Solving high-index DAEs by Taylor series

被引：41

作者：

Pryce, JD ^{[1
]}

机构：

[1] Cranfield Univ, Royal Mil Coll Sci, Swindon SN6 8LA, Wilts, England

来源：

NUMERICAL ALGORITHMS | 1998年 / 19卷 / 1-4期

关键词：

algorithms; combinatorics; linear programming; Taylor series; index; assignment problem;

D O I：

10.1023/A:1019150322187

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present a general method of solving differential-algebraic equations by expanding the solution as a Taylor series. It seems especially suitable for (piecewise) smooth problems of high index. We describe the method in general, discuss steps to be taken if the method, as initially applied, fails because it leads to a system of equations with identically singular Jacobian, and illustrate by solving two problems of index 5.

引用

页码：195 / 211

页数：17

共 12 条

[1]

Bertsekas DP., 1991, Linear network optimization: algorithms and codes

[2]

Brenan K. E., 1989, NUMERICAL SOLUTION I

[3] THE INDEX OF GENERAL NONLINEAR DAES [J].

CAMPBELL, SL ;

GEAR, CW .

NUMERISCHE MATHEMATIK, 1995, 72 (02) :173-196

[4]

CAMPBELL SL, 1997, IN PRESS SIAM J SCI

[5] SOLVING ORDINARY DIFFERENTIAL-EQUATIONS USING TAYLOR-SERIES [J].

CORLISS, G ;

CHANG, YF .

ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE, 1982, 8 (02) :114-144

[6]

CORLISS GF, 1996, ROLE CONSTRAINTS VAL

[7]

FLANDERS H, 1991, SIAM PROC S, P95

[8]

LOHNER R. J., 1987, WILEY TEUBNER SERIES, P255

[9] INDEX REDUCTION IN DIFFERENTIAL-ALGEBRAIC EQUATIONS USING DUMMY DERIVATIVES [J].

MATTSSON, SE ;

SODERLIND, G .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 1993, 14 (03) :677-692

[10] THE CONSISTENT INITIALIZATION OF DIFFERENTIAL-ALGEBRAIC SYSTEMS [J].

PANTELIDES, CC .

SIAM JOURNAL ON SCIENTIFIC AND STATISTICAL COMPUTING, 1988, 9 (02) :213-231

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