On obtaining a consistent set of initial values for a system of differential-algebraic equations

Technical Report · Fri May 01 04:00:00 EDT 1987

OSTI ID:6485994

Leimkuhler, B J; Petzold, L R; Gear, C W

Discussed are some of the difficulties in designing a general algorithm for determining a consistent initial vector for a DAE when only part of the vector is known. A set of relations (the consistency equations) are derived which an initial vector should satisfy in order for there to be a smooth solution through the point which is also consistent with known initial data. An approximation to one of the individual derivative equations was constructed, and the solution of the resulting system of approximated consistency equations was considered. In particular, it was noted that the system does not admit an exact solution so that some sort of least-squares approximation is called for. Finally, some preliminary numerical experiments were described. These experiments tend to validate some of the concepts discussed in this report, although they are too limited in scope to suggest anything meaningful about the applicability of this work. Two critical obstacles prevent the implementation of these ideas: a method must be found to efficiently solve (in the least-squares sense) a large system of overdetermined nonlinear equations with a sparse, rank-deficient Jacobian, and there is the need for an error estimation and control mechanism which can adjust various parameters to meet a required accuracy.

• Research Organization: Illinois Univ., Urbana (USA). Dept. of Computer Science
• DOE Contract Number: FG02-87ER25026
• OSTI ID: 6485994
• Report Number(s): DOE/ER/25026-5; UILU-ENG-87-1732; UIUCDCS-R-87-1344; ON: DE87010572
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
990230* -- Mathematics & Mathematical Models-- (1987-1989)
ALGORITHMS
EQUATIONS
MATHEMATICAL LOGIC
NUMERICAL SOLUTION