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SpringerBriefs in Mathematics

Numerical Approximation of Exact Controls for Waves

Authors: Ervedoza, Sylvain, Zuazua, Enrique

  • Devoted to fully developing and comparing continuous and the discrete approaches to the numerical approximation of controls for wave propagation phenomena
  • 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
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  • ISBN 978-1-4614-5808-1
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  • ISBN 978-1-4614-5807-4
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About this book

​​​​​​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.​

Table of contents (5 chapters)

  • Numerical Approximation of Exact Controls for Waves

    Ervedoza, Sylvain (et al.)

    Pages 1-48

  • Observability for the 1—d Finite-Difference Wave Equation

    Ervedoza, Sylvain (et al.)

    Pages 49-58

  • Convergence of the Finite-Difference Method for the 1—d Wave Equation with Homogeneous Dirichlet Boundary Conditions

    Ervedoza, Sylvain (et al.)

    Pages 59-78

  • Convergence with Nonhomogeneous Boundary Conditions

    Ervedoza, Sylvain (et al.)

    Pages 79-114

  • Further Comments and Open Problems

    Ervedoza, Sylvain (et al.)

    Pages 115-118

Buy this book

eBook $34.99
price for USA (gross)
  • ISBN 978-1-4614-5808-1
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.95
price for USA
  • ISBN 978-1-4614-5807-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Numerical Approximation of Exact Controls for Waves
Authors
Series Title
SpringerBriefs in Mathematics
Copyright
2013
Publisher
Springer-Verlag New York
Copyright Holder
The Editor(s) (if applicable) and The Author(s) 2018
eBook ISBN
978-1-4614-5808-1
DOI
10.1007/978-1-4614-5808-1
Softcover ISBN
978-1-4614-5807-4
Series ISSN
2191-8198
Edition Number
1
Number of Pages
XVII, 122
Number of Illustrations and Tables
14 b/w illustrations, 3 illustrations in colour
Topics