Differential Algebraic Equations A Projector Based Analysis
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Differential-Algebraic Equations: A Projector Based Analysis
Author: René Lamour
language: en
Publisher: Springer Science & Business Media
Release Date: 2013-01-19
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 constraints, in order to simulate and to control processes in various application fields such as network simulation, chemical kinematics, mechanical engineering, system biology. 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.
Progress in Differential-Algebraic Equations II
This book contains articles presented at the 9th Workshop on Differential-Algebraic Equations held in Paderborn, Germany, from 17–20 March 2019. The workshop brought together more than 40 mathematicians and engineers from various fields, such as numerical and functional analysis, control theory, mechanics and electromagnetic field theory. The participants focussed on the theoretical and numerical treatment of “descriptor” systems, i.e., differential-algebraic equations (DAEs). The book contains 14 contributions and is organized into four parts: mathematical analysis, numerics and model order reduction, control as well as applications. It is a useful resource for applied mathematicians with interest in recent developments in the field of differential algebraic equations but also for engineers, in particular those interested in modelling of constraint mechanical systems, thermal networks or electric circuits.
Progress in Differential-Algebraic Equations
This book contains the proceedings of the 8th Workshop on Coupled Descriptor Systems held March 2013 in the Castle of Eringerfeld, Geseke in the neighborhood of Paderborn, Germany. It examines the wide range of current research topics in descriptor systems, including mathematical modeling, index analysis, wellposedness of problems, stiffness and different time-scales, cosimulation and splitting methods and convergence analysis. In addition, the book also presents applications from the automotive and circuit industries that show that descriptor systems provide challenging problems from the point of view of both theory and practice. The book contains nine papers and is organized into three parts: control, simulation, and model order reduction. It will serve as an ideal resource for applied mathematicians and engineers, in particular those from mechanics and electromagnetics, who work with coupled differential equations.