向前型分段连续微分方程θ-方法的振动性(英文)  

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

作　　者：王琦[1] 温洁嫦[1] 

机构地区：[1]广东工业大学应用数学学院,广东广州510006

出　　处：《安徽大学学报（自然科学版）》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)

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.

关 键 词：振动性 稳定性 Θ-方法 向前型 分段连续项 

分 类 号：O241.81[理学—计算数学]