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
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
收藏
页码:693 / 711
页数:19
相关论文
共 32 条
[1]  
[Anonymous], 2003, Numerical Methods for Delay Differential Equations
[2]   Asymptotic stability properties of Theta-methods for the pantograph equation [J].
Bellen, A ;
Guglielmi, N ;
Torelli, L .
APPLIED NUMERICAL MATHEMATICS, 1997, 24 (2-3) :279-293
[3]  
Bellen A, 2009, ACTA NUMER, V18, P1, DOI 10.1017/S0962492906390010
[4]  
Brunner H., 2004, Cambridge Monographs on Applied and Computational Mathematics, V15
[5]   Current work and open problems in the numerical analysis of Volterra functional equations with vanishing delays [J].
Brunner, Hermann .
FRONTIERS OF MATHEMATICS IN CHINA, 2009, 4 (01) :3-22
[6]  
BUHMANN M, 1993, MATH COMPUT, V60, P575, DOI 10.1090/S0025-5718-1993-1176707-2
[7]  
BUHMANN M, 1992, PITMAN RES, V260, P17
[8]  
BUHMANN MD, 1993, CONTRIBUTIONS NUMERI, P85
[9]  
Cermák J, 2009, MATH COMPUT, V78, P2107, DOI 10.1090/S0025-5718-09-02245-5
[10]  
Fox L., 1971, Journal of the Institute of Mathematics and Its Applications, V8, P271