分段连续微分方程θ-方法的稳定性(英文)  

The differential equation with piecewise continuous arguments

作　　者：张如[1] 徐阳[2] 

机构地区：[1]西北工业大学计算机信息技术系,西安710124 [2]哈尔滨工业大学数学系,哈尔滨150001

出　　处：《黑龙江大学自然科学学报》2010年第5期639-644,共6页Journal of Natural Science of Heilongjiang University

基　　金：Supported by Natural Science Foundation of Heilongjiang Province(A200602);the Science Research Foundation(HITC200710);the Natural Scientific Research Innovation Foundation(HIT.NSRIF.2009053)

摘　　要：讨论分段连续型微分方程x′(t)=ax(t)+a1x([t+3])的解析解的稳定性,得出其渐进稳定的一个充分必要条件。应用θ-方法求解此分段连续型微分方程,得到相应的数值稳定区域,给出数值解的稳定区域包含解析解的稳定区域的一个充分必要条件。应用线性θ-方法求解了微分方程x′(t)=ax(t)+a1x([t+p]),给出此类数值方法渐进稳定的一个充分条件,得出数值解的稳定区域包含解析解的稳定区域的充分条件。The stability of the analytic solution of the differential equation x′（t）=ax（t）＋a1x（） with piecewise continuous arguments is considered.The conditions of asymptotic stability for the equation are obtained.Moreover,θ-methods are applied to this kind of equations,and the stability region of θ-method is obtained.A necessary and sufficient condition under which the analytic stability region is contained in the numerical stability region is also obtained.Then,apply the linear θ-method to the equation x′（t）=ax（t）＋a1x（）,a sufficient condition of the asymptotic stability is investigated,and a sufficient condition is obtained under which the analytic stability region is contained in the numerical stability region.

关 键 词：分段连续微分方程 Θ-方法 稳定性 

分 类 号：O189.1[理学—数学]