非线性中立型延迟积分微分方程单支方法的稳定性分析

本文研究求解R(α,β1,β2,γ)类非线性中立型延迟积分微分方程单支方法的数值稳定性,结果表明:在一定条件下,A-稳定的单支方法是数值稳定的,强A-稳定的单支方法是渐近稳定的,最后的数值试验验证了所获理论的正确性.     

求解刚性Volterra延迟积分微分方程的隐显单支方法的稳定性与误差分析

本文主要研究用隐显单支方法求解一类刚性Volterra延迟积分微分方程初值问题时的稳定性与误差分析.我们获得并证明了结论:若隐显单支方法满足2阶相容条件,且其中的隐式单支方法是A-稳定的,则隐显单支方法是2阶收敛且关于初值扰动是稳定的.最后,由数值算例验证了相关结论.     

刚性延迟积分微分方程单支方法的B-收敛性

本文研究刚性延迟积分微分方程单支方法的B-收敛性,结果表明：A-稳定的单支方法是B-收敛的,其B-收敛阶等于其经典相容阶．最后的数值试验验证了上述理论结果．     

时滞奇异摄动问题单支方法的收敛性

讨论数值求解一类单参数多刚性时滞奇异摄动问题的单支方法的误差分析.获得了A-稳定的单支方法关于这类时滞奇异摄动问题(在时滞部分用线性插值时)的收敛性结果.数值例子进一步证实了理论结果的正确性.     

求解时滞微分方程组的Rosenbrock方法的GP-稳定性

讨论了求解延时微分方程组的Rosenbrock方法的数值稳定性,分析了求解线性试验方程组的Rosenbrock方法的稳定性态,并证明了数值求解延时微分方程组的Rosenbrock方法是GP-稳定的充分必要条件是Rosenbrock方法是A-稳定的．     

非线性中立型延迟积分微分方程单支方法的收敛性

获得了求解非线性中立型延迟积分微分方程单支方法的收敛性结果.证明了当且仅当相应的常微分方程方法是A-稳定的且经典相容阶为p（p=1,2）时,单支方法是p阶E（或EB）-收敛的.数值实验结果验证了所获理论的正确性.     

线性Volterra多延迟积分微分方程线性多步法的GPm稳定性

讨论了多步法求解线性Volterra多延迟积分微分方程数值方法的GPm稳定.证明了对任给的步长h>0,A-稳定的线性多步法保持原线性系统的渐近稳定性,从而是GPm稳定.     

块θ-方法的PL-稳定性

1．引言在［6］中作者介绍了所谓块0一方法求解初值问题：这个方法具有精度高，数值稳定性好等优点，并证明了它是A-稳定的充分必要条件为051．本文将给出数值方法求解滞后微分方程时的PL一稳定性的概念，然后给出块0一方法为PL一稳定的充分必要条件．我们沿用［61中的记号介绍块0一方法及它的一些基本性质．所谓H一维块0一方法是使用已知k个点上的函数值求出后面k个点上的值．令其中O／L＼＿如果知道最初的yo，yi，…，yk－1，便能由（1．2）式设法求出yk，yk＋1；…，yZk－1，如此继续．下面两个定理是块令方法的基本性质．定理1．1［…     

单支方法关于多延迟Pantograph方程的稳定性分析

本文主要讨论了单支方法关于多延迟pantograph方程解的存在唯一性及渐近稳定性 ,同时将非线性多延迟系统数值解的有关结论推广到多延迟pantograph方程 ,证明了单支方法对于ODEs的A(α) 稳定等价于单支方法关于多延迟pantograph方程NGPk(α) 稳定 .     

一类多级隐式Hybrid单步法

§1 引言 众所周知,对于stiff常微分方程组的初值问题,能构造高阶A-稳定的隐式Rung-Kutta方法,但是,对非线性stiff系统的数值试验结果表明[2],[3],某些A-稳定的RK方法却得不到稳定的数值解。为此,A.Prothero在[4]中引入了更为合理的S-稳定的概念,证明了某些A-稳定的RK方法并不是S-稳定的。[3]中的数值试验结果恰好说明,这些A-稳定但不是S-稳定的方法的数值结果是不稳定的。     

一类随机大系统的稳定性

本文对随机大系统dx(t)=b(t,x(t))dt σ(t,x(t)dω(t)采用较文[1]更一般的分解形式，利用比较法和分解－集结法得到该随机大系统随机（一致）稳定性和渐近（一致）稳定性的比较准则。     

关于扰动微分方程组零解部分变元的稳定性

本文讨论未被扰动运动关于部分变元的稳定性，一致稳定性和全局渐近稳定性，给出了一种判定，改进了文［１］中的相应定理。     

一类非线性时滞差分方程的稳定性

得到了一类线性非自治时滞差分方程的零解的一致稳定、一致渐近稳定和全局渐近稳定的充分条件.     

Stabilization in elastic solids with voids

In this paper we study the asymptotic behavior and the analyticity of the solutions of the one-dimensional porous-elasticity problem with thermal effect. Our main result is to prove the lack of exponential stability in case of the porous-elasticity with thermal effect when viscoelasticity is present. We prove the analyticity of the problem when a porous viscosity is present. We conclude by showing the impossibility of localization in time of the solutions in the isothermal case.     

Virtual stability: Constructing a simulation model

After a discussion of the importance of stability and instability for complex systems theory, we define the concept of virtual stability as a state in which a system employs self‐monitoring and adaptive control to maintain itself in a configuration that would otherwise be unstable. The energy expended in this gains the system an increase in its flexibility of behavioral response to environmental changes. A model designed to illustrate virtual stability is presented, followed by a brief discussion of the evolutionary advantage this capacity provides. This leads to the suggestion that such advantage gives an argument both for the directionality of evolution and for the emergence of self‐consciousness. © 2008 Wiley Periodicals, Inc. Complexity, 2009     

随机时滞混杂区间系统的鲁棒稳定性

利用Lyapunov泛函方法及线性矩阵不等式，得到了随机时滞混杂区间系统的能失性及鲁棒稳定性的充分判据。     

STABILITY RESULTS OF RANDOM IMPULSIVE SEMILINEAR DIFFERENTIAL EQUATIONS

In this paper, we study the existence, uniqueness, continuous dependence, Ulam stabilities and exponential stability of random impulsive semilineax differential equations under sufficient condition. The results are obtained by using the contraction mapping principle. Finally an example is given to illustrate the applications of the abstract results.     

Stability results of random impulsive semilinear differential equations

In this paper, we study the existence, uniqueness, continuous dependence, Ulam stabilities and exponential stability of random impulsive semilinear differential equations under sufficient condition. The results are obtained by using the contraction mapping principle. Finally an example is given to illustrate the applications of the abstract results.     

一类非线性动力系统实用稳定域的研究及应用

借助于李雅普诺夫函数讨论了一类非线性动力系统的实用稳定性和实用稳定域的估计问题,得到了实用稳定域存在的充分条件,给出了一类动力系统实用稳定域的具体形式.通过具体实例说明了所给条件的实用性,改进了已有的结果.     

On stability concepts in nonlinear programming

Kojima's strong stability of stationary solutions can be characterized by means of first and second order terms. We treat the problem whether there is a characterization of the stability concept allowing perturbations of the objective function only, keeping the feasible set unchanged. If the feasible set is a convex polyhedron, then there exists a characterization which is in fact weaker than that one of strong stability. However, in general it appears that data of first and second order do not characterize that kind of stability. As an interpretation we have that the strong stability is the only concept of stability which both admits a characterization and works for large problem classes.Supported by the Deutsche Forschungsgemeinschaft, Graduiertenkolleg Analyse und Konstruktion in der Mathematik.Partial support under Support Center for Advanced Telecommunications Technology Research.