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.
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；
