Abstract
This paper is an extension of parts of two earlier papers [3, 4] which dealt with the problems of maintaining invariants in the numerical solution of ODEs and the index reduction of differential-algebraic equations (DAEs). DAEs with their constraints ignored can be viewed as undeterminated ODEs, while ODEs with their invariants appended can be viewed as overdetermined DAEs. Index reduction applied to DAEs appends additional equations derived by differentiating some of the equations to get an overdetermined system. Methods for maintaining invariants in the solution of ODEs are extended to DAEs to handle this case.
Work supported in part by the US Department of Energy under grant DOE DEFG02-87ER25026.
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© 1989 Springer-Verlag
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Gear, C.W. (1989). DAEs: ODEs with constraints and invariants. In: Bellen, A., Gear, C.W., Russo, E. (eds) Numerical Methods for Ordinary Differential Equations. Lecture Notes in Mathematics, vol 1386. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0089231
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DOI: https://doi.org/10.1007/BFb0089231
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