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自变量分段连续超前型延迟微分方程的θ-方法的数值振动性(英文) 被引量：4

Numerical oscillations of the θ-method for advanced delay differential equations with piecewise continuous arguments
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摘要 讨论θ-方法对自变量分段连续超前型延迟微分方程x′(t)=ax(t)+a1x([t+1])的数值振动性。把θ-方法应用到方程x′(t)=ax(t)+a1x([t+1]),得到了数值解的差分格式。证明了任意数值节点上数值解的振动性等价于整数节点上数值解的振动性。利用差分方程的所有解振动等价于其特征方程没有正根这一重要结论,得到了整数节点上数值解振动的充要条件,从而得到了任意节点上数值解振动的充要条件。 Numerical oscillations of the θ - method for advanced delay differential equation x1（t） = ax（t） ＋a1x（ It ＋ 1 ] ） with piecewise continuous arguments is investigated. Applying the θ- method to the equation, the formula of the numerical solution is obtained. It is proven that numerical oscillations on the integer nodes are equivalent to numerical oscillations on the any nodes. By the important conclusion that all solutions of the difference equation oscillate if and only if its corresponding characteristic equation has no positive roots, the sufficient and necessary condition of numerical oscillation on the integer nodes is given, and the sufficient and necessary condition of numerical oscillation on any nodes is also investigated.
作者 高建芳 刘明珠
机构地区 哈尔滨工业大学数学系
出处 《黑龙江大学自然科学学报》 CAS 北大核心 2008年第2期196-198,203,共4页 Journal of Natural Science of Heilongjiang University
基金 Supported by the Natural Science Foundation of China (10671047)
关键词 振动性 数值解 延迟微分方程 oscillation numerical solution delay differential equations
分类号 O189.1 [理学—基础数学]
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参考文献10

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同被引文献21

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引证文献4

二级引证文献4

黑龙江大学自然科学学报
2008年 第2期

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