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Differential-Algebraic Equations: A Projector Based Analysis / by René Lamour, Roswitha März, Caren Tischendorf
(Differential-Algebraic Equations Forum. ISSN:2199840X)
版 | 1st ed. 2013. |
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出版者 | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
出版年 | 2013 |
本文言語 | 英語 |
大きさ | XXVII, 649 p. 24 illus., 19 illus. in color : online resource |
著者標目 | *Lamour, René author März, Roswitha author Tischendorf, Caren author SpringerLink (Online service) |
件 名 | LCSH:Differential equations LCSH:Mathematics LCSH:Mathematics -- Data processing 全ての件名で検索 FREE:Differential Equations FREE:Applications of Mathematics FREE:Computational Mathematics and Numerical Analysis |
一般注記 | Notations -- Introduction -- Part I. Projector based approach -- 1 Linear constant coefficient DAEs.-.2 Linear DAEs with variable coefficients -- 3 Nonlinear DAEs -- Part II. Index-1 DAEs: Analysis and numerical treatment -- 4 Analysis -- 5 Numerical integration -- 6 Stability issues -- Part III. Computational aspects -- 7 Computational linear algebra aspects -- 8 Aspects of the numerical treatment of higher index DAEs -- Part IV. Advanced topics -- 9 Quasi-regular DAEs -- 10 Nonregular DAEs -- 11 Minimization with constraints described by DAEs -- 12 Abstract differential algebraic equations -- A. Linear Algebra – Basics.-.B. Technical Computations -- C Analysis -- References -- Index 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. HTTP:URL=https://doi.org/10.1007/978-3-642-27555-5 |
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電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
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電子ブック | オンライン | 電子ブック |
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Springer eBooks | 9783642275555 |
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EB00232261 |
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