Download or read book Numerical Solution of Sturm Liouville Problems written by John Derwent Pryce and published by . This book was released on 1993 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sturm-Liouville problems (SLPs)--an applied mathematics tool developed in the nineteenth century and a driving force of pure mathematics in the early twentieth century--became of vital interest to physicists with the advent of Schrodinger's equations. Today's fascinating variety of SL-related computations reflects this diverse historical background. This book was written for scientists and engineers who desire an introduction to simple SLPs, their limitations, the algorithms that overcome these limitations, and available software. Numerical analysts seeking a reference on good SLP methods, theory, implementation, and performance will also want to own a copy of this book. Treatments of the underlying mathematical theories and numerous helpful problems round out this superb new volume.
Download or read book Sturm Liouville Problems written by Ronald B. Guenther and published by CRC Press. This book was released on 2018-10-25 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sturm-Liouville problems arise naturally in solving technical problems in engineering, physics, and more recently in biology and the social sciences. These problems lead to eigenvalue problems for ordinary and partial differential equations. Sturm-Liouville Problems: Theory and Numerical Implementation addresses, in a unified way, the key issues that must be faced in science and engineering applications when separation of variables, variational methods, or other considerations lead to Sturm-Liouville eigenvalue problems and boundary value problems.
Download or read book Direct and Inverse Sturm Liouville Problems written by Vladislav V. Kravchenko and published by Birkhäuser. This book was released on 2020-08-18 with total page 154 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 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 Elementary Differential Equations with Boundary Value Problems written by William F. Trench and published by Thomson Brooks/Cole. This book was released on 2001 with total page 766 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written in a clear and accurate language that students can understand, Trench's new book minimizes the number of explicitly stated theorems and definitions. Instead, he deals with concepts in a conversational style that engages students. He includes more than 250 illustrated, worked examples for easy reading and comprehension. One of the book's many strengths is its problems, which are of consistently high quality. Trench includes a thorough treatment of boundary-value problems and partial differential equations and has organized the book to allow instructors to select the level of technology desired. This has been simplified by using symbols, C and L, to designate the level of technology. C problems call for computations and/or graphics, while L problems are laboratory exercises that require extensive use of technology. Informal advice on the use of technology is included in several sections and instructors who prefer not to emphasize technology can ignore these exercises without interrupting the flow of material.
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 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 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 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 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.
Download or read book Numerical Solution of Sturm Liouville Problems Via Fer Streamers written by Alberto Gil Couto Pimentel Ramos and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Numerical Solution of Differential Equations written by Zhilin Li and published by Cambridge University Press. This book was released on 2017-11-30 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: A practical and concise guide to finite difference and finite element methods. Well-tested MATLAB® codes are available online.
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 Partial Differential Equations and Boundary Value Problems with Applications written by Mark A. Pinsky and published by American Mathematical Soc.. This book was released on 2011 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: Building on the basic techniques of separation of variables and Fourier series, the book presents the solution of boundary-value problems for basic partial differential equations: the heat equation, wave equation, and Laplace equation, considered in various standard coordinate systems--rectangular, cylindrical, and spherical. Each of the equations is derived in the three-dimensional context; the solutions are organized according to the geometry of the coordinate system, which makes the mathematics especially transparent. Bessel and Legendre functions are studied and used whenever appropriate throughout the text. The notions of steady-state solution of closely related stationary solutions are developed for the heat equation; applications to the study of heat flow in the earth are presented. The problem of the vibrating string is studied in detail both in the Fourier transform setting and from the viewpoint of the explicit representation (d'Alembert formula). Additional chapters include the numerical analysis of solutions and the method of Green's functions for solutions of partial differential equations. The exposition also includes asymptotic methods (Laplace transform and stationary phase). With more than 200 working examples and 700 exercises (more than 450 with answers), the book is suitable for an undergraduate course in partial differential equations.
Download or read book Fourier Series and Numerical Methods for Partial Differential Equations written by Richard Bernatz and published by John Wiley & Sons. This book was released on 2010-07-30 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: The importance of partial differential equations (PDEs) in modeling phenomena in engineering as well as in the physical, natural, and social sciences is well known by students and practitioners in these fields. Striking a balance between theory and applications, Fourier Series and Numerical Methods for Partial Differential Equations presents an introduction to the analytical and numerical methods that are essential for working with partial differential equations. Combining methodologies from calculus, introductory linear algebra, and ordinary differential equations (ODEs), the book strengthens and extends readers' knowledge of the power of linear spaces and linear transformations for purposes of understanding and solving a wide range of PDEs. The book begins with an introduction to the general terminology and topics related to PDEs, including the notion of initial and boundary value problems and also various solution techniques. Subsequent chapters explore: The solution process for Sturm-Liouville boundary value ODE problems and a Fourier series representation of the solution of initial boundary value problems in PDEs The concept of completeness, which introduces readers to Hilbert spaces The application of Laplace transforms and Duhamel's theorem to solve time-dependent boundary conditions The finite element method, using finite dimensional subspaces The finite analytic method with applications of the Fourier series methodology to linear version of non-linear PDEs Throughout the book, the author incorporates his own class-tested material, ensuring an accessible and easy-to-follow presentation that helps readers connect presented objectives with relevant applications to their own work. Maple is used throughout to solve many exercises, and a related Web site features Maple worksheets for readers to use when working with the book's one- and multi-dimensional problems. Fourier Series and Numerical Methods for Partial Differential Equations is an ideal book for courses on applied mathematics and partial differential equations at the upper-undergraduate and graduate levels. It is also a reliable resource for researchers and practitioners in the fields of mathematics, science, and engineering who work with mathematical modeling of physical phenomena, including diffusion and wave aspects.
Download or read book Advances in High Performance Computing written by Ivan Dimov and published by Springer Nature. This book was released on 2020-08-07 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: Every day we need to solve large problems for which supercomputers are needed. High performance computing (HPC) is a paradigm that allows to efficiently implement large-scale computational tasks on powerful supercomputers unthinkable without optimization. We try to minimize our effort and to maximize the achieved profit. Many challenging real world problems arising in engineering, economics, medicine and other areas can be formulated as large-scale computational tasks. The volume is a comprehensive collection of extended contributions from the High performance computing conference held in Borovets, Bulgaria, September 2019. This book presents recent advances in high performance computing. The topics of interest included into this volume are: HP software tools, Parallel Algorithms and Scalability, HPC in Big Data analytics, Modelling, Simulation & Optimization in a Data Rich Environment, Advanced numerical methods for HPC, Hybrid parallel or distributed algorithms. The volume is focused on important large-scale applications like Environmental and Climate Modeling, Computational Chemistry and Heuristic Algorithms.
Download or read book High Precision Methods in Eigenvalue Problems and Their Applications written by Leonid D. Akulenko and published by CRC Press. This book was released on 2004-10-15 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
