The index of general nonlinear DAEs |
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Authors: | Stephen L Campbell C William Gear |
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Institution: | (1) Department of Mathematics, North Carolina State University, Raleigh, NC 27695-8205 USA phone: 1-919-515-3300; email: slc@math.ncsu.edu; fax: 1-919-515-3798 , US;(2) NEC Research Institute, 4 Independence Way, Princeton, NJ 08540, USA , US |
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Abstract: | Summary.
In the
last few years there has been considerable research
on differential algebraic equations (DAEs)
where is identically singular. Much of the
mathematical effort has focused on computing a solution
that is assumed to exist. More recently there has been
some discussion of solvability of DAEs. There has
historically been some imprecision in the use of the two
key concepts of solvability and index for DAEs. The
index is also important in control and systems theory
but with different terminology. The consideration of
increasingly complex nonlinear DAEs makes a
clear and correct development necessary. This paper will
try to clarify several points concerning the index. After
establishing some new and more precise terminology that
we need, some inaccuracies in the literature will be
corrected. The two types of indices most frequently used,
the differentiation index and the perturbation index, are
defined with respect to solutions of unperturbed
problems. Examples are given to show that these indices
can be very different for the same problem. We define
new "maximum indices," which are the maxima of earlier
indices in a neighborhood of the solution over a set of
perturbations and show that these indices are simply
related to each other. These indices are also related to an
index defined in terms of Jacobians.
Received November 15, 1993 /
Revised version received December 23, 1994 |
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Keywords: | Mathematics Subject Classification (1991):65L20 |
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