共查询到20条相似文献,搜索用时 140 毫秒
1.
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
2.
A series of contractivity and exponential stability results for the solutions to nonlinear neutral functional differential equations (NFDEs) in Banach spaces are obtained,which provide unified theoretical foundation for the contractivity analysis of solutions to nonlinear problems in functional differential equations (FDEs),neutral delay differential equations (NDDEs) and NFDEs of other types which appear in practice. 相似文献
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This paper deals with the numerical solution of initial value problems for systems of differential equations with a delay argument. The numerical stability of a linear multistep method is investigated by analysing the solution of the lest equation y'(t)=Ay(t) + By(1-t),where A,B denote constant complex N×N-matrices,and t>0.We investigate carefully the characterization of the stability region. 相似文献
4.
陈永劭 《应用数学学报(英文版)》1989,5(3):234-241
In this paper, we consider the oscillation of the second order neutral delay differential equations[x(t) cx(t-τ)]" p(t)x(t-σ)=0 (1)and obtain some sufficient conditions of the oscillation of (1) for the case c≥0, -1≤c<0 and c<-1. 相似文献
5.
The authors establish sufficient conditions for the oscillation of all solution of neutral deiay differential equations of even and odd order of the formd~n/dt~n[y(t)+p(t)y(t-τ)]+Q(t)y(t-C)=0, t≥t_n,where P, Q ∈ C[[t_0, ∞), R], τ, σ∈ R~+ and n≥1. 相似文献
6.
Oscillation for systems of nonlinear neutral type parabolic partial functional differential equations 总被引:14,自引:0,他引:14
YANGJUN GUANXINPING 《高校应用数学学报(英文版)》1997,12(2):165-178
This paper discusses the oscillation of solutions for systems of nonlinear neutral type parabolic partial fuctional differential equations of the form 相似文献
7.
Stability analysis of Runge-Kutta methods for nonlinear neutral delay integro-differential equations 总被引:1,自引:0,他引:1
Yue-xin YU & Shou-fu LI Department of Mathematics Xiangtan University Xiangtan China 《中国科学A辑(英文版)》2007,50(4):464-474
The sufficient conditions for the stability and asymptotic stability of Runge-Kutta methods for nonlinear neutral delay integro-differential equations are derived. A numerical test that confirms the theoretical results is given in the end. 相似文献
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In this paper we consider nonlinear delay diffusion-reaction equations with initial and Dirichlet boundary conditions. The behaviour and the stability of the solution of such initial boundary value problems (IBVPs) are studied using the energy method. Simple numerical methods are considered for the computation of numerical approximations to the solution of the nonlinear IBVPs. Using the discrete energy method we study the stability and convergence of the numerical approximations. Numerical experiments are carried out to illustrate our theoretical results. 相似文献
9.
On the Existence of Oscillating Periodic Solutions of Differential Difference Equation With N Time Lags 总被引:2,自引:0,他引:2
In this paper,the existence of nonconstant oscillating periodic solution of differential difference e-quation with n time lags is stutied:x′(t)=-g(x(t))[f(x(t-τ1)) f(x(t-τ2)) … f(x(t-τn))] the results of Paper[1-6] are extended and improved. 相似文献
10.
Li-ping Wen Shou-fu Li 《计算数学(英文版)》2005,23(4):393-400
This paper is concerned with the stability of theoretical solution and numerical solutionof a class of nonlinear differential equations with piecewise delays.At first,a sufficientcondition for the stability of theoretical solution of these problems is given,then numericalstability and asymptotical stability are discussed for a class of multistep methods whenapplied to these problems. 相似文献
11.
George Karakostas 《Applicable analysis》2013,92(4):225-231
By using some facts from limiting equations theory we prove that the solution x(.;?), with continuous initial condition ?, of the neutral functional differential equation [x(t)-cx(t-r)]' =-F(x(t))+F(x(t-r)), t>0, where c ε [0,1), r≧0 and F is (not necessarily strictly) increasing. satisfies lim x(t;?) = &;, where &; is the unique root of the algebraic equation [math001] 相似文献
12.
11尬roductlonIn recent ye肘s,there has been extensive literatures(see for lustmce 11-7I)about the oscillations ofneutral dl地rentlal dl征rence equations such asMt)一c川叫一r)]’+>Pi川x(t—a;)=0,(川江1and卜(t)一 ex(t一 r刀’+ f(t;x(t);x(t一 o-》二 0.(B)But there are few papers about the exponentlal stability for neutral dl洗rentialdl地rence euuatlons because of its difficulty (sc [8-9]).In [9],Li made asurvey on the asymptotlc stability and exponentlally asymptotlc stability inC(‘)I… 相似文献
13.
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
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15.
正负系数的扰动的中立型微分方程的稳定性 总被引:1,自引:0,他引:1
In this paper the perturbed neutral differential equation with positive and negative coefficients d/dt[x(t)-C(t)x(t-r)] p(t)x(t-x)-Q(t)x(t-δ)=f(t,x(t)),t≥t0is considered. Sufficient conditions for the zero solution of this equation to be uniformly stable as well as asymptotically stable are obtained. 相似文献
16.
Liping Wen Wansheng Wang Yuexin Yu 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(3-4):1746-1754
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. 相似文献
17.
1DefinitionandPropertyInthematrixdifferentialequation,weconsider(p(t)y,(t)), Q(t)y(t) F(t,y(t),y'(t))=0(1)P,Q,y,Farearealcontinuousnxn-th--ordermatrixintheinterval[a, co),andP,Q,Fareasymmetricmatrix,andPisapositivedefinitematrix.F(t,:!/(t),y'(t))gfij(t,yl… 相似文献
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中立型时滞模型的周期正解 总被引:18,自引:0,他引:18
本文通过使用某些新技巧,研究了中立型时滞模型N'(t)=N(t)[a(t)--β(t)-b(t)N(t-T(t))-C(t)N'(t-T(t))]周期正解的存在性,解决了文[1]中的一个公开问题,并改正了文[2]中的错误。 相似文献