多步块格式求解微分-代数方程

多步块格式是一类新的一般线性方法,在求解微分-代数方程的过程中不会出现精度降低现象。研究了多步块格式的构造方法,精度条件及具有Runge-Kutta稳定性的多步块格式,多步块格式具有刚性精确的优点,且级精度与格式精度相等。构造了具有Runge-Kutta稳定性的2级和3级多步块格式,具有L-稳定性。数值算例证实多步块格式在求解微分-代数方程不会精度降低。

Abstract：

The multistep block methods are a new class of general linear methods,and the methods solve the differential-algebraic equations with no order reduction.The construction of the multistep block methods was described,and order condition and stability was studied.The multistep block methods with Runge-Kutta stability were also constructed.The multistep block methods have many nice properties,for example,stiffly accurate,and stage order is equal to order of method.At last the methods of 2-stage and 3-stage with Runge-Kutta stability were constructed,and they have the property of L-stability.The numerical example shows that the multistep block methods can solve the differential-algebraic equations without the order reduction.     

多延迟中立型方程Runge-Kutta方法的NGPG-稳定性

讨论了多延迟中立型微分方程解析解及由隐式Runge-Kutta方法应用于方程得到的数值解的稳定性.给出了方程解析解渐近稳定的一个充分条件.在此基础上将隐式Runge-Kutta方法应用于方程,证明了数值解NGPG-稳定的充分必要条件为隐式Runge-Kutta方法是A-稳定的.     

不确定Lurie型控制系统的绝对稳定性

讨论了区间非线性Lurie型控制系统的鲁棒绝对稳定性.用Lyapunov函数法研究了区间非线性Lurie型直接控制系统和间接控制系统的鲁棒绝对稳定性;给出了区间非线性Lurie型直接控制系统和间接控制系统鲁棒绝对稳定的充分条件;建立了区间非线性Lurie型控制系统鲁棒绝对稳定与区间矩阵稳定的关系.     

非线性控制系统单支方法的IS稳定性

控制系统在实际问题中有广泛应用,众多文献对系统本身及其数值方法的稳定性进行了深入研究。将单支方法用于求解非线性控制系统,获得了方法IS稳定的条件,可视为单支方法关于非线性常微分方程的稳定性分析在非线性控制系统的进一步推广。最后给出了一些常用的单支方法IS稳定的条件。     

分段连续型延迟Logistic方程Runge-Kutta方法的稳定性

讨论了用Runge-Kutta方法求解分段连续型延迟Logistic方程的稳定性,分析了直接运用Runge-Kutta方法会产生伪解,从而建立了不产生伪解的Runge-Kutta方法,讨论了该方法的收敛阶,证明了该方法是局部和全局渐近稳定的.数值实验进一步验证了算法理论分析的正确性.     

两步Runge-Kutta法求解延迟微分方程的GPL_m-稳定性

讨论了两步Runge-Kutta方法求解延迟微分方程的数值稳定性,分析了求解线性试验方程的两步Runge-Kutta方法的稳定性态。证明了两步Runge-Kutta方法是GPLm-稳定的,当且仅当它求解常微分方程是L-稳定的。     

基于神经网络的非线性动态系统的多内模控制研究

由于非线性动态系统的复杂性,目前还没有统一的控制器设计方法,用传统的线性系统理论来设计,当工作点大范围变化时,很难保证其性能及稳定性.在人工神经网络内模控制系统中建立了神经网络内部模型和神经网络内模控制器,提出了基于多模型的内模控制方法,它对非线性动态过程的控制具有良好的性能.在此基出上,给出了方便易行控制算法,仿真分析结果验证了控制算法的有效性.     

基于计算机仿真的控制系统新型稳定性判据

在分析Lyapunov稳定性理论局限性的基础上,提出了一种新型的基于计算机仿真的非线性定常控制系统稳定性分析方法,规范和简化了Lyapunov函数的选择办法,扩展了Lyapunov稳定性理论.将Lyapunov稳定性判据第二法(即直接法)中的有关局部稳定性的充分条件扩展成为充分必要条件.给出了该方法的理论证明,并且将该方法成功地在MATLAB环境下应用于单级倒立摆模糊控制系统的稳定性分析.实验结果证明该方法是有效的.     

RK-方法求解广义滞时微分方程的GPL-稳定性

讨论了用隐式Runge-Kutta方法求解广义滞时微分方程的数值稳定性，分析了用隐式Runge-Kutta方法求解线性模型方程的GPL-稳定性，证明了隐式Runge-Kutta方法是GPL稳定的，当且仅当它是L-稳定的。     

奇异延迟微分方程数值仿真的两步连续Runge-Kutta方法

提出在当前的积分步内计算级值时，放松延迟对计算的影响的思想，构造了一类奇异延迟微分方程数值仿真的两步连续Runge-Kutta方法(TSCRK)，讨论了方法的构造，方法阶条件，证明了方法的收敛性，分析了方法的稳定性。这类方法具有优良的稳定性和较高的阶级，并保持了显式的求解过程。数值试验表明方法是有效的。     

THE 8~(th) INTERNATIONAL CONGRESS ON INDUSTRIAL AND APPLIED MATHEMATICS

正August 10-14,2015Beijing,ChinaThe International Congress on Industrial and Applied Mathematics(ICIAM)is the premier international congress in the field of applied mathematics held every four years under the auspices of the International Council for Industrial and Applied Mathematics.From August 10 to 14,2015,mathematicians,scientists     

2014 List of Referees

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TSINGHUA UNIVERSITY,Beijing, China

正AF:Any Field The School of Economics and Management at Tsinghua University(Tsinghua SEM)invites applications for faculty positions at all levels(Assistant Professor,Associate Professor and Full Professor)in any fields of business administration and management.Tsinghua SEM is the only school     

《Journal of Systems Science and Systems Engineering》Contents of Volume 23,2014

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Call for Papers The 12th International Conference on Service Systems and Service Management ICSSSM'15

正June 22-24,2015Guangzhou,China http://iec.cnsba.com/index.htmlCo-Sponsored by:ffiEE SMC(pending)South China University of Technology The Chinese University of Hong Kong Tsinghua UniversityHosted bv:School of Business Administration,South China University of Technology,China Conference Co-Chairs:     

分布交互仿真技术综述

介绍了ＤＩＳ的技术特点,综述了ＤＩＳ中关键技术和相关技术,并对目前ＤＩＳ发展过程中遇到的问题进行了深入的分析与论证。     

Innovation Versus Environmental Protection Presumptions

The paper is about negotiating with issues that discourage innovation. The subject is environmental deterioration, with concern directed at the impediments that keep it from being innovatively resolved. The paper is organized around three issues. (1) The dominant model of environmental concern, called environmental protection, is managed predominantly via command and control approaches. (2) Command and control, by relying on analytical segmentation to subdivide the problem into digestible bits and using formal legislation to direct it, are not up to emerging challenges in the area. (3) More robust models are available but difficult to experiment with due to impediments that discourage change. These impediments are seen in ideals associated with protection, prevention, recycling, and sustainability that tend to do more to sustain harmful practices than to seek beneficial alternatives. Being able to appreciate the underlying restrictions of entropy could help stimulate a more innovative agenda. These issues are tested via a project funded by the EPA entitled ENERGY STAR Homes.