θ方法解滞时微分方程的动力学性质  

Dynamics of 0 Methods for Delay Differential Equations

作　　者：郭谦[1] 杨忠华[2] 

机构地区：[1]上海大学数学系,上海200436 [2]上海师范大学数理信息学院,上海200234

出　　处：《应用数学与计算数学学报》2002年第2期7-14,共8页Communication on Applied Mathematics and Computation

基　　金：国家自然科学基金(19971057);上海市教委科技发展基金;上海市高校科技发展基金资助

摘　　要：本文研究求解滞时微分方程的θ-方法数值解的渐近性质和方程真实解的关系。首先,我们把数值方法看成以步长为参数的动力系统,考察非线性滞时微分方程θ-方法的数值稳定性,并且证明了A-稳定的θ-方法是NP-稳定的。其次我们证明θ-方法没有伪不动点,还研究了伪周期2解的存在性。最后我们给出一个例子说明了滞时微分方程θ-方法产生的伪周期2解是不稳定的。In this paper we study the relationship between the asymptotic behavior of a numerical simulation by 6 method for delay differential equation and that of the true solution itself for fixed step sizes. The numerical method is viewed as a dynamical system in which the step size acts as a parameter. Numerical stability of 0 method for nonlinear delay differential equation is investigated and we prove that A-stable 9 methods are NP-stable. It is shown that a consistent 0 method does not admit spurious fixed points. The existence of spurious period 2 solution in the time-step is also studied. Finally we give a simple example to illustrate instability of the spurious period two solutions.

关 键 词：θ方法 滞时微分方程 动力学 数值动力系统 不动点 伪解 周期2解 稳定性 

分 类 号：O241.8[理学—计算数学]