Overview
- 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
- Includes supplementary material: sn.pub/extras
Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (5 chapters)
Keywords
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.
Authors and Affiliations
Bibliographic Information
Book Title: Spectral Methods for Non-Standard Eigenvalue Problems
Book Subtitle: Fluid and Structural Mechanics and Beyond
Authors: Călin-Ioan Gheorghiu
Series Title: SpringerBriefs in Mathematics
DOI: https://doi.org/10.1007/978-3-319-06230-3
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Author(s) 2014
Softcover ISBN: 978-3-319-06229-7Published: 08 May 2014
eBook ISBN: 978-3-319-06230-3Published: 22 April 2014
Series ISSN: 2191-8198
Series E-ISSN: 2191-8201
Edition Number: 1
Number of Pages: XII, 120
Number of Illustrations: 3 b/w illustrations, 49 illustrations in colour
Topics: Computational Mathematics and Numerical Analysis, Numerical Analysis, Ordinary Differential Equations, Applications of Mathematics, Computational Science and Engineering, Numerical and Computational Physics, Simulation