向前型分段连续微分方程θ-方法的振动性(英文) 被引量：2

Oscillation of θ-methods for differential equations with piecewise constant arguments of advanced type

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摘要将两种θ-方法:线性θ-方法和单腿θ-方法用于求解一类自变量分段连续向前型微分方程,通过对差分格式进行分析,得到了一般节点与整数节点处非振动的等价性,进而获得了θ-方法振动的条件.证明了θ-方法能够保持解析解的振动性,进一步分析了稳定性与振动性的关系,最后给出几个数值例子. Applying two θ-methods,namely the linear θ-method and one-leg θ-method to the differential equations with piecewise constant arguments of advanced type.The equivalence of the non-oscillation between the integer nodes and the any nodes were obtained by analyzing the difference form.Moreover,the conditions of oscillation for the θ-methods were given.It was proved that the θ-methods preserved the oscillation of analytic solution.In addition,the relationship between stability and oscillation were investigated.Finally,several numerical examples were given.

作者王琦温洁嫦

机构地区广东工业大学应用数学学院

出处《安徽大学学报（自然科学版）》 CAS 北大核心 2011年第1期15-20,共6页 Journal of Anhui University(Natural Science Edition)

基金 Supported by the Natural Science Foundation of China(51008084) the Natural Science Foundation of Guangdong Province(9451009001002753)

关键词振动性稳定性 Θ-方法向前型分段连续项 oscillation； stability； θ-methods； advanced type； piecewise constant arguments；

分类号 O241.81 [理学—计算数学]

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参考文献1

1高建芳,刘明珠.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)[J].黑龙江大学自然科学学报,2008,25(2):196-198. 被引量：4

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