摘要
运用线性θ-方法和单腿θ-方法处理了带有一个延迟项(t)的分段连续型延迟微分方程数值解的渐近稳定性问题.应用线性θ-方法和单腿θ-方法解方程时,由于这个方程是定义在[n,n+1)上,即不包含区间的右端点,结果两种θ-方法得到了相同的差分方程.运用θ-方法给出了在单位时段[n,n+1)任意分划情况下的解析解的稳定区域包含在数值解的稳定区域的充分必要条件,最后相应地给出了几个数值算例.
The linear θ- method and one - leg θ- method are applied to the delay differential equation with piece-wise continuous arguments with one delay[t]. The asymptotic stability of numerical solutions is studied. Since the equation is defined in [ n, n + 1 ) , i.e. , don' t include the right - hand side end - point of the subinterval, the result of applying linear θ- method and one - leg θ- method to the equation is that the same difference equations are derived. Using the θ-method, the necessary and sufficient conditions under which the analytic stability region is contained in the numerical stability region are obtained in the condition of any partition of [ n, n + 1). Eventually, some numerical experiments are given.
出处
《黑龙江大学自然科学学报》
CAS
北大核心
2005年第2期158-162,共5页
Journal of Natural Science of Heilongjiang University
基金
国家自然科学基金资助项目(10271036)
关键词
Θ-方法
渐近稳定
分段连续型延迟微分方程
θ- method
asymptotic stability
delay differential equations with piecewise continuous arguments
