非线性变延迟微分方程隐式Euler方法的数值稳定性

在减弱对非线性刚性变延迟微分方程初值问题本身的约束条件的前提下 ,将已有的文献中隐式Euler方法数值稳定性的结论由常延迟的情形推广到了变延迟的情形 ,证明了隐式Euler方法是稳定的     

时变脉冲时滞微分方程的稳定性

本文讨论脉冲时滞微分方程零解的稳定性 .应用Lyapunov函数法结合Razu mikhin技巧得到这类方程零解一致稳定和渐近稳定的充分性条件 ,并给出例子以说明所得结论     

Stochastic Differential Games with Multiple Modes and a Small Parameter

Abstract

Two persons stochastic differential games with multiple modes where the system is driven by a wideband noise is considered. The state of the system at time t is given by a pair (x ^ε(t), θ^ε(t)), where θ^ε(t) takes values in S = {1, 2,…, N} and ε is a small parameter. The discrete component θ^ε(t) describes various modes of the system. The continuous component x ^ε(t) is governed by a “controlled process” with drift vector which depends on the discrete component θ^ε (t). Thus, the state of the system, x ^ε(t), switches from one random path to another at random times as the mode θ^ε(t) changes. The discrete component θ^ε (t) is a “controlled Markov chain” with transition rate matrix depending on the continuous component. Both zero-sum and nonzero-sum games will be considered. In a zero-sum game, player I is trying to maximize certain expected payoff over his/her admissible strategies, where as player II is trying to minimize the same over his/her admissible strategies. This kind of game typically occurs in a pursuit-evation problem where an interceptor tries to destroy a specific target. Due to swift manuaring of the evador and the corresponding reaction by the interceptor, the trajectory keep switching rapidly at random times. We will show that the process (x ^ε(t), θ^ε(t)) converges to a process whose evolution is given by a “controlled diffusion process” with switching random paths. We will also establish the existence of randomized δ -optimal strategies for both players.     

非线性变延迟微分方程隐式Euler法的渐近稳定性

本讨论非线性变延迟微分方程隐式Euler法的渐近稳定性。我们证明，在方程真解渐近稳定的条件下，隐式Euler法也是渐近稳定的。     

带有积分条件的泛函微分方程的稳定性分析

本文讨论了下列泛函微分方程: 这里T>0,T_1≥0。令Q=bf(a)/c。若Q≤1,则上述方程有唯一平衡点且全局稳定。若Q>1,则上述方程的正平衡点渐近稳定,另一平衡点不稳定。所采用的证明方法是构成Lyapunov泛函和利用广义持征方程,与[2]、[3]不同.当f(y)=y即可得K.L.cooke[3]的结论.当T=T_1=O,f(y)=y即可得[2]的讨论。     

Stochastic Differential Games With a Small Parameter

Much of stochastic game theory is concerned with diffusion models. Such models are often only idealizations of the actual physical process, which might be driven by a wide bandwidth process or be a discrete parameter system with correlated driving noises. For a two person zero-sum game, under quite general conditions, the optimal or nearly optimal strategies derived for the diffusion model are shown to be “nearly optimal” for the physical (say wideband noise driven) process. An approach based on occupation measures are used. We treat the problem of discounted cost, as well as the average cost per unit time problem. Weak convergence methods are utilized in the analysis     

延迟微分方程隐式Euler方法的收敛性

本文讨论了用隐式Euler方法求解一类延迟量满足Lipschitz条件且Lipschitz常数小于1的非线性变延迟微分方程初值问题的收敛性.获得了带线性插值的隐式Euler方法的收敛性结果.     

非线性中立型随机延迟微分方程随机θ方法的稳定性

本文研究非线性中立型随机延迟微分方程随机θ方法的均方稳定性.在方程解析解均方稳定的条件下,证明了如下结论:当θ∈[0,1/2)时,随机θ方法对于适当小的时间步长是均方稳定的;当θ∈[1/2,1]时,随机θ方法对于任意步长都是均方稳定的.数值结果验证了所获结论的正确性.     

一个非线性时滞偏微分方程种群模型的稳定性与周期性

讨论了一个具有年龄结构非线性非自治时滞偏微分方程种群模型解的渐近性态,得到了零解稳定以及周期解存在的充分条件.     

The Milstein Scheme for Stochastic Delay Differential Equations Without Using Anticipative Calculus

The Milstein scheme is the simplest nontrivial numerical scheme for stochastic differential equations with a strong order of convergence one. The scheme has been extended to the stochastic delay differential equations but the analysis of the convergence is technically complicated due to anticipative integrals in the remainder terms. This article employs an elementary method to derive the Milstein scheme and its first order strong rate of convergence for stochastic delay differential equations.     

Stability Analysis of Runge-Kutta Methods for Non-Linear Delay Differential Equations

This paper is concerned with the numerical solution of delay differential equations(DDEs). We focus on the stability behaviour of Runge-Kutta methods for nonlinear DDEs. The new concepts of GR(l)-stability, GAR(l)-stability and weak GAR(l)-stability are further introduced. We investigate these stability properties for (k, l)-algebraically stable Runge-Kutta methods with a piecewise constant or linear interpolation procedure.     

p-Moment Stability of Stochastic Nonlinear Delay Systems with Impulsive Jump and Markovian Switching

Abstract

This article is concerned with the problem of p-moment stability of stochastic differential delay equations with impulsive jump and Markovian switching. In this model, the features of stochastic systems, delay systems, impulsive systems, and Markovian switching are all taken into account, which is scarce in the literature. Based on Lyapunov–Krasovskii functional method and stochastic analysis theory, we obtain new criteria ensuring p-moment stability of trivial solution of a class of impulsive stochastic differential delay equations with Markovian switching.     

变分迭代法解时滞微分方程(英文)

变分迭代法被用于解时滞微分方程,通过这种方法我们得到了他们的准确解和数值解。一些例子说明了这种方法的有效性,结果显示这种方法对于解时滞微分方程是一种有力的直接的数学方法。     

The Lambert Function on the Solution of a Delay Differential Equation

Recently, a new method for computing the analytical solution of a delay differential equation was developed considering a constant initial function. It is based on the existence of a specific class of polynomials in the delay. In this article, we extend this new method to the case of a continuous initial function. We also show the relationship between the new solution's method and the solution expressed in terms of the Lambert function.     

Nonlinear Stability of General Linear Methods for Delay Differential Equations

This paper is devoted to a study of nonlinear stability of general linear methods for the numerical solution of delay differential equations in Hilbert spaces. New stability concepts are further introduced. The stability properties of (k,p,q)-algebraically stable general linear methods with piecewise constant or linear interpolation procedure are investigated. We also discuss stability of linear multistep methods viewed as a special subset of the class of general linear methods.     

一类随机微分方程的稳定性

本文用Rn中一类半线性椭圆方程正解结果讨论了随机微分方程的随机稳定性.     

随机延迟微分方程的Milstein方法的非线性均方稳定性

本文针对一般的非线性随机延迟微分方程,证明了当系统理论解满足均方稳定性条件时,则当方程的漂移和扩散项满足一定的条件时,Milstein方法也是均方稳定的.数学实验进一步验证了我们的结论.     

Markov调制的随机微分延迟方程的函数稳定性

随机微分延迟方程的指数稳定性被人们广泛研究,但讨论带Markov调制的随机微分延迟方程的函数稳定性的不多.本文主要研究了两种类型的函数稳定性.我们采用了一例特定的Lyapunov函数,来研究带Markov调制的随机微分延迟方程的p阶矩ψα-函数稳定性,并对其几乎必然ψβ/p-函数稳定性也进行了探讨.     

求解延迟微分代数方程的多步Runge-Kutta方法的渐近稳定性

延迟微分代数方程(DDAEs)广泛出现于科学与工程应用领域．本文将多步Runge-Kutta方法应用于求解线性常系数延迟微分代数方程，讨论了该方法的渐近稳定性．数值试验表明该方法对求解DDAEs是有效的．     

具有脉冲的时滞微分方程的全局吸引性

研究具有脉冲的时滞微分方程其中τ＞0,bk＞-1.本文给出了保证方程每一解趋于0的充分条件.限制在bk≡0时的推论包含了[4]等的结果.