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Spectral Methods for Non-Standard Eigenvalue Problems

Fluid and Structural Mechanics and Beyond

  • Călin-Ioan Gheorghiu

Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Călin-Ioan Gheorghiu
    Pages 1-18
  3. Călin-Ioan Gheorghiu
    Pages 19-39
  4. Călin-Ioan Gheorghiu
    Pages 41-84
  5. Călin-Ioan Gheorghiu
    Pages 85-110
  6. Călin-Ioan Gheorghiu
    Pages 111-114
  7. Back Matter
    Pages 115-120

About this book

Introduction

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.

Keywords

Galerkin spectral collocation spectral high order eigenvalue problems singular nonlinear boundary value problems tau spectral

Authors and affiliations

  • Călin-Ioan Gheorghiu
    • 1
  1. 1.T.Popoviciu Inst. of Numerical Analysiscalin, Romanian AcademyCluj-NapocaRomania

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-06230-3
  • Copyright Information The Author(s) 2014
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-06229-7
  • Online ISBN 978-3-319-06230-3
  • Series Print ISSN 2191-8198
  • Series Online ISSN 2191-8201
  • Buy this book on publisher's site
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