参数的表示式，以使差分方程的截断误差阶尽可能高地达到了O(Δt2+Δx4)；其次用稳定性分析的Fourier方法给出了所得格式的稳定性条件；然后给出了确定差分格式中参数的两种方法，得到了一个稳定性条件为r/3的分支稳定的高精度显式差分格式；最后给出了数值例子，数值结果表明了本文格式较现有同类格式的优越性和理论分析的正确性。

This paper studied a filtering high order numerical method for one dimension constant coefficient hy2 perbolic function. The stability and error analysis show the efficiency of this method. Numerical examples are also given to verify the analysis results.

摘 要 考虑一维常系数双曲型方程的高阶数值解法，引进了一种稳定性过滤算子FN ，最后从理论和数值实验上分析了该过滤算子对数值解稳定性和精度的影响。

In the third chapter, the contractilities and asymptotical stabilities of neutral delay integro-differential equations are concerned. The extended Runge-Kutta methods, with the compound quadrature formula and the Pouzet quadrature formula, are numerically stable under suitable conditions. The numerical experiments prove this result.

第三章，研究了中立型延迟积分微分方程，其理论解的收缩性和渐近稳定性，利用复合求积公式与Pouzet求积公式扩展Runge-Kutta方法，并获得了数值方法的稳定性条件，随后的数值试验结果进一步证明了方法是数值稳定的。

By means of different subjects and te chniques,the paper makes an overall study on the crustal stability of Beihuaiyang region and its adjace nt areas from the aspects of current t ectonic stress fields,principal fa ult structures,analysis of regional fa ults and neotectonic activity,seis mic activity and numerical modeling,etc.

运用多学科、多技术相结合的研究方法，从现今构造应力场特征、现代地壳形变特征、主干断裂构造以及区域断裂活动性分析、新构造运动、地震活动、数值模拟等方面入手，对北淮阳及其邻接区地壳稳定性进行了全面而系统的研究，指出本区地震活动受走滑活动断裂控制，中、强地震集中于区内东南部和西北部NW向与NE向断裂交汇处；第四纪无大规模差异升降运动；数值模拟等综合分析表明，信阳地区的区域构造稳定性高，现代地壳形变量小，应力平缓，地震活动少且弱。

Through such a study, it is also shown that when the time delay is long enough such that the stability switches of the equilibrium of system halt, the bifurcation branches originated from the critical time delays cannot be surely stable or unstable in the whole solution space, that is, their stability depends on cases.

利用打靶法的数值结果说明了当系统平衡点不再发生稳定性切换时，源自这些临界时滞处的解支的稳定性在整个解空间的稳定性具有不可判定性，这也说明由多尺度法所得高阶近似判定的解支的稳定性事实上只表示解支在局部中心流形上的稳定性，而非在整个解空间中的稳定性。

Based on parabolized stability equations , the stability of nonparallel boundary layer is calculated and analyzed by using recursion numerical method.

该文从抛物化稳定性方程出发，采用从上游往下游递推的数值方法，对非平行边界层稳定性问题进行了数值计算和分析。

The results showed compared with the native state the shear strength of rockmass under the saturation state decreased by 11.17%, cohesion force decreased by 16.09%, internal frictional angle decreased by 10.02%.(3) 3D-σFEM numerical simulation software is used to simulate the slope stability on the native state and saturation state. Compared with the nature state the displacement of the discontinuity and stress concentration in the saturation state is largened clearly, the results showed slope stability under the rainfall is weakened.

更多含有天然结构面的岩体试件进行了不同含水量下的强度试验，试验结果证明在岩体试件处于饱水状态时的结构面抗剪强度比天然状态下平均下降了11.17%、粘聚力平均下降了16.09%、内摩擦角平均下降了10.02%；(3)采用3D-σ有限元数值软件对K86+180～K86+470段岩质边坡进行了三维有限元数值模拟，并且分天然状态分阶段开挖和饱水状态分阶段开挖两种不同状况进行了稳定性分析，从分析结果可以看出与天然状态相比，饱水状态下软弱层水平方向位移明显增大，坡脚及软弱层特别是软弱层临空面附近的剪应力值显著增大，并且其安全系数与天然状态相比也显著减小，说明在有大的降雨发生当岩体处于饱水状态时边坡整体稳定性被削弱，边坡失稳可能性增大。

According to the analysis and computational results in this thesis, although the actual structure and work conditions of the pressure vessel in nuclear power station are much more complex than that of the pressure vessel model, the program FEARPV still can get quite good convergence on the plasticity andcontact iteration. And also the program FEARPV has good value stability, and good regularity. During the heating, compression, constant temperature, constant pressure, cooling and decompression process, the regularity is basically in common with that of the pressure vessel model.

由本文分析计算可知，虽然电站核压力容器的结构及计算工况较压力容器模拟体复杂得多，然而反应堆压力容器瞬态密封有限元分析程序对塑性迭代和接触迭代仍具有很好的收敛性，数值稳定性好，得到的结果具有良好的规律性，在升温、升压、恒温、恒压、降温和降压等过程中其规律和压力容器模拟体基本相似。

In the second part of the paper, the sport techniques of the flight elements was analysised in-depth theoretically by the movement technical structure:①the giant swing was first analysised in mechanics by applying the Kane's method, the dynamic equation of 5-link multi-body model was established, and the computer simulation software of the giant swing on the high bar was developed.

其次，作为单杠上飞行动作系统性研究的另一主要方面，本论文对飞行动作一般技术结构中的各技术环节进行了深入的理论分析：①着重对飞行动作准备阶段的回环运动技术进行了动力学分析，主要采用了多体力学理论中的Kane方法，建立了5环节人体回环运动的动力学方程，并应用计算机数值仿真技术研制开发了用于回环运动动力学分析的数值仿真软件，进而以动作实例对回环运动进行了数值仿真与误差分析，其所得到的数值仿真结果能够满足对人体回环运动的动力学分析和仿真要求；②对于飞行动作的撒手技术环节，本论文从人体环节相对运动角度，来分析撒手时人体质心的运动以及撒手时角动量参数，并列举了几种飞行动作撒手技术的基本力学指标；③关于飞行动作的空中技术，论文在总结了空翻转体动力学机理的研究成果基础上，对人体空中运动定量化问题进行了一般性描述，并进一步应用刚体动力学理论，着重建立起了描述空翻与转体技术之间定量化的关系，讨论了空翻转体运动的稳定性及其运动模式的转换问题，它对于定量地评定空翻转体技术以及今后对空翻转体动作进行数值仿真都具有理论上和实践上的重要意义；④关于飞行动作再握技术环节，本论文避免了以再握瞬时性的力学参数指标来描述再握技术特征的简单化途径，提出以再握下摆与回环下摆相对比的方法来研究再握技术，并以飞行动作再握技术的具体实例进行了对比分析，表明再握下摆技术相比回环下摆技术有着相当的困难性和复杂性，运动员对再握下摆过程中各环节的相对运动实施有效的控制，是连接高难动作以及顺利流畅地完成成套动作的关键。

High order Godunov's scheme was used, presenting good numerical stability and shock capturing capability. Viscous effects and secondary flow losses were treated as source terms.

求解过程采用具有TVD性质的高阶Godunov格式，具有良好的数值稳定性和激波捕获能力。

This one mode pays close attention to network credence foundation of the businessman very much.

这一模式非常关注商人的网络信用基础。

Cell morphology of bacterial ghost of Pasteurella multocida was observed by scanning electron microscopy and inactivation ratio was estimated by CFU analysi.

扫描电镜观察多杀性巴氏杆菌细菌幽灵和菌落形成单位评价遗传灭活率。