Differential-algebraic equation index transformations

Journal Article · Fri Jan 01 04:00:00 EST 1988 · SIAM J. Sci. Stat. Comput.; (United States)

DOI:https://doi.org/10.1137/0909004· OSTI ID:5398249

Gear, C W

In this paper the authors show an equivalence between semi-explicit and implicit differential-algebraic equations so that the theory for the former applies to the latter of one low index. They also discuss techniques for the reduction by differentiation of higher index problems to lower index ones that can be solved numerically without introducing additional constants of integration. Furthermore, they give transformations between general DAEs and ones in semi-explicit form, and, by these techniques, show how a problem can be reduced to an index 1, semi-explicit form that can be reduced to an implicit differential equation from whose solution to the original problem can be retrieved by at most a differentiation and a linear transformation.

• Research Organization: Dept. of Computer Science, Univ. of Illinois at Urbana-Champaign, Urbana, IL 61801
• OSTI ID: 5398249
• Journal Information: SIAM J. Sci. Stat. Comput.; (United States), Journal Name: SIAM J. Sci. Stat. Comput.; (United States) Vol. 9:1; ISSN SIJCD
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
990220* -- Computers
Computerized Models
& Computer Programs-- (1987-1989)
ALGORITHMS
DIFFERENTIAL EQUATIONS
EQUATIONS
MATHEMATICAL LOGIC
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS