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100   $a20140422d2014      u|         0
101 0 $aeng
135   $aur|n|---|||||
181   $ctxt
182   $cc
183   $acr
200 10$aSpectral Methods for Non-Standard Eigenvalue Problems $eFluid and Structural Mechanics and Beyond /$fby C?lin-Ioan Gheorghiu
205   $a1st ed. 2014.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2014.
215   $a1 online resource (130 p.)
225 1 $aSpringerBriefs in Mathematics,$x2191-8198
300   $aDescription based upon print version of record.
311   $a3-319-06229-8 
320   $aIncludes bibliographical references at the end of each chapters and index.
327   $a1 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.
330   $aThis book focuses on the constructive and practical aspects of spectral methods. It rigorously examines the most important qualities as well as drawbacks of spectral methods in the context of numerical methods devoted to solve non-standard eigenvalue problems. In addition, the book also considers some nonlinear singularly perturbed boundary value problems along with eigenproblems obtained by their linearization around constant solutions. The book is mathematical, poising problems in their proper function spaces, but its emphasis is on algorithms and practical difficulties. The range of applications is quite large. High order eigenvalue problems are frequently beset with numerical ill conditioning problems. The book describes a wide variety of successful modifications to standard algorithms that greatly mitigate these problems. In addition, the book makes heavy use of the concept of pseudospectrum, which is highly relevant to understanding when disaster is imminent in solving eigenvalue problems. It also envisions two classes of applications, the stability of some elastic structures and the hydrodynamic stability of some parallel shear flows. This book is an ideal reference text for professionals (researchers) in applied mathematics, computational physics and engineering. It will be very useful to numerically sophisticated engineers, physicists and chemists. The book can also be used as a textbook in review courses such as numerical analysis, computational methods in various engineering branches or physics and computational methods in analysis.
410  0$aSpringerBriefs in Mathematics,$x2191-8198
606   $aComputer mathematics
606   $aNumerical analysis
606   $aDifferential equations
606   $aApplied mathematics
606   $aEngineering mathematics
606   $aPhysics
606   $aComputational Mathematics and Numerical Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M1400X
606   $aNumerical Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M14050
606   $aOrdinary Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12147
606   $aApplications of Mathematics$3https://scigraph.springernature.com/ontologies/product-market-codes/M13003
606   $aComputational Science and Engineering$3https://scigraph.springernature.com/ontologies/product-market-codes/M14026
606   $aNumerical and Computational Physics, Simulation$3https://scigraph.springernature.com/ontologies/product-market-codes/P19021
615  0$aComputer mathematics.
615  0$aNumerical analysis.
615  0$aDifferential equations.
615  0$aApplied mathematics.
615  0$aEngineering mathematics.
615  0$aPhysics.
615 14$aComputational Mathematics and Numerical Analysis.
615 24$aNumerical Analysis.
615 24$aOrdinary Differential Equations.
615 24$aApplications of Mathematics.
615 24$aComputational Science and Engineering.
615 24$aNumerical and Computational Physics, Simulation.
676   $a512.9436
700   $aGheorghiu$b C?lin-Ioan$4aut$4http://id.loc.gov/vocabulary/relators/aut$0721612
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910300147303321
996   $aSpectral methods for non-standard eigenvalue problems$91410312
997   $aUNINA