双比例延迟微分方程改进的单支θ-方法的H_α-稳定性  

H_α-STABILITY OF THE MODIFIED ONE-LEGθ-METHOD FOR SYSTEM OF PANTOGRAPH EQUATION WITH TWO DELAYS

作　　者：马淑芳[1] 巩云野 刘明珠[2] 

机构地区：[1]东北林业大学理学院数学系,哈尔滨150040 [2]哈尔滨工业大学理学院数学系,哈尔滨150010

出　　处：《高等学校计算数学学报》2014年第3期193-206,共14页Numerical Mathematics A Journal of Chinese Universities

基　　金：黑龙江省自然科学基金(A201113);中央高校基本科研业务费专项资金资助(DL11BB09)

摘　　要：In[13],the author constructes the modified Runge-Kutta method and proves that the modified Runge-Kutta method preserves the order of accuracy of the original one.As a result,it is obtained that theθ-method with 1/2<θ<1is asymptotically stable.The modified one-legθ-method is a specific form of the modified Runge-Kutta method.This paper deals with H_α-stability for the modified one-legθ-method for system of pantograph equation with two delays.It is proved that the modified one-legθ-method with 0<θ≤1 is H_α-stable.Some experiments are given.In [13], the author constructes the modified Runge-Kutta method and proves that the modified Runge-Kutta method preserves the order of accuracy of 1 the original one. As a result, it is obtained that the θ- method with 1/2 〈 θ 〈 1 is asymptotically stable. The modified one-leg P-method is a specific form of the modified Runge-Kutta method. This paper deals with Hα--stability for the modified one-leg P-method for system of pantograph equation with two delays. It is proved that the modified one-leg P-method with 0 〈 θ≤1 is Ha-stable. Some experiments are given.

关 键 词：比例延迟微分方程 单支Θ-方法 α-稳定性 一般形式 生物学 经济学 

分 类 号：O241.8[理学—计算数学]