Stability of collocation methods for delay differential equations with vanishing delays

被引：21

作者：

Brunner, Hermann ^{[1
,3
]}

Liang, Hui ^{[2
]}

机构：

[1] Mem Univ Newfoundland, Dept Math & Stat, St John, NF A1C 5S7, Canada

[2] Heilongjiang Univ, Sch Math Sci, Harbin, Heilongjiang, Peoples R China

[3] Hong Kong Baptist Univ, Dept Math, Kowloon Tong, Hong Kong, Peoples R China

来源：

BIT NUMERICAL MATHEMATICS | 2010年 / 50卷 / 04期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Delay differential equations; Pantograph equation; Proportional vanishing delay; Collocation methods; Implicit Runge-Kutta methods; Asymptotic stability on uniform meshes; PANTOGRAPH EQUATION; ASYMPTOTIC STABILITY; THETA-METHODS;

D O I：

10.1007/s10543-010-0285-1

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

We analyze the asymptotic stability of collocation solutions in spaces of globally continuous piecewise polynomials on uniform meshes for linear delay differential equations with vanishing proportional delay qt (0 < q < 1) (pantograph DDEs). It is shown that if the collocation points are such that the analogous collocation solution for ODEs is A-stable, then this asymptotic behaviour is inherited by the collocation solution for the pantograph DDE.

引用

页码：693 / 711

页数：19

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