SpringerBriefs in Mathematics

Spectral Methods for Non-Standard Eigenvalue Problems

Fluid and Structural Mechanics and Beyond

Authors: Gheorghiu, Călin-Ioan

  • Constructive, practical approach of spectral solutions to non-standard differential problems
  • Numerous and varied examples assist the reader in smoothly understanding and learning
  • Text shows what kind of spectral method works for a particular problem and how it can be efficiently implemented
  • Less academic examples but more real examples from elasticity and hydrodynamics
  • Complete solutions for classical Mathieu’s system as a multi parameter eigenvalue problem, i.e., in its natural setting
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eBook $39.99
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  • ISBN 978-3-319-06230-3
  • Digitally watermarked, DRM-free
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  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $54.99
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  • ISBN 978-3-319-06229-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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About this book

This book focuses on the constructive and practical aspects of spectral methods. It rigorously examines the most important qualities as well as drawbacks of spectral methods in the context of numerical methods devoted to solve non-standard eigenvalue problems. In addition, the book also considers some nonlinear singularly perturbed boundary value problems along with eigenproblems obtained by their linearization around constant solutions.

The book is mathematical, poising problems in their proper function spaces, but its emphasis is on algorithms and practical difficulties. The range of applications is quite large. High order eigenvalue problems are frequently beset with numerical ill conditioning problems. The book describes a wide variety of successful modifications to standard algorithms that greatly mitigate these problems.

In addition, the book makes heavy use of the concept of pseudospectrum, which is highly relevant to understanding when disaster is imminent in solving eigenvalue problems. It also envisions two classes of applications, the stability of some elastic structures and the hydrodynamic stability of some parallel shear flows.

This book is an ideal reference text for professionals (researchers) in applied mathematics, computational physics and engineering. It will be very useful to numerically sophisticated engineers, physicists and chemists. The book can also be used as a textbook in review courses such as numerical analysis, computational methods in various engineering branches or physics and computational methods in analysis.

Table of contents (5 chapters)

  • General Formulation of Spectral Approximation

    Gheorghiu, Călin-Ioan

    Pages 1-18

  • Tau and Galerkin Methods for Fourth Order GEPs

    Gheorghiu, Călin-Ioan

    Pages 19-39

  • The Chebyshev Collocation Method

    Gheorghiu, Călin-Ioan

    Pages 41-84

  • The Laguerre Collocation Method

    Gheorghiu, Călin-Ioan

    Pages 85-110

  • Conclusions and Further Developments

    Gheorghiu, Călin-Ioan

    Pages 111-114

Buy this book

eBook $39.99
price for USA (gross)
  • ISBN 978-3-319-06230-3
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $54.99
price for USA
  • ISBN 978-3-319-06229-7
  • 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
Spectral Methods for Non-Standard Eigenvalue Problems
Book Subtitle
Fluid and Structural Mechanics and Beyond
Authors
Series Title
SpringerBriefs in Mathematics
Copyright
2014
Publisher
Springer International Publishing
Copyright Holder
The Author(s)
eBook ISBN
978-3-319-06230-3
DOI
10.1007/978-3-319-06230-3
Softcover ISBN
978-3-319-06229-7
Series ISSN
2191-8198
Edition Number
1
Number of Pages
XII, 120
Number of Illustrations and Tables
3 b/w illustrations, 49 illustrations in colour
Topics