Download or read book Direct and Inverse Sturm Liouville Problems written by Vladislav V. Kravchenko and published by Springer Nature. This book was released on 2020-07-28 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the most recent developments in the theory and practice of direct and inverse Sturm-Liouville problems on finite and infinite intervals. A universal approach for practical solving of direct and inverse spectral and scattering problems is presented, based on the notion of transmutation (transformation) operators and their efficient construction. Analytical representations for solutions of Sturm-Liouville equations as well as for the integral kernels of the transmutation operators are derived in the form of functional series revealing interesting special features and lending themselves to direct and simple numerical solution of a wide variety of problems. The book is written for undergraduate and graduate students, as well as for mathematicians, physicists and engineers interested in direct and inverse spectral problems.
Download or read book Numerical Solution of the Inverse Sturm Liouville Problem written by Albert Chingkwang Yen and published by . This book was released on 1978 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Numerical Approach to Singular Inverse Sturm liouville Problems written by Michael Allen Siebold and published by . This book was released on 2010 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: Develops the theory necessary to obtain a numerical solution to the inverse Sturm-Liouville problem, which was applied to four test functions.
Download or read book Inverse Sturm Liouville Problems written by B. M. Levitan and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-07-12 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: The interest in inverse problems of spectral analysis has increased considerably in recent years due to the applications to important non-linear equations in mathematical physics. This monograph is devoted to the detailed theory of inverse problems and methods of their solution for the Sturm-Liouville case. Chapters 1--6 contain proofs which are, in many cases, very different from those known earlier. Chapters 4--6 are devoted to inverse problems of quantum scattering theory with attention being focused on physical applications. Chapters 7--11 are based on the author's recent research on the theory of finite- and infinite-zone potentials. A chapter discussing the applications to the Korteweg--de Vries problem is also included. This monograph is important reading for all researchers in the field of mathematics and physics.
Download or read book Inverse Sturm Liouville Problems and Their Applications written by G. Freiling and published by Nova Biomedical Books. This book was released on 2001 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the main results and methods on inverse spectral problems for Sturm-Liouville differential operators and their applications. 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 sciences. Inverse problems also play an important role in solving non-linear evolution equations in mathematical physics. Interest in this subject has been increasing permanently because of the appearance of new important applications, resulting in intensive study of inverse problem theory all over the world.
Download or read book Sturm Liouville Theory written by Werner O. Amrein and published by Springer Science & Business Media. This book was released on 2005-12-05 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Numerical Solutions for Singular Inverse Sturm Liouville Problems written by Gerhard Freiling and published by . This book was released on 2007 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Numerical Methods for Solving Inverse Eigenvalue Problems Classic Reprint written by Jorge Nocedal and published by Forgotten Books. This book was released on 2017-11-26 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from Numerical Methods for Solving Inverse Eigenvalue Problems A slight reformulation of describes the additive inverse eigenvalue problem, which arises in the solution of inverse Sturm Liouville problems. In practice it happens frequently that only some eigenvalues are given. However, for the purpose of analysis it is convenient to consider the case where the number of parameters, eigen values and the order of the matrices is the same. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Download or read book Inverse Problems written by CANNON and published by Birkhäuser. This book was released on 2013-03-13 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume contains manuscripts of lectures or topics related to the lectures which were given at the conference on "Inverse Problems" at the mathematical Research Institute at Oberwolfach. The conference took place during the week of May 18-24, 1986, and was managed by the editors. Recalling Professor Joseph Keller's paper entitled Inverse Problems, American Mathematical Monthly, 83 (1976), we give two direct quotes. "We call two problems inverses of one another if the formulation of each involves all or part of the solution of the other. Often, for historical reasons, one of the two problems has been studied extensively for some time, while the other is newer and not so well understood. In such cases, the former is called the direct problem, while the latter is called the inverse problem. " "The main sources of inverse problems are science and engineering. Often these problems concern the determination of the properties of some inaccess ible regions from observations on the boundary of that region. " Often, inverse problems are not well posed. This increases the difficulty in their analysis and numerical solution. As can be seen from the table of content of this volume, the conference covered inverse problems in scattering theory, seismology, tomography, estimation of coefficients and source terms in parabolic and elliptic differential equations, the inverse Sturm-Liouville problem, and numerical methods. The editors wish to thank Professor M. Barner and his co-workers of the Mathematical Research Institute for their help in creating the conference.
Download or read book Spectral Theory Computational Methods of Sturm Liouville Problems written by Don Hinton and published by CRC Press. This book was released on 2021-02-28 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Formulation and Analysis of Numerical Methods for Inverse Eigenvalue Problems Classic Reprint written by S. Friedland and published by Forgotten Books. This book was released on 2018-02-09 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from The Formulation and Analysis of Numerical Methods for Inverse Eigenvalue Problems Both the additive and multiplicative inverse eigenvalue problems were posed by Down ing and Householder In practical applications of the inverse sturm-liouville and inverse vibrating string problems, only a few of the smallest eigenvalues may be given. In order for the problem to be well-posed, the number of parameters must be reduced accordingly. This can be done by expressing the potential or density function as a linear combination of a few given basis functions. See Osborne (1971) and Hald (1972) for details. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Download or read book Spectral Theory Computational Methods of Sturm Liouville Problems written by Don Hinton and published by CRC Press. This book was released on 1997-05-06 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Inverse Eigenvalue Problems written by Moody Chu and published by Oxford University Press. This book was released on 2005-06-16 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse eigenvalue problems arise in a remarkable variety of applications and associated with any inverse eigenvalue problem are two fundamental questions--the theoretical issue of solvability and the practical issue of computability. Both questions are difficult and challenging. In this text, the authors discuss the fundamental questions, some known results, many applications, mathematical properties, a variety of numerical techniques, as well as several open problems.This is the first book in the authoritative Numerical Mathematics and Scientific Computation series to cover numerical linear algebra, a broad area of numerical analysis. Authored by two world-renowned researchers, the book is aimed at graduates and researchers in applied mathematics, engineering and computer science and makes an ideal graduate text.
Download or read book Sturm Liouville Theory and its Applications written by Mohammed Al-Gwaiz and published by Springer Science & Business Media. This book was released on 2008-01-15 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: Developed from a course taught to senior undergraduates, this book provides a unified introduction to Fourier analysis and special functions based on the Sturm-Liouville theory in L2. The text’s presentation follows a clear, rigorous mathematical style that is highly readable. The author first establishes the basic results of Sturm-Liouville theory and then provides examples and applications to illustrate the theory. The final two chapters, on Fourier and Laplace transformations, demonstrate the use of the Fourier series method for representing functions to integral representations.
Download or read book Sturm Liouville Theory written by Werner O. Amrein and published by Springer Science & Business Media. This book was released on 2005-05-19 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Discontinuous Inverse Sturm liouville Problems with Symmetric Potentials written by Mei Kobayashi and published by . This book was released on 1988 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Sturm Liouville Theory written by Anton Zettl and published by American Mathematical Soc.. This book was released on 2005 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
