Spectral Methods for Non-Standard Eigenvalue Problems: Fluid and Structural Mech

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Spectral Methods for Non-Standard Eigenvalue Problems by Călin-Ioan Gheorghiu

In addition, the book also considers some nonlinear singularly perturbed boundary value problems along with eigenproblems obtained by their linearization around constant book is mathematical, poising problems in their proper function spaces, but its emphasis is on algorithms and practical difficulties.

FORMAT
Paperback LANGUAGE
English CONDITION
Brand New Publisher Description

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 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 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 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

1 General Formulation of Spectral Approximation.- 2 Tau and Galerkin Methods for Fourth Order GEPs.- 3 The Chebyshev Collocation Method.- 4 The Laguerre Collocation Method.- 5 Conclusions and Further Developments.- Appendix: Algebraic Two-Parameter Eigenvalue Problems.- Index.

Feature

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

Details ISBN3319062298 Year 2014 ISBN-10 3319062298 ISBN-13 9783319062297 Format Paperback Short Title SPECTRAL METHODS FOR NON-STAND Language English Media Book Imprint Springer International Publishing AG Subtitle Fluid and Structural Mechanics and Beyond Place of Publication Cham Country of Publication Switzerland Edition 2014th Pages 120 DOI 10.1007/978-3-319-06230-3 Author Clin-Ioan Gheorghiu Publisher Springer International Publishing AG Edition Description 2014 ed. Series SpringerBriefs in Mathematics Publication Date 2014-05-08 DEWEY 515.7222 Audience Postgraduate, Research & Scholarly Country of Origin NL Product Class Description Mathematics Alternative 9783319062303 Illustrations 49 Illustrations, color; 3 Illustrations, black and white
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