Numerical Approximation of Exact Controls for Waves

Name: Numerical Approximation of Exact Controls for Waves
Brand: Springer, Berlin
SKU: 9781461458074
Price: 276.48 RON
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Autor: Sylvain Ervedoza, Enrique Zuazua

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Editura: Springer, Berlin

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This book is devoted to fully developing and comparing the two main approaches to the numerical appr...

Informații despre carte

Autor

Sylvain Ervedoza, Enrique Zuazua

Limbă

engleză

Legare

Carte - Carte broșată

Publicat

2012

Pagini

122

EAN

9781461458074

ISBN

1461458072

Enbook ID

01428381

Editura

Springer, Berlin

Greutate

225

Dimensiuni

157 x 238 x 11

Descriere completă

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.

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