共查询到17条相似文献,搜索用时 156 毫秒
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建立了广义中立型延迟系统理论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的A-稳定的。 相似文献
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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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本文讨论Milstein方法用于求解线性中立型随机延迟微分方程初值问题时数值解的稳定性,给出了Milstein方法均方稳定的一个充分条件.文末的数值试验证实了本文所获理论结果的正确性. 相似文献
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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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讨论了广义中立型延迟系统理论的渐近稳定性,给出了广义中立型系统渐近稳定的一些充分条件。 相似文献
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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的一般线性方法的数值稳定性,获得了代数稳定的一般线性方法稳定及渐近稳定的条件,最后的数值试验验证了所获理论的正确性.
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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
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Cheng-jianZhang GengSun 《计算数学(英文版)》2004,22(3):447-456
In this paper, we deal with the boundedness and the asymptotic stability of linear and one-leg multistep methods for generalized pantograph equations of neutral type, which arise from some fields of engineering. Some criteria of the boundedness and the asymptotic stability for the methods are obtained. 相似文献
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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
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The asymptotic stability of theoretical and numerical solutions for systems of neutral multidelay-differential equations 总被引:2,自引:0,他引:2
The asymptotic stability of theoretical and numerical solutions for neutral multidelay-differential equations (NMDEs) is dealt
with. A sufficient condition on the asymptotic stability of theoretical solutions for NMDEs is obtained. On the basis of this
condition, it is proved that A-stability of the multistep Runge-Kutta methods for ODEs is equivalent to NGPk-stability of the induced methods for NMDEs.
Project supported by the National Natural Science Foundation of China (Grant No. 19771034). 相似文献
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This paper deals with the asymptotic stability of exact and discrete solutions of neutral multidelay-integro-differential
equations. Sufficient conditions are derived that guarantee the asymptotic stability of the exact solutions. Adaptations of
classical Runge–Kutta and linear multistep methods are suggested for solving such systems with commensurate delays. Stability
criteria are constructed for the asymptotic stability of these numerical methods and compared to the stability criteria derived
for the continuous problem. It is found that, under suitable conditions, these two classes of numerical methods retain the
stability of the continuous systems. Some numerical examples are given that illustrate the theoretical results.
This research is supported by Fellowship F/02/019 of the Research Council of the K.U.Leuven, NSFC (No.10571066) and SRF for
ROCS, SEM. 相似文献
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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