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Field name	Details
Dewey Class	511.4
Title	Numerical Approximation of Exact Controls for Waves ([Ebook]) / by Sylvain Ervedoza, Enrique Zuazua.
Author	Ervedoza, Sylvain
Added Personal Name	Zuazua, Enrique
Other name(s)	SpringerLink (Online service)
Publication	New York, NY : Springer
Publication	, 2013.
Physical Details	XVII, 122 pages : 17 illus., 3 illus. in color. : online resource.
Series	SpringerBriefs in Mathematics 2191-8198
ISBN	9781461458081
Summary Note	This book is devoted to fully developing and comparingÂ the two main approaches to the numerical approximation of controls for wave propagation phenomena: the continuous and the discrete.Â This is accomplishedÂ in the abstract functional setting of conservative semigroups.The main results of the work unify, to a large extent, these twoÂ approaches, which yieldÂ similaralgorithms and convergence rates. The discrete approach, however, givesÂ not only efficient numerical approximations of the continuous controls, but also ensures some partial controllability propertiesÂ of the finite-dimensional approximated dynamics. Moreover, it hasÂ theÂ 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.Â 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 andÂ will be of interest to researchers who deal with wave approximations.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	http://dx.doi.org/10.1007/978-1-4614-5808-1
Links to Related Works	Subject References: Algorithms . Applications of Mathematics . Approximations and Expansions . Differential equations, Partial . Mathematics . Numerical Analysis . Partial differential equations . Systems theory . Systems Theory, Control . Authors: author . Ervedoza, Sylvain . Zuazua, Enrique . Corporate Authors: SpringerLink (Online service) . Series: SpringerBriefs in Mathematics . Classification: 511.4 . 511.4 (DDC 23) .

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Numerical Approximation of Exact Controls for Waves

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