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Differential-Algebraic Equations: Examples and Benchmarks

Stephen Campbell, Achim Ilchmann, Volker Mehrmann, Timo Reis, eds.
Publication Date: 
Number of Pages: 
Differential-Algebraic Equations Forum
[Reviewed by
Andrzej Sokolowski
, on
Differential algebraic equations (DAEs) are difficult for students, therefore any publications that strive to bring forth not only the processes of their solutions but also their applications and interpretations of solutions are welcome. The book Applications of Differential -Algebraic Equations: Examples and Benchmarks by Campbell, IIchmann, Mehrmann, and Reis stands out by its substance, clarity exposition, and diversity of advanced algebraic representations applied to formulate and solve DAEs. The reader will appreciate high quality innovative and original examples of DAEs from areas such as underactuated mechanical systems, electrodynamics, gas networks, multibody dynamics but also from robotics and semi-discretized Navier-Stokes equations. The reader will also be immersed into tracking problems and non-smooth, nonlinear DAEs. Each of these areas constitutes a separate chapter initiated by the details of the modeling technique and followed by a mathematical analysis and discussion of the solutions that often includes simulations. As such, the book will not only deepen the reader’s understanding and widen DAEs spectrum of applications but also suggest own paths of explorations.
More specifically,  in the chapter Topological Index Analysis to Coupled  Flow Networks, Baun, Kolmbauer and Offner propose a unique method of using a system of DAEs to analyze multi-physical models stemming from automated modeling processes in system simulation software. The novice approach of applying topological based index analysis for coupled system was conducted through exploring the network structure via graphs and allowed to develop topological criteria for the existence of solutions of coupled systems. There are several state-of-the-art modeling and simulation packages available:  Dymola, Open-Modelica, Matlab/Simulink, Flowmaster, Amesim, SimulationX or CruiseM. All offer many concepts for the automatic generation of dynamic system models. Topology based index analysis for networks connects the research fields of Analysis for DAEs and Graph Theory making it a unique tool to analyze DAEs resulting from automatically generated system models.
The book can be of special interest to mathematicians, STEM students, and engineers working in multidisciplinary industry settings where the insight provided by differential-algebraic equations can be determinant in decision making.


Andrzej Sokolowski, PhD, is a researcher interested in inducing mathematical modeling as a method of exercising scientific inquiry in physical science. He is also a mathematics and physics professor at Lone Star College, TX.

See the publisher's web page.