Spectral Theory Computational Methods Of Sturm Liouville Problems
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Author |
: Don Hinton |
Publisher |
: CRC Press |
Total Pages |
: 414 |
Release |
: 2021-02-27 |
ISBN-10 |
: 9781000657760 |
ISBN-13 |
: 1000657760 |
Rating |
: 4/5 (60 Downloads) |
Synopsis Spectral Theory & Computational Methods of Sturm-Liouville Problems by : Don Hinton
Presenting the proceedings of the conference on Sturm-Liouville problems held in conjunction with the 26th Barrett Memorial Lecture Series at the University of Tennessee, Knoxville, this text covers both qualitative and computational theory of Sturm-Liouville problems. It surveys questions in the field as well as describing applications and concepts.
Author |
: Werner O. Amrein |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 348 |
Release |
: 2005-12-05 |
ISBN-10 |
: 9783764373597 |
ISBN-13 |
: 3764373598 |
Rating |
: 4/5 (97 Downloads) |
Synopsis Sturm-Liouville Theory by : Werner O. Amrein
This is a collection of survey articles based on lectures presented at a colloquium and workshop in Geneva in 2003 to commemorate the 200th anniversary of the birth of Charles François Sturm. It aims at giving an overview of the development of Sturm-Liouville theory from its historical roots to present day research. It is the first time that such a comprehensive survey has been made available in compact form. The contributions come from internationally renowned experts and cover a wide range of developments of the theory. The book can therefore serve both as an introduction to Sturm-Liouville theory and as background for ongoing research. The volume is addressed to researchers in related areas, to advanced students and to those interested in the historical development of mathematics. The book will also be of interest to those involved in applications of the theory to diverse areas such as engineering, fluid dynamics and computational spectral analysis.
Author |
: Anton Zettl |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 346 |
Release |
: 2005 |
ISBN-10 |
: 9780821852675 |
ISBN-13 |
: 0821852671 |
Rating |
: 4/5 (75 Downloads) |
Synopsis Sturm-Liouville Theory by : Anton Zettl
In 1836-1837 Sturm and Liouville published a series of papers on second order linear ordinary differential operators, which started the subject now known as the Sturm-Liouville problem. In 1910 Hermann Weyl published an article which started the study of singular Sturm-Liouville problems. Since then, the Sturm-Liouville theory remains an intensely active field of research, with many applications in mathematics and mathematical physics. The purpose of the present book is (a) to provide a modern survey of some of the basic properties of Sturm-Liouville theory and (b) to bring the reader to the forefront of knowledge about some aspects of this theory. To use the book, only a basic knowledge of advanced calculus and a rudimentary knowledge of Lebesgue integration and operator theory are assumed. An extensive list of references and examples is provided and numerous open problems are given. The list of examples includes those classical equations and functions associated with the names of Bessel, Fourier, Heun, Ince, Jacobi, Jorgens, Latzko, Legendre, Littlewood-McLeod, Mathieu, Meissner, Morse, as well as examples associated with the harmonic oscillator and the hydrogen atom. Many special functions of applied mathematics and mathematical physics occur in these examples.
Author |
: Boris Moiseevich Levitan |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 542 |
Release |
: 1975 |
ISBN-10 |
: 9780821815892 |
ISBN-13 |
: 082181589X |
Rating |
: 4/5 (92 Downloads) |
Synopsis Introduction to spectral theory: selfadjoint ordinary differential operators by : Boris Moiseevich Levitan
Presents a monograph that is devoted to the spectral theory of the Sturm- Liouville operator and to the spectral theory of the Dirac system. This book concerns with nth order operators that can serve as simply an introduction to this domain. It includes a chapter that discusses this theory.
Author |
: Carsten Trunk |
Publisher |
: |
Total Pages |
: |
Release |
: 2010 |
ISBN-10 |
: OCLC:845929823 |
ISBN-13 |
: |
Rating |
: 4/5 (23 Downloads) |
Synopsis Spectral Theory for Second Order Systems and Indefinite Sturm-Liouville Problems by : Carsten Trunk
Author |
: Vacheslav A. Yurko |
Publisher |
: Walter de Gruyter |
Total Pages |
: 316 |
Release |
: 2013-10-10 |
ISBN-10 |
: 9783110940961 |
ISBN-13 |
: 3110940965 |
Rating |
: 4/5 (61 Downloads) |
Synopsis Method of Spectral Mappings in the Inverse Problem Theory by : Vacheslav A. Yurko
Inverse problems of spectral analysis consist in recovering operators from their spectral characteristics. Such problems often appear in mathematics, mechanics, physics, electronics, geophysics, meteorology and other branches of natural science. This monograph is devoted to inverse problems of spectral analysis for ordinary differential equations. Its aim ist to present the main results on inverse spectral problems using the so-called method of spectral mappings, which is one of the main tools in inverse spectral theory. The book consists of three chapters: In Chapter 1 the method of spectral mappings is presented in the simplest version for the Sturm-Liouville operator. In Chapter 2 the inverse problem of recovering higher-order differential operators of the form, on the half-line and on a finite interval, is considered. In Chapter 3 inverse spectral problems for differential operators with nonlinear dependence on the spectral parameter are studied.
Author |
: Aiping Wang |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 250 |
Release |
: 2019-11-08 |
ISBN-10 |
: 9781470453664 |
ISBN-13 |
: 1470453665 |
Rating |
: 4/5 (64 Downloads) |
Synopsis Ordinary Differential Operators by : Aiping Wang
In 1910 Herman Weyl published one of the most widely quoted papers of the 20th century in Analysis, which initiated the study of singular Sturm-Liouville problems. The work on the foundations of Quantum Mechanics in the 1920s and 1930s, including the proof of the spectral theorem for unbounded self-adjoint operators in Hilbert space by von Neumann and Stone, provided some of the motivation for the study of differential operators in Hilbert space with particular emphasis on self-adjoint operators and their spectrum. Since then the topic developed in several directions and many results and applications have been obtained. In this monograph the authors summarize some of these directions discussing self-adjoint, symmetric, and dissipative operators in Hilbert and Symplectic Geometry spaces. Part I of the book covers the theory of differential and quasi-differential expressions and equations, existence and uniqueness of solutions, continuous and differentiable dependence on initial data, adjoint expressions, the Lagrange Identity, minimal and maximal operators, etc. In Part II characterizations of the symmetric, self-adjoint, and dissipative boundary conditions are established. In particular, the authors prove the long standing Deficiency Index Conjecture. In Part III the symmetric and self-adjoint characterizations are extended to two-interval problems. These problems have solutions which have jump discontinuities in the interior of the underlying interval. These jumps may be infinite at singular interior points. Part IV is devoted to the construction of the regular Green's function. The construction presented differs from the usual one as found, for example, in the classical book by Coddington and Levinson.
Author |
: L.A. Sakhnovich |
Publisher |
: Birkhäuser |
Total Pages |
: 201 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9783034887137 |
ISBN-13 |
: 3034887132 |
Rating |
: 4/5 (37 Downloads) |
Synopsis Spectral Theory of Canonical Differential Systems. Method of Operator Identities by : L.A. Sakhnovich
Theorems of factorising matrix functions and the operator identity method play an essential role in this book in constructing the spectral theory (direct and inverse problems) of canonical differential systems. Includes many varied applications of the general theory.
Author |
: Leonid D. Akulenko |
Publisher |
: CRC Press |
Total Pages |
: 260 |
Release |
: 2004-10-15 |
ISBN-10 |
: 9781134390229 |
ISBN-13 |
: 113439022X |
Rating |
: 4/5 (29 Downloads) |
Synopsis High-Precision Methods in Eigenvalue Problems and Their Applications by : Leonid D. Akulenko
This book presents a survey of analytical, asymptotic, numerical, and combined methods of solving eigenvalue problems. It considers the new method of accelerated convergence for solving problems of the Sturm-Liouville type as well as boundary-value problems with boundary conditions of the first, second, and third kind. The authors also present high
Author |
: Mitsuhiro T. Nakao |
Publisher |
: Springer Nature |
Total Pages |
: 469 |
Release |
: 2019-11-11 |
ISBN-10 |
: 9789811376696 |
ISBN-13 |
: 9811376697 |
Rating |
: 4/5 (96 Downloads) |
Synopsis Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations by : Mitsuhiro T. Nakao
In the last decades, various mathematical problems have been solved by computer-assisted proofs, among them the Kepler conjecture, the existence of chaos, the existence of the Lorenz attractor, the famous four-color problem, and more. In many cases, computer-assisted proofs have the remarkable advantage (compared with a “theoretical” proof) of additionally providing accurate quantitative information. The authors have been working more than a quarter century to establish methods for the verified computation of solutions for partial differential equations, mainly for nonlinear elliptic problems of the form -∆u=f(x,u,∇u) with Dirichlet boundary conditions. Here, by “verified computation” is meant a computer-assisted numerical approach for proving the existence of a solution in a close and explicit neighborhood of an approximate solution. The quantitative information provided by these techniques is also significant from the viewpoint of a posteriori error estimates for approximate solutions of the concerned partial differential equations in a mathematically rigorous sense. In this monograph, the authors give a detailed description of the verified computations and computer-assisted proofs for partial differential equations that they developed. In Part I, the methods mainly studied by the authors Nakao and Watanabe are presented. These methods are based on a finite dimensional projection and constructive a priori error estimates for finite element approximations of the Poisson equation. In Part II, the computer-assisted approaches via eigenvalue bounds developed by the author Plum are explained in detail. The main task of this method consists of establishing eigenvalue bounds for the linearization of the corresponding nonlinear problem at the computed approximate solution. Some brief remarks on other approaches are also given in Part III. Each method in Parts I and II is accompanied by appropriate numerical examples that confirm the actual usefulness of the authors’ methods. Also in some examples practical computer algorithms are supplied so that readers can easily implement the verification programs by themselves.