differentialalgebraic equations
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Linear differentialalgebraic equations with properly stated leading term: Bcritical points
Roswitha März
März
Roswitha
Ricardo Riaza
Riaza
Ricardo
Institut für Mathematik, HumboldtUniversität zu Berlin (ISSN 08630976), 0709, 15 pages
Linear differentialalgebraic equations with properly stated leading term: Bcritical points
Roswitha März
,
Ricardo Riaza
Preprint series:
Institut für Mathematik, HumboldtUniversität zu Berlin (ISSN 08630976), 0709, 15 pages
MSC 2000
 34A09 Implicit equations, differentialalgebraic equations

34A30 Linear equations and systems, general
Abstract
We examine in this paper socalled Bcritical points
of linear, timevarying differentialalgebraic equations (DAEs)
of the form A(t)(D(t)x(t))'+B(t)x(t)=q(t). These critical or singular points, which cannot be handled by classical projector
methods, require adapting a recently introduced framework based on $\Pi$projectors. Via a continuation of certain invariant spaces through the singularity, we arrive at an scenario which
accommodates both A and Bcritical DAEs.The working hypotheses apply in particular to standardform analytic systems although, in contrast to other approaches to critical problems, the scope of our approach extends beyond the analytic setting. Some examples illustrate the results.
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