非线性中立型延迟微分方程稳定性分析
STABILITY ANALYSIS OF NONLINEAR DELAY DIFFERENTIAL EQUATIONS OF NEUTRAL TYPE
查看参考文献16篇
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文摘
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1.引言
延迟微分方程广泛出现于物理,生物,工程,经济学,环境论,控制理论等领域.其算法的理论研究具有十分重要的意义,对滞后型非线性延迟微分方程研究已日趋成熟.但对中立型延迟微分方程(NDDEs)特别是其非线性数值稳定性的研究则进展缓慢.对于线性NDDEs,几位作者已研究了其真解以及数值解的渐近稳定性(见[1,2,3,4]).…… |
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其他语种文摘
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This paper is devoted to the stability analysis of both the true solution and the numerical approximations for nonlinear systems of neutral delay differential equa-tions(NDDEs) of the general form y'(t) = F(t,y(t),y(t-τ(t)),y'(t-τ(t))). We first present a sufficient condition on the stability and asymptotic stability of theoretical solution for the nonlinear systems. This work extends the results recently obtained by A.Bellen et al. for the form y'(t) = F(t,y(t), G(t,y(t-τ(t)),y'(t-τ(t)))). Then numerical stability of Runge-Kutta methods for the systems of neutral delay dif-ferential equations is also investigated. Several numerical tests listed at the end of this paper to confirm the above theoretical results.
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来源
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计算数学
,2004,26(3):303-314 【核心库】
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关键词
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中立型延迟微分方程
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Runge-Kutta法
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稳定性
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地址
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湘潭大学数学系, 湖南, 湘潭, 411105
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语种
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中文 |
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文献类型
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研究性论文 |
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ISSN
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0254-7791 |
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学科
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数学 |
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文献收藏号
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CSCD:1598545
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参考文献 共
16
共1页
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