求解变延迟微分方程的一类线性多步方法的收缩性

This paper presents a sufficient condition on the contractivity of theoretical solution for a class of nonlinear systems of delay differential equations with many variable delays(MDDEs), which is weak,compared with the sufficient condition of previous articles.In addition,it discusses the numerical stability properties of a class of special linear nmltistep methods for this class nonlinear problems.And it is pointed out that not only the backwm‘d Euler method but also this class of linear multistep methods are GRNm-stable if linear interpolation is used.     

一类求解分片延迟微分方程的线性多步法的散逸性

本文研究分片延迟微分方程本身及数值方法的散逸性问题．给出了一个关于此类问题本身散逸性的充分条件,同时得到了一类求解此类问题的线性多步法的数值散逸性结果,此结果表明所考虑的数值方法继承了方程本身的散逸性．数值试验进一步验证了理论结果的正确性．     

一类奇异方程两点边值问题的差分—样条校正解

本文考虑一类奇异方程两点边值问题的差分解和样条数值解法,证明了差分解,样条解分别从两侧逼近精确解,从而得到高精度的差分-样条校正解. 考虑如下形式的奇异边值问题:     

耗散对称正则长波方程的有限差分逼近

本文对耗散对称正则长波方程的初边值问题进行了数值研究,提出了一个两层隐式Crank-Nicolson差分格式,讨论了差分解的存在唯一性,并利用能量方法分析了该格式的二阶收敛性与稳定性,数值算例表明本文的格式是可靠的.     

THE EXISTENCE, UNIQUENESS AND STABILITY OF ALMOST PERIODIC SOLUTION FOR A CLASS OF NONLINEAR SYSTEM

In this paper, we study the problems on the existence, uniqueness and stability of almost periodic solution for a class of nonlinear system. Using fixed point theorem and Lyapunov functional, the sufficient conditions are given which guarantee the existence, uniqueness and stability of almost periodic solution for the system.     

基于RBC模型的动态随机一般均衡的数值解

以一般均衡为框架,引入随机变量的动态随机一般均衡系统,由于模型的庞大和函数形式的复杂,往往不能给出明确的数值解.本文给出几种操作性强的、有效的寻求一般化模型数值解的方法,并通过介绍模型参数确定的办法,使得理论的模型有了现实的含义.     

一类线性多步法关于变延迟非线性中立型微分方程的渐近稳定性

1引言中立型微分方程广泛出现于生物学、物理学及工程技术等诸多领域.数值求解中立型微分方程时,数值方法的稳定性研究具有无容置疑的重要性,其中渐近稳定性的研究是其重要组成部分.对于线性中立型延迟微分方程,渐近稳定性研究已有许多重要结果,如文献[1,2,3,4,5,6]等.对于非线性中立型变延迟微分方程,数值方法的稳定性研究近几年才有进展.2000年,Bellen等在文献[7]中讨论了Runge-Kutta法求解一类特殊的中立型延迟微分     

A sufficient condition for the stability of direct quadrature methods for Volterra integral equations

Within the theoretical framework of the numerical stability analysis for the Volterra integral equations, we consider a new class of test problems and we study the long-time behavior of the numerical solution obtained by direct quadrature methods as a function of the stepsize. Furthermore, we analyze how the numerical solution responds to certain perturbations in the kernel.     

基于GA-Chebyshev神经网络的分数阶Bagley-Torvik方程数值解法

本文基于现有的切比雪夫神经网络,提出了一种利用遗传算法优化切比雪夫神经网络求解分数阶Bagley-Torvik方程数值解的新方法,结合多点处的泰勒公式原理,给出数值解的一般形式,将原问题转化为求解无约束最小化问题.与现有数值方法的数值结果进行比较表明了本文方法的可行性和有效性,为分数阶微分方程中类似问题的求解提供了新的思路.     

线性流形上矩阵方程AX=B的一类反问题及数值解法

1．引言本文用＊-"m表示全体nX。实矩阵的集合，人表示n阶单位矩阵，汉"m一《ME＊""叫rank（川一r），＊＊"""＝HE＊"""卜"A＝v，＊＊"""一仰E＊"""卜"一M｝，SR；""（SR7""）表示全体7。阶实对称半正定（正定）阵集合．N（A）表示矩阵A的零空间，即N（A）＝（xlAx＝0），ID叫D表示Frobenius范数，A"表示矩阵A的Moors－Penrose广义逆，［EI十表示在Frobenius范数意义下n阶方阵E在SR；""中唯一的最佳k逼近解，即口一［E］＋11-inf。。、。。x，IllE-All．（［E］十求法见文［7］）．还用A三0（A三0）表示A（的k阶顺序主子矩…     

NUMERICAL SOLUTION OF THE UNSTEADY INCOMPRESSIBLE NAVIER-STOKES EQUATIONS ON THE CURVILINEAR HALF-STAGGERED MESH NUMERICAL SOLUTION OF THE UNSTEADY INCOMPRESSIBLE NAVIER-STOKES EQUATIONS ON THE CURVILINEAR HALF-STAGGERED MESH

1. IntroductionLet us consider the unsteady incompressible Navier--Stokes equatinns (qSE)on a twedimensional reginn n with boundary On. Here w is the velocity vector; interms of its Caxtesian,components w = (u, v)"; p is the Pressure. The initial conditionis given assatisheng (1.2). We are concerned mainly with the solid wall boundary conditiollbut we will also briefly discuss the outflow boundary conditinn. Note the convectionterm can ajBo be written in conservative form (w' glad)w = div(…     

中立型比例延迟微分系统线性θ-方法的渐近估计

本文研究了一类线性非自治中立型比例延迟微分系统线性θ-方法的渐近稳定性,并借助于泛函不等式得到了数值解的渐近估计.此渐近估计不仅比数值渐近稳定性描述得更加精确,而且还能给出非稳定情形数值解的上界估计式.数值算例验证了相关理论结果.     

THE STABILITY OF A VARIATIONAL METHOD FOR THE SOLUTION OF A LINEAR HYPERBOLIC INITIAL BOUNDARY VALUE PROBLEM

Abstract

The numerical stability of a variational method that is used to obtain the solution of a one space dimension wave equation with initial and boundary conditions is analyzed. The phase speed and group velocity of the numerical solution are also investigated with respect to that of the exact solution.     

关于广义KPP方程的数值解

广义KPP(Kolmogorov-Petrovskii-Piskunov)方程是一个积分微分方程.为了要研究其数值解,我们首先将该方程转化为一个非线性双曲型方程,然后构造了一个线性化的差分格式,得到了差分格式解的存在唯一性,利用能量不等式证明了差分格式二阶收敛性和关于初值的无条件稳定性,数值结果验证了本文提出的方法.     

线性方程组通解并行数值方法

1预备知识 线性方程组消息传递MIMD算法是20世纪90年代至今的活跃课题，但尚无此问题 的通用有效算法发表.用!.}.}表示矩阵列分块划分，记AX=b为[AI司.定理1、2是文 {l]、[s]成果综述和推广. 定理i[‘]设有线性方程组!e}己l，e〔尺”“m，d〔R”“‘，rank(e)=r.当且仅当rank(!     

Dissipativity and asymptotic stability of nonlinear neutral delay integro-differential equations

This paper is concerned with the dissipativity and asymptotic stability of the theoretical solutions of a class of nonlinear neutral delay integro-differential equations (NDIDEs). We first give a generalization of the Halanay inequality which plays an important role in the study of dissipativity and stability of differential equations. Then, we apply the generalization of the Halanay inequality to NDIDEs and the dissipativity and the asymptotic stability results of the theoretical solution of NDIDEs are obtained. From a numerical point of view, it is important to study the potential of numerical methods in preserving the qualitative behavior of the analytical solutions. Therefore, the results, presented in this paper, provide the theoretical foundation for analyzing the dissipativity and the asymptotic stability of the numerical methods when they are applied to these systems.     

Mean-square stability of stochastic age-dependent delay population systems with jumps

In this paper, we present the compensated stochastic θ method for stochastic age-dependent delay population systems (SADDPSs) with Poisson jumps. The definition of mean-square stability of the numerical solution is given and a sufficient condition for mean-square stability of the numerical solution is derived. It is shown that the compensated stochastic θ method inherits stability property of the numerical solutions. Finally, the theoretical results are also confirmed by a numerical experiment.     

Theoretical and numerical comparison of relaxation methods for mathematical programs with complementarity constraints

Mathematical programs with equilibrium constraints (MPECs) are difficult optimization problems whose feasible sets do not satisfy most of the standard constraint qualifications. Hence MPECs cause difficulties both from a theoretical and a numerical point of view. As a consequence, a number of MPEC-tailored solution methods have been suggested during the last decade which are known to converge under suitable assumptions. Among these MPEC-tailored solution schemes, the relaxation methods are certainly one of the most prominent class of solution methods. Several different relaxation schemes are available in the meantime, and the aim of this paper is to provide a theoretical and numerical comparison of these schemes. More precisely, in the theoretical part, we improve the convergence theorems of several existing relaxation methods. There, we also take a closer look at the properties of the feasible sets of the relaxed problems and show which standard constraint qualifications are satisfied for these relaxed problems. Finally, the numerical comparison is based on the MacMPEC test problem collection.     

一类两相Stefan问题的弱解的局部存在性

本文讨论一维情形下一类两相Ｓｔｅｆａｎ问题，证明了弱解的局部存在性。     

快速求解参数化偏微分方程的缩减基有限元方法及其在核工程中的应用

基于求解偏微分方程的高保真数值模拟已经广泛应用于科学研究和工程设计.然而,即使借助超级计算机的并行计算能力,经典的有限元方法和其它数值方法在面对需要多次求解或需要快速甚至实时求解的问题时仍然面临效率的挑战.针对可用参数化微分方程表示的问题,缩减基有限元方法利用少数代表性的经典有限元解构造基函数,同时通过仿射分解使得系统矩阵和载荷向量的组装变为简单的代数叠加,因此该方法可以大幅度地提高这类问题的求解效率.本文介绍了这种方法的原理,并以固体热传导和中子扩散的快速求解为例,展示了这种方法的优良特性.结果表明,在线阶段的求解效率可以实现两到三个数量级的提升.基于高保真模拟的缩减基模型是将高性能计算应用于工程优化设计、应急指挥以及复杂问题的反分析等工作的有效手段.