上海师范大学学报（自然科学版）
上海師範大學學報（自然科學版）
상해사범대학학보（자연과학판）
JOURNAL OF SHANGHAI TEACHERS UNIVERSITY(NATURAL SCIENCES)
2007年
3期
6-11
,共6页
谭秀丽%李顺道%项家祥%丛玉豪
譚秀麗%李順道%項傢祥%叢玉豪
담수려%리순도%항가상%총옥호
延迟微分方程%块θ-方法%数值稳定性
延遲微分方程%塊θ-方法%數值穩定性
연지미분방정%괴θ-방법%수치은정성
delay differential equation%block θ- method%numerical stability
讨论了带有多个滞时量的延时微分方程的数值稳定性,分析了块θ-方法求解多延迟微分方程的Pm-稳定性和PLm-稳定性的条件,证明了块θ-方法Pm-稳定的充要条件是1/2≤θ≤1,块θ-方法PLm-稳定的充要条件是θ=1.
討論瞭帶有多箇滯時量的延時微分方程的數值穩定性,分析瞭塊θ-方法求解多延遲微分方程的Pm-穩定性和PLm-穩定性的條件,證明瞭塊θ-方法Pm-穩定的充要條件是1/2≤θ≤1,塊θ-方法PLm-穩定的充要條件是θ=1.
토론료대유다개체시량적연시미분방정적수치은정성,분석료괴θ-방법구해다연지미분방정적Pm-은정성화PLm-은정성적조건,증명료괴θ-방법Pm-은정적충요조건시1/2≤θ≤1,괴θ-방법PLm-은정적충요조건시θ=1.
The stability behavior of the numerical solution of delay differential equations with many delays is studied. The conditions of the Pm -stability and the PLm -stability of the block θ- method for delay differential equations with many delays are discussed. It is shown that the block θ- method is Pm -stable if and only if 1/2≤θ≤1, the block θ- method is PLm- stable if and only if θ = 1.
