Numerical Solution Of A Non Self Adjoint Differential Eigenvalue Problem
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Numerical Solution Of A Non Self Adjoint Differential Eigenvalue Problem
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Author : H. Bruun Nielsen
language : en
Publisher:
Release Date : 1977
Numerical Solution Of A Non Self Adjoint Differential Eigenvalue Problem written by H. Bruun Nielsen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977 with categories.
Numerisk Institut Danmarks Tekniske H Jskole
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Author : Hans Bruun Nielsen
language : en
Publisher:
Release Date : 1977
Numerisk Institut Danmarks Tekniske H Jskole written by Hans Bruun Nielsen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977 with categories.
Guaranteed Computational Methods For Self Adjoint Differential Eigenvalue Problems
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Author : Xuefeng Liu
language : en
Publisher: Springer Nature
Release Date :
Guaranteed Computational Methods For Self Adjoint Differential Eigenvalue Problems written by Xuefeng Liu and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Numerical Methods For Eigenvalue Problems
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Author : Steffen Börm
language : en
Publisher: Walter de Gruyter
Release Date : 2012-05-29
Numerical Methods For Eigenvalue Problems written by Steffen Börm and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-29 with Mathematics categories.
Eigenvalues and eigenvectors of matrices and linear operators play an important role when solving problems from structural mechanics and electrodynamics, e.g., by describing the resonance frequencies of systems, when investigating the long-term behavior of stochastic processes, e.g., by describing invariant probability measures, and as a tool for solving more general mathematical problems, e.g., by diagonalizing ordinary differential equations or systems from control theory. This textbook presents a number of the most important numerical methods for finding eigenvalues and eigenvectors of matrices. The authors discuss the central ideas underlying the different algorithms and introduce the theoretical concepts required to analyze their behavior with the goal to present an easily accessible introduction to the field, including rigorous proofs of all important results, but not a complete overview of the vast body of research. Several programming examples allow the reader to experience the behavior of the different algorithms first-hand. The book addresses students and lecturers of mathematics, physics and engineering who are interested in the fundamental ideas of modern numerical methods and want to learn how to apply and extend these ideas to solve new problems.
Domain Decomposition Methods For The Numerical Solution Of Partial Differential Equations
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Author : Tarek Mathew
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-06-25
Domain Decomposition Methods For The Numerical Solution Of Partial Differential Equations written by Tarek Mathew and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-06-25 with Mathematics categories.
Domain decomposition methods are divide and conquer computational methods for the parallel solution of partial differential equations of elliptic or parabolic type. The methodology includes iterative algorithms, and techniques for non-matching grid discretizations and heterogeneous approximations. This book serves as a matrix oriented introduction to domain decomposition methodology. A wide range of topics are discussed include hybrid formulations, Schwarz, and many more.
A Method For Approximating The Eigenvalues Of Non Self Adjoint Ordinary Differential Operators
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Author : John E. Osborn
language : en
Publisher:
Release Date : 1979
A Method For Approximating The Eigenvalues Of Non Self Adjoint Ordinary Differential Operators written by John E. Osborn and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Differential operators categories.
Numerical Methods For Computing Solutions To The Non Self Adjoint Zakharov Shabat Eigenvalue Problem
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Author : Kristen N. Shavlik
language : en
Publisher:
Release Date : 2019
Numerical Methods For Computing Solutions To The Non Self Adjoint Zakharov Shabat Eigenvalue Problem written by Kristen N. Shavlik and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Eigenvalues categories.
For special nonlinear PDEs that may be decomposed into a Lax pair, solutions may be found using the inverse scattering transform. In the case of the focusing nonlinear Schrödinger equation, the forward scattering step of this transform amounts to solving the non-self-adjoint Zakharov-Shabat eigenvalue problem. Our interest is in the semiclassical (zero-dispersion) limit, and this step proves to be rather challenging in this context. Many authors have chosen to use eigenvalue approximations instead of computing true eigenvalues. Given the sensitive nature of this problem (and, in particular, the ellipticity of the modulation equations), the role of these approximations is unclear. In this dissertation, we compute eigenvalues for a specific class of initial data in the semiclassical limit and compare them with WKB approximations of these eigenvalues. We begin by implementing two existing methods, Bronski’s shooting method and Hill’s method. We then introduce the two main contributions of this dissertation: the continuation method and a method for numerically computing reflection coefficients. The continuation method allows for tracking of eigenvalues as the dispersion parameter epsilon varies, which we demonstrate for sech x initial data. Computing reflection coefficients provides us with additional information to explore the stability of some of the initial data we consider.
Linear Differential Operators
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Author : Cornelius Lanczos
language : en
Publisher: SIAM
Release Date : 1997-12-01
Linear Differential Operators written by Cornelius Lanczos and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-12-01 with Mathematics categories.
Originally published in 1961, this Classics edition continues to be appealing because it describes a large number of techniques still useful today. Although the primary focus is on the analytical theory, concrete cases are cited to forge the link between theory and practice. Considerable manipulative skill in the practice of differential equations is to be developed by solving the 350 problems in the text. The problems are intended as stimulating corollaries linking theory with application and providing the reader with the foundation for tackling more difficult problems. Lanczos begins with three introductory chapters that explore some of the technical tools needed later in the book, and then goes on to discuss interpolation, harmonic analysis, matrix calculus, the concept of the function space, boundary value problems, and the numerical solution of trajectory problems, among other things. The emphasis is constantly on one question: "What are the basic and characteristic properties of linear differential operators?" In the author's words, this book is written for those "to whom a problem in ordinary or partial differential equations is not a problem of logical acrobatism, but a problem in the exploration of the physical universe. To get an explicit solution of a given boundary value problem is in this age of large electronic computers no longer a basic question. But of what value is the numerical answer if the scientist does not understand the peculiar analytical properties and idiosyncrasies of the given operator? The author hopes that this book will help in this task by telling something about the manifold aspects of a fascinating field."
Spectral Methods For Non Standard Eigenvalue Problems
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Author : Călin-Ioan Gheorghiu
language : en
Publisher: Springer Science & Business
Release Date : 2014-04-22
Spectral Methods For Non Standard Eigenvalue Problems written by Călin-Ioan Gheorghiu and has been published by Springer Science & Business this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-04-22 with Mathematics categories.
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.
Non Self Adjoint Boundary Eigenvalue Problems
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Author : R. Mennicken
language : en
Publisher: Gulf Professional Publishing
Release Date : 2003-06-26
Non Self Adjoint Boundary Eigenvalue Problems written by R. Mennicken and has been published by Gulf Professional Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-06-26 with Mathematics categories.
The 'North-Holland Mathematics Studies' series comprises a set of cutting-edge monographs and studies. This volume explores non-self-adjoint boundary eigenvalue problems for first order systems of ordinary differential equations and n-th order scalar differential equations.