变系数线性多延迟微分方程θ-方法的稳定性分析  

Stability analysis of θ-methods for linear differential equations with many delay and variable coefficients

作　　者：赵景军[1] 徐阳[1] 

机构地区：[1]哈尔滨工业大学数学系,黑龙江哈尔滨150001

出　　处：《哈尔滨工业大学学报》2000年第3期98-101,共4页Journal of Harbin Institute of Technology

基　　金：国家自然科学基金资助项目!( 198710 19)

摘　　要：考虑变系数线性双延迟微分方程y′(t) =a(t)y(t) +b1(t)y(t -τ1) +b2 (t)y(t -τ2 ) ,t≥ 0 ,y(t) =Φ(t) . ( )其中y(t) :R→C ;a(t) ,b1(t) ,b2 (t) :[0 ,+∞ ]→C ;τ1>0 ,τ2 >0 ,R为实数集 ,C是复数集 .分析了方程 ( )的有界稳定性和渐近稳定性 .证明当且仅当θ =1时 ,线性θ 方法和单腿θ 法是GPN-稳定且NGP-稳定的 .最后将结论推广到变系数线性多延迟微分方程上 .Studies linear two delay differential equations with variable coefficients:y′(t)=a(t) y(t)+b 1(t)y(t-τ 1)+b 2(t) y(t-τ 2), t≥0, y(t)=Φ(t).(*)where y(t): R→C; a(t), b 1(t), b 2(t): [0,+∞]→C; τ 1>0, τ 2>0. Bounded stability and asymptotical stability of the equation (*) are both analysed. Linear θ-methods and one leg θ-methods are proved to be GPN-stable and NGP-stable if and only if θ=1. The conclusions are further generalized for linear differential equations with many delay and variable coefficients.

关 键 词：延迟微分方程 渐近稳定 有界稳定 

分 类 号：O241.8[理学—计算数学]