Linear differential-algebraic equations with properly stated leading term: B -critical points |
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Authors: | Roswitha März |
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Affiliation: | Institut für Mathematik, Humboldt-Universit?t zu Berlin , Berlin , Germany |
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Abstract: | We examine in this article so-called B-critical points of linear, time-varying differential-algebraic 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 Π-projectors. Via a continuation of certain invariant spaces through the singularity, we arrive at a scenario which accommodates both A- and B-critical DAEs. The working hypotheses apply in particular to standard-form 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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Keywords: | differential-algebraic equation index projector critical point singularity |
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