Block boundary value methods for delay differential equations

被引：37

作者：

Zhang, Chengjian ^{[1
]}

Chen, Hao ^{[1
]}

机构：

[1] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Peoples R China

来源：

APPLIED NUMERICAL MATHEMATICS | 2010年 / 60卷 / 09期

关键词：

Block boundary value methods; Delay differential equations; Initial value problems; Linear stability; RUNGE-KUTTA METHODS; D-CONVERGENCE; LINEAR MULTISTEP; STABILITY; COLLOCATION;

D O I：

10.1016/j.apnum.2010.05.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, a class of block boundary value methods (BBVMs) for the initial value problems of delay differential equations are suggested. It is proven under the classical Lipschitz condition that a BBVM is convergent of order p if it is consistent of order p. Several linear stability criteria for the BBVMs are derived. Numerical experiments further confirm the convergence and the effectiveness of the methods. (C) 2010 IMACS. Published by Elsevier B.V. All rights reserved.

引用

页码：915 / 923

页数：9

共 22 条

[1] On the relations between B2VMs and Runge-Kutta collocation methods [J].

Aceto, L. ;

Magherini, C. .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2009, 231 (01) :11-23

[2] BOUNDARY-VALUE METHODS BASED ON ADAMS-TYPE METHODS [J].

AMODIO, P ;

MAZZIA, F .

APPLIED NUMERICAL MATHEMATICS, 1995, 18 (1-3) :23-35

[3]

[Anonymous], 2003, Numerical Methods for Delay Differential Equations

[4]

AXELSSON AOH, 1985, MATH COMPUT, V45, P153, DOI 10.1090/S0025-5718-1985-0790649-9

[5] A global convergence theorem for a class of parallel continuous explicit Runge-Kutta methods and vanishing lag delay differential equations [J].

Baker, CTH ;

Paul, CAH .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1996, 33 (04) :1559-1576

[6]

Barwell V. K., 1975, BIT (Nordisk Tidskrift for Informationsbehandling), V15, P130, DOI 10.1007/BF01932685

[7] ONE-STEP COLLOCATION FOR DELAY DIFFERENTIAL-EQUATIONS [J].

BELLEN, A .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1984, 10 (03) :275-283

[8] Boundary value methods: The third way between linear multistep and Runge-Kutta methods [J].

Brugnano, L ;

Trigiante, D .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 1998, 36 (10-12) :269-284

[9] Convergence and stability of boundary value methods for ordinary differential equations [J].

Brugnano, L ;

Trigiante, D .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1996, 66 (1-2) :97-109

[10]

Brugnano L., 1998, Solving Differential Problems by Multistep Initial and Boundary Value Methods

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