共查询到20条相似文献,搜索用时 671 毫秒
1.
建立了广义中立型延迟系统理论解渐近稳定的充分条件 ,分析了用线性多步方法求解广义中立型延迟系统数值解的稳定性 ,在一定的Lagrange插值条件下 ,证明了数值求解广义中立型系统的线性多步方法NGPG_稳定的充分必要条件是线性多步方法是A_稳定的· 相似文献
2.
This paper is concerned with the numerical solution to initial value problems of nonlinear delay differential equations of neutral type. We use A-stable linear multistep methods to compute the numerical solution. The asymptotic stability of the A-stable linear multistep methods when applied to the nonlinear delay differential equations of neutral type is investigated, and it is shown that the A-stable linear multistep methods with linear interpolation are GAS-stable. We validate our conclusions by numerical experiments. 相似文献
3.
This paper is devoted to investigating the nonlinear stability properties of linear multistep methods for the solution to neutral delay differential equations in Banach space. Two approaches to numerically treating the “neutral term” are considered, which allow us to prove several results on numerical stability of linear multistep methods. These results provide some criteria for choosing the step size such that the numerical method is stable. Some examples of application and a numerical experiment, which further confirms the main results, are given. 相似文献
4.
广义时滞微分方程的渐近稳定性和数值分析 总被引:3,自引:0,他引:3
考虑了广义时滞微分方程的初值问题,分析了用线性多步法求解一类广义滞后型微分系统数值解的稳定性,在一定的Lagrange插值条件下,给出并证明了求解广义滞后型微分系统的线性多步法数值稳定的充分必要条件。 相似文献
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6.
求解延迟微分代数方程的多步Runge-Kutta方法的渐近稳定性 总被引:4,自引:0,他引:4
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. 相似文献
7.
The asymptotic stability of multistep multiderivative methods for systems of delay differential equations 总被引:1,自引:0,他引:1
Chengming HUANG Qianshun CHANG Institute of Applied Mathematics Chinese Academy of Sciences P. O. Box Beijing China 《Communications in Nonlinear Science & Numerical Simulation》2000,5(1)
IntroductionFor many years, many papers investigated the linear stabilit}' of delay differential equation(DDE) solvers and a significant number of important results have already been found for bothRunge-Kutta methods and linear multistep methods (see, for example, [l--8]). In this paper,we firstly consider stability of numerical methods with derivative for DDEs. It is shown thatA-stability of multistep multiderivative methods for ordinary differential equations (ODEs) isequit,alent to p-s… 相似文献
8.
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 相似文献
9.
This paper deals with the delay-dependent stability of numerical methods for delay differential equations. First, a stability criterion of Runge-Kutta methods is extended to the case of general linear methods. Then, linear multistep methods are considered and a class of r(0)-stable methods are found. Later, some examples of r(0)-stable multistep multistage methods are given. Finally, numerical experiments are presented to confirm the theoretical results. 相似文献
10.
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. 相似文献
11.
Summary.
We consider the application of linear multistep methods (LMMs)
for the numerical solution of initial value problem for stiff delay
differential equations (DDEs) with several constant delays, which are
used in mathematical modelling of immune response. For the approximation
of delayed variables the Nordsieck's interpolation technique, providing
an interpolation procedure consistent with the underlying linear
multistep formula, is used. An analysis of the convergence for a
variable-stepsize and structure of the asymptotic expansion of global
error for a fixed-stepsize is presented. Some absolute stability
characteristics of the method are examined. Implementation details of
the code DIFSUB-DDE, being a modification of the Gear's DIFSUB, are
given. Finally, an efficiency of the code developed for solution of
stiff DDEs over a wide range of tolerances is illustrated on biomedical
application model.
Received
March 23, 1994 / Revised version received March 13,
1995 相似文献
12.
Efficient computation of characteristic roots of delay differential equations using LMS methods 总被引:1,自引:0,他引:1
We aim at the efficient computation of the rightmost, stability-determining characteristic roots of a system of delay differential equations. The approach we use is based on the discretization of the time integration operator by a linear multistep (LMS) method. The size of the resulting algebraic eigenvalue problem is inversely proportional to the steplength. We summarize theoretical results on the location and numerical preservation of roots. Furthermore, we select nonstandard LMS methods, which are better suited for our purpose. We present a new procedure that aims at computing efficiently and accurately all roots in any right half-plane. The performance of the new procedure is demonstrated for small- and large-scale systems of delay differential equations. 相似文献
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14.
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. 相似文献
15.
Asymptotic behavior of multistep runge-kutta methods for systems of delay differential equations 总被引:2,自引:0,他引:2
1. IntroductionIn order to assess the asymptotic behavior of numerical methods for DDEs, much attention has been given in the literature to the scalar case (cL [1-6]). UP to now) only partialresults (of. [7-10]) have dealt with the delay systemswhere y(t) = (yi(t), so(t),' ) yp(t))" E Cd, which is unknown for t > 0, L and M areconstat complex p x Hmatrices, T > 0 is a constat delay and W(t) 6 CP is a specifiedinitial function.In [111, C.J. Zhang and S.Z. Zhou made an investigation on… 相似文献
16.
《Mathematical and Computer Modelling》2002,35(3-4):241-257
In this paper, variable stepsize multistep methods for delay differential equations of the type y(t) = f(t, y(t), y(t − τ)) are proposed. Error bounds for the global discretization error of variable stepsize multistep methods for delay differential equations are explicitly computed. It is proved that a variable multistep method which is a perturbation of strongly stable fixed step size method is convergent. 相似文献
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18.
Angelamaria Cardone Zdzislaw Jackiewicz Adrian Sandu Hong Zhang 《Numerical Algorithms》2014,65(3):377-399
For many systems of differential equations modeling problems in science and engineering, there are natural splittings of the right hand side into two parts, one non-stiff or mildly stiff, and the other one stiff. For such systems implicit-explicit (IMEX) integration combines an explicit scheme for the non-stiff part with an implicit scheme for the stiff part. In a recent series of papers two of the authors (Sandu and Zhang) have developed IMEX GLMs, a family of implicit-explicit schemes based on general linear methods. It has been shown that, due to their high stage order, IMEX GLMs require no additional coupling order conditions, and are not marred by order reduction. This work develops a new extrapolation-based approach to construct practical IMEX GLM pairs of high order. We look for methods with large absolute stability region, assuming that the implicit part of the method is A- or L-stable. We provide examples of IMEX GLMs with optimal stability properties. Their application to a two dimensional test problem confirms the theoretical findings. 相似文献
19.
Stability analysis of numerical methods for systems of neutral delay-differential equations 总被引:19,自引:0,他引:19
Stability analysis of some representative numerical methods for systems of neutral delay-differential equations (NDDEs) is considered. After the establishment of a sufficient condition of asymptotic stability for linear NDDEs, the stability regions of linear multistep, explicit Runge-Kutta and implicitA-stable Runge-Kutta methods are discussed when they are applied to asymptotically stable linear NDDEs. Some mentioning about the extension of the results for the multiple delay case is given. 相似文献
20.
数值求解延时微分方程的步长准则 总被引:2,自引:0,他引:2
1.引言 用一个数值方法求解下列延时微分方程:其中, f: R × Cd × Cd → Cd为给定函数, U(t)当上> 0时为未知函数,τ> 0为常数延时量,ф(t)∈Cd为已知向量值函数.为了检验一个数值方法的数值稳定性,常用如下试验方程:来观察方法的数值稳定性,这里a,b∈C(C为复数集)为已知常数,ф(t)为给定的连续函数(t≤0). 定义 1[2].延时微分方程(简记为DDES)(3)被称为是渐近稳定的,如果(3)的每一个解U(t)满足 方程(3)的特征方程为: 定义 2[2].一数值方法求解DDES称为… 相似文献