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Differential-Algebraic Equations: A Projector Based Analysis

2013-01-19 Mathematics
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Release : 2013-01-19
Genre : Mathematics
Kind : eBook
Book Rating : 559/5 ( reviews)

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Book Synopsis Differential-Algebraic Equations: A Projector Based Analysis by : René Lamour

Download or read book Differential-Algebraic Equations: A Projector Based Analysis written by René Lamour. This book was released on 2013-01-19. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Projector Based Analysis of Linear Differential Algebraic Equations

2011
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Release : 2011
Genre :
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Book Synopsis Projector Based Analysis of Linear Differential Algebraic Equations by : René Lamour

Download or read book Projector Based Analysis of Linear Differential Algebraic Equations written by René Lamour. This book was released on 2011. Available in PDF, EPUB and Kindle. Book excerpt:

Differential-Algebraic Systems

2008 Mathematics
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Release : 2008
Genre : Mathematics
Kind : eBook
Book Rating : 817/5 ( reviews)

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Book Synopsis Differential-Algebraic Systems by : Ricardo Riaza

Download or read book Differential-Algebraic Systems written by Ricardo Riaza. This book was released on 2008. Available in PDF, EPUB and Kindle. Book excerpt: Differential-algebraic equations (DAEs) provide an essential tool for system modeling and analysis within different fields of applied sciences and engineering. This book addresses modeling issues and analytical properties of DAEs, together with some applications in electrical circuit theory.Beginning with elementary aspects, the author succeeds in providing a self-contained and comprehensive presentation of several advanced topics in DAE theory, such as the full characterization of linear time-varying equations via projector methods or the geometric reduction of nonlinear systems. Recent results on singularities are extensively discussed. The book also addresses in detail differential-algebraic models of electrical and electronic circuits, including index characterizations and qualitative aspects of circuit dynamics. In particular, the reader will find a thorough discussion of the state/semistate dichotomy in circuit modeling. The state formulation problem, which has attracted much attention in the engineering literature, is cleverly tackled here as a reduction problem on semistate models.

Differential Equations

2024-04-01 Mathematics
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Release : 2024-04-01
Genre : Mathematics
Kind : eBook
Book Rating : 717/5 ( reviews)

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Book Synopsis Differential Equations by : Svetlin G. Georgiev

Download or read book Differential Equations written by Svetlin G. Georgiev. This book was released on 2024-04-01. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a projector analysis of dynamic systems on time scales. The dynamic systems are classified as first, second, third and fourth kinds. For each classes of dynamic systems the basic matrix chains are constructed. The proposed theory is applied for decoupling of dynamic equations on time scales. Properly involved derivatives, constraints and consistent initial values for the considered equations are defined. A linearization for nonlinear dynamic systems is introduced and the total derivative for regular linearized equations with tractability index one is investigated.

Progress in Differential-Algebraic Equations II

2020-10-10 Mathematics
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Release : 2020-10-10
Genre : Mathematics
Kind : eBook
Book Rating : 059/5 ( reviews)

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Book Synopsis Progress in Differential-Algebraic Equations II by : Timo Reis

Download or read book Progress in Differential-Algebraic Equations II written by Timo Reis. This book was released on 2020-10-10. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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