Overview
- New comprehensive analysis of general nonlinear DAEs
- First book describing the projector approach for nonlinear, higher-index DAEs
- Rigorous description, multitude of examples highlighting analytical and numerical challenges in this field
- Suitable for students, researchers and users from different application fields (e.g. circuit and electromagnetic simulation, mechanical engineering, system biology)
- Includes supplementary material: sn.pub/extras
Part of the book series: Differential-Algebraic Equations Forum (DAEF)
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Table of contents (12 chapters)
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Front Matter
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Projector based approach
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Front Matter
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Index-1 DAEs: Analysis and numerical treatment
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Front Matter
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Computational aspects
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Front Matter
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Advanced topics
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Front Matter
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Back Matter
Keywords
About this book
DAEs and their more abstract versions in infinite-dimensional spaces comprise a great potential for future mathematical modeling of complex coupled processes.
The purpose of the book is to expose the impressive complexity of general DAEs from an analytical point of view, to describe the state of the art as well as open problems and so to motivate further research to this versatile, extra-ordinary topic from a broader mathematical perspective.
The book elaborates a new general structural analysis capturing linear and nonlinear DAEs in a hierarchical way. The DAE structure is exposed by means of special projector functions. Numerical integration issues and computational aspects are treated also in this context.
Reviews
From the reviews:
“This book is devoted to the projector-based analysis and numerical treatment of differential-algebraic equations (DAEs), which is a research direction established by Roswitha März (Humboldt University, Berlin, Germany) about 30 years ago. … The book presents a rigorous and detailed analytical treatment of DAEs. … This nicely written book is an excellent textbook addressed to graduate students and researchers, who are interested in DAEs. It is also recommendable for people working on various DAE-related industrial applications.” (Vu Hoang Linh, zbMATH, Vol. 1276, 2014)Authors and Affiliations
About the authors
Dr. René Lamour, Humbold University of Berlin, Department of Mathematics, Germany
Prof. Dr. Roswitha März, Humbold University of Berlin, Department of Mathematics, Germany
Prof. Dr. Caren Tischendorf, University of Cologne, Mathematical Institute, Germany
Bibliographic Information
Book Title: Differential-Algebraic Equations: A Projector Based Analysis
Authors: René Lamour, Roswitha März, Caren Tischendorf
Series Title: Differential-Algebraic Equations Forum
DOI: https://doi.org/10.1007/978-3-642-27555-5
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2013
Softcover ISBN: 978-3-642-27554-8Published: 18 January 2013
eBook ISBN: 978-3-642-27555-5Published: 19 January 2013
Series ISSN: 2199-7497
Series E-ISSN: 2199-840X
Edition Number: 1
Number of Pages: XXVII, 649
Number of Illustrations: 5 b/w illustrations, 19 illustrations in colour
Topics: Ordinary Differential Equations, Applications of Mathematics, Computational Mathematics and Numerical Analysis