Abstract
We investigate the structure of general nonlinear index-1 DAEs with properly involved linear derivative term. We show that each solution is actually a somewhat wrapped solution of the inherent explicit ODE. A certain implicitly given decoupling function plays its role when describing both the inherent ODE and the wrapping. With this background, we describe the set of consistent initial values, provide consistent initializations and prove local solvability and perturbation results. In turn, these results prove of value in Chapter 5 to analyze numerical integration methods and in Chapter 6 to investigate the asymptotical flow behavior.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Lamour, R., März, R., Tischendorf, C. (2013). Analysis. In: Differential-Algebraic Equations: A Projector Based Analysis. Differential-Algebraic Equations Forum. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27555-5_4
Download citation
DOI: https://doi.org/10.1007/978-3-642-27555-5_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-27554-8
Online ISBN: 978-3-642-27555-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)