Numerical Approximation of Exact Controls for Waves / by Sylvain Ervedoza, Enrique Zuazua
(SpringerBriefs in Mathematics)
| データ種別 | 電子ブック |
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| 出版情報 | New York, NY : Springer New York : Imprint: Springer , 2013 |
| 本文言語 | 英語 |
| 大きさ | XVII, 122 p. 17 illus., 3 illus. in color : online resource |
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| 内容注記 | 1.Numerical approximation of exact controls for waves 2.The discrete 1-d wave equation 3.Convergence for homogeneous boundary conditions 4.Convergence with non-homogeneous data 5. Further comments and open problems References |
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| 一般注記 | This book is devoted to fully developing and comparing the two main approaches to the numerical approximation of controls for wave propagation phenomena: the continuous and the discrete. This is accomplished in the abstract functional setting of conservative semigroups.The main results of the work unify, to a large extent, these two approaches, which yield similaralgorithms and convergence rates. The discrete approach, however, gives not only efficient numerical approximations of the continuous controls, but also ensures some partial controllability properties of the finite-dimensional approximated dynamics. Moreover, it has the advantage of leading to iterative approximation processes that converge without a limiting threshold in the number of iterations. Such a threshold, which is hard to compute and estimate in practice, is a drawback of the methods emanating from the continuous approach. To complement this theory, the book provides convergence results for the discrete wave equation when discretized using finite differences and proves the convergence of the discrete wave equation with non-homogeneous Dirichlet conditions. The first book to explore these topics in depth, "On the Numerical Approximations of Controls for Waves" has rich applications to data assimilation problems and will be of interest to researchers who deal with wave approximations |
| 著者標目 | *Ervedoza, Sylvain author Zuazua, Enrique author SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Approximation theory LCSH:Partial differential equations LCSH:Applied mathematics LCSH:Engineering mathematics LCSH:System theory LCSH:Algorithms LCSH:Numerical analysis FREE:Mathematics FREE:Approximations and Expansions FREE:Partial Differential Equations FREE:Systems Theory, Control FREE:Numerical Analysis FREE:Algorithms FREE:Applications of Mathematics |
| 分 類 | DC23:511.4 |
| 巻冊次 | ISBN:9781461458081 
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| ISBN | 9781461458081 |
| URL | http://dx.doi.org/10.1007/978-1-4614-5808-1 |
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