TY - BOOK ID - 8434347 TI - Differential-algebraic equations : a projector based analysis AU - Lamour, Rene. AU - Marz, Roswitha. AU - Tischendorf, Caren. PY - 2013 SN - 3642275540 3642275559 1299197515 PB - New York : Springer, DB - UniCat KW - Differential equations. KW - Differential-algebraic equations. KW - Electric circuits -- Mathematical models. KW - Quantum groups. KW - Differential-algebraic equations KW - Mathematics KW - Physical Sciences & Mathematics KW - Calculus KW - Algebraic-differential equations KW - Differential-algebraic systems KW - Equations, Algebraic-differential KW - Equations, Differential-algebraic KW - Systems, Differential-algebraic KW - Mathematics. KW - Applied mathematics. KW - Engineering mathematics. KW - Computer mathematics. KW - Ordinary Differential Equations. KW - Applications of Mathematics. KW - Computational Mathematics and Numerical Analysis. KW - Differential equations KW - Differential Equations. KW - Computer science KW - Computer mathematics KW - Discrete mathematics KW - Electronic data processing KW - Math KW - Science KW - 517.91 Differential equations KW - Engineering KW - Engineering analysis KW - Mathematical analysis UR - https://www.unicat.be/uniCat?func=search&query=sysid:8434347 AB - 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. . ER -