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© 2013

Differential-Algebraic Equations: A Projector Based Analysis

  • 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)

Book

Part of the Differential-Algebraic Equations Forum book series (DAEF)

Table of contents

  1. Front Matter
    Pages I-XXVII
  2. Projector based approach

    1. Front Matter
      Pages 1-2
    2. René Lamour, Roswitha März, Caren Tischendorf
      Pages 3-56
    3. René Lamour, Roswitha März, Caren Tischendorf
      Pages 57-181
    4. René Lamour, Roswitha März, Caren Tischendorf
      Pages 183-314
  3. Index-1 DAEs: Analysis and numerical treatment

    1. Front Matter
      Pages 315-316
    2. René Lamour, Roswitha März, Caren Tischendorf
      Pages 317-337
    3. René Lamour, Roswitha März, Caren Tischendorf
      Pages 339-373
    4. René Lamour, Roswitha März, Caren Tischendorf
      Pages 375-395
  4. Computational aspects

    1. Front Matter
      Pages 397-398
    2. René Lamour, Roswitha März, Caren Tischendorf
      Pages 399-417
    3. René Lamour, Roswitha März, Caren Tischendorf
      Pages 419-438
  5. Advanced topics

    1. Front Matter
      Pages 439-440
    2. René Lamour, Roswitha März, Caren Tischendorf
      Pages 441-476
    3. René Lamour, Roswitha März, Caren Tischendorf
      Pages 477-503
    4. René Lamour, Roswitha März, Caren Tischendorf
      Pages 505-538
    5. René Lamour, Roswitha März, Caren Tischendorf
      Pages 539-580
  6. Back Matter
    Pages 581-649

About this book

Introduction

Differential algebraic equations (DAEs), including so-called descriptor systems, began to attract significant research interest in applied and numerical mathematics in the early 1980s, no more than about three decades ago. In this relatively short time, DAEs have become a widely acknowledged tool to model processes subjected to certain constraints in order to simulate and to control processes in various application fields such as network simulation, chemical kinematics, mechanical engineering and systems biology.
DAEs and their more abstract versions in infinite dimensional spaces comprise a great potential for the 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 in so doing to motivate further research of this versatile, extraordinary topic from a broader mathematical perspective.
The book elaborates on 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. Some issues on numerical integration and computational aspects are also treated in this context.  


Keywords

Abstract Differential-Algebraic Equations Applied Analysis Descriptor Systems Differential-Algebraic Equations Ordinary Differential Equiations

Authors and affiliations

  1. 1.Department of MathematicsHumboldt-University of BerlinBerlinGermany
  2. 2.Department of MathematicsHumboldt-University of BerlinBerlinGermany
  3. 3.Mathematical InstituteUniversity of CologneCologneGermany

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

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)