Analysis and numerical solution of linear delay differential-algebraic equations

被引：13

作者：

Ha, Phi ^{[2
]}

Mehrmann, Volker ^{[1
]}

机构：

[1] Tech Univ Berlin, Inst Math, MA 4-5,Str 17 Juni 136, D-10623 Berlin, Germany

[2] Humboldt Univ, Dept Math, D-10099 Berlin, Germany

来源：

BIT NUMERICAL MATHEMATICS | 2016年 / 56卷 / 02期

关键词：

Delay differential-algebraic equation; Differential-algebraic equation; Delay differential equations; Method of steps; Derivative array; Classification of DDAEs; ASYMPTOTIC STABILITY; VARIABLE-COEFFICIENTS; COLLOCATION METHODS; DESCRIPTOR SYSTEMS; NEUTRAL TYPE; DAES;

D O I：

10.1007/s10543-015-0577-6

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

The analysis and numerical solution of initial value problems for linear delay differential-algebraic equations (DDAEs) is discussed. Characteristic properties of DDAEs are analyzed and the differences between causal and noncausal DDAEs are studied. The method of steps is analyzed and it is shown that it has to be modified for general DDAEs. The classification of ordinary delay differential equations is generalized to DDAEs, and a numerical solution procedure for general retarded and neutral DDAEs is constructed. The properties of the algorithm are studied and the theoretical results are illustrated with a numerical example.

引用

页码：633 / 657

页数：25

共 43 条

[1]

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

[2]

[Anonymous], 2014, MATLAB VERS 8 3 0 53

[3]

[Anonymous], MATH SCI ENG

[4]

Antognetti P., 1997, SEMICONDUCTOR DEVICE

[5] IMPROVING THE ACCURACY OF BDF METHODS FOR INDEX 3 DIFFERENTIAL-ALGEBRAIC EQUATIONS [J].

AREVALO, C ;

LOTSTEDT, P .

BIT, 1995, 35 (03) :297-308

[6] THE NUMERICAL-SOLUTION OF DELAY-DIFFERENTIAL-ALGEBRAIC EQUATIONS OF RETARDED AND NEUTRAL TYPE [J].

ASCHER, UM ;

PETZOLD, LR .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1995, 32 (05) :1635-1657

[7] Differential algebraic equations with after-effect [J].

Baker, CTH ;

Paul, CAH ;

Tian, H .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2002, 140 (1-2) :63-80

[8]

Betts J.T., 2013, P 14 TH IASTED INT S, P166, DOI 10.2316/p.2013.807-003

[9] Lobatto IIIA methods, direct transcription, and DAEs with delays [J].

Betts, John T. ;

Campbell, Stephen L. ;

Thompson, Karmethia .

NUMERICAL ALGORITHMS, 2015, 69 (02) :291-300

[10]

Brenan K.E., 1996, Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations

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