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Generalized Abels Integral Equation
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Book Synopsis Abel Integral Equations by : Rudolf Gorenflo
Download or read book Abel Integral Equations written by Rudolf Gorenflo and published by Springer. This book was released on 2006-11-14 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: In many fields of application of mathematics, progress is crucially dependent on the good flow of information between (i) theoretical mathematicians looking for applications, (ii) mathematicians working in applications in need of theory, and (iii) scientists and engineers applying mathematical models and methods. The intention of this book is to stimulate this flow of information. In the first three chapters (accessible to third year students of mathematics and physics and to mathematically interested engineers) applications of Abel integral equations are surveyed broadly including determination of potentials, stereology, seismic travel times, spectroscopy, optical fibres. In subsequent chapters (requiring some background in functional analysis) mapping properties of Abel integral operators and their relation to other integral transforms in various function spaces are investi- gated, questions of existence and uniqueness of solutions of linear and nonlinear Abel integral equations are treated, and for equations of the first kind problems of ill-posedness are discussed. Finally, some numerical methods are described. In the theoretical parts, emphasis is put on the aspects relevant to applications.
Book Synopsis Generalized Abel's Integral Equation ... by : Donald Lee Schmidt
Download or read book Generalized Abel's Integral Equation ... written by Donald Lee Schmidt and published by . This book was released on 1955 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Boundary Value Problems by : F. D. Gakhov
Download or read book Boundary Value Problems written by F. D. Gakhov and published by Elsevier. This book was released on 2014-07-10 with total page 585 pages. Available in PDF, EPUB and Kindle. Book excerpt: Boundary Value Problems is a translation from the Russian of lectures given at Kazan and Rostov Universities, dealing with the theory of boundary value problems for analytic functions. The emphasis of the book is on the solution of singular integral equations with Cauchy and Hilbert kernels. Although the book treats the theory of boundary value problems, emphasis is on linear problems with one unknown function. The definition of the Cauchy type integral, examples, limiting values, behavior, and its principal value are explained. The Riemann boundary value problem is emphasized in considering the theory of boundary value problems of analytic functions. The book then analyzes the application of the Riemann boundary value problem as applied to singular integral equations with Cauchy kernel. A second fundamental boundary value problem of analytic functions is the Hilbert problem with a Hilbert kernel; the application of the Hilbert problem is also evaluated. The use of Sokhotski's formulas for certain integral analysis is explained and equations with logarithmic kernels and kernels with a weak power singularity are solved. The chapters in the book all end with some historical briefs, to give a background of the problem(s) discussed. The book will be very valuable to mathematicians, students, and professors in advanced mathematics and geometrical functions.
Book Synopsis Regularization of a generalized Abel integral equation by : Dang Dinh Ang
Download or read book Regularization of a generalized Abel integral equation written by Dang Dinh Ang and published by . This book was released on 1990 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Regularization of a Generalized Abel Integral Equation by : Dang Dinh Ang
Download or read book Regularization of a Generalized Abel Integral Equation written by Dang Dinh Ang and published by . This book was released on 1990 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Singular Integral Equations by : Ricardo Estrada
Download or read book Singular Integral Equations written by Ricardo Estrada and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many physical problems that are usually solved by differential equation techniques can be solved more effectively by integral equation methods. This work focuses exclusively on singular integral equations and on the distributional solutions of these equations. A large number of beautiful mathematical concepts are required to find such solutions, which in tum, can be applied to a wide variety of scientific fields - potential theory, me chanics, fluid dynamics, scattering of acoustic, electromagnetic and earth quake waves, statistics, and population dynamics, to cite just several. An integral equation is said to be singular if the kernel is singular within the range of integration, or if one or both limits of integration are infinite. The singular integral equations that we have studied extensively in this book are of the following type. In these equations f (x) is a given function and g(y) is the unknown function. 1. The Abel equation x x) = l g (y) d 0
Book Synopsis A First Course in Integral Equations by : Abdul-Majid Wazwaz
Download or read book A First Course in Integral Equations written by Abdul-Majid Wazwaz and published by World Scientific. This book was released on 1997 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the subject of integral equations in an accessible manner for a variety of applications. Emphasis is placed on understanding the subject while avoiding the abstract and compact theorems. A distinctive feature of the book is that it introduces the recent powerful and reliable developments in this field, which are not covered in traditional texts. The newly developed decomposition method, the series solution method and the direct computation method are thoroughly implemented, which allows the topic to be far more accessible. The book also includes some of the traditional techniques for comparison.Using the newly developed methods, the author successfully handles Fredholm and Volterra integral equations, singular integral equations, integro-differential equations and nonlinear integral equations, with promising results for linear and nonlinear models. Many examples are given to introduce the material in a clear and thorough fashion. In addition, many exercises are provided to build confidence, ease and skill in using the new methods.This book may be used as a text for advanced undergraduates and graduate students in mathematics and scientific areas, and as a work of reference for research study of differential equations and numerical analysis.
Book Synopsis Singular Integral Equations by : Harendra Singh
Download or read book Singular Integral Equations written by Harendra Singh and published by . This book was released on 2021-04-24 with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many interesting problems of engineering, mechanics, statistics, physics, elasticity, potential theory, plasticity, fluid dynamics, population dynamics, and aero dynamics can be solved by defining in terms of singular integral equations. Singular integral equations have very unusual properties.This book is to explore the basic concepts of singular integral equation (Abel's integral equation, generalized Abel's integral equation, weakly singular (Abel's type) integral equation of second kind and weakly singular (generalized Abel's type) integral equation of second kind in a simple, systematic and easy-to-understand manner. The present book is divided into five chapters.Chapter 1 contains the definition and examples of integral equation, Volterra integral equation, Fredholm integral equation, singular integral equation with Laplace and inverse Laplace transforms. Chapter 2 deals the solution of Abel's integral equation using Laplace transforms with numerical problems. Chapter 3 discusses the solution of generalized Abel's integral equation using Laplace transforms with numerical problems. Chapter 4 discusses the solution of weakly singular (Abel's type) integral equation of second kind using Laplace transforms with numerical problems.Chapter 5 discusses the solution of weakly singular (generalized Abel's type) integral equation of second kind using Laplace transforms with numerical problems.
Book Synopsis On the Numerical Solution of the Generalized Abel Integral Equation by : Stanisław Lewanowicz
Download or read book On the Numerical Solution of the Generalized Abel Integral Equation written by Stanisław Lewanowicz and published by . This book was released on 1988 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numerical Solutions of Realistic Nonlinear Phenomena by : J. A. Tenreiro Machado
Download or read book Numerical Solutions of Realistic Nonlinear Phenomena written by J. A. Tenreiro Machado and published by Springer Nature. This book was released on 2020-02-19 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection covers new aspects of numerical methods in applied mathematics, engineering, and health sciences. It provides recent theoretical developments and new techniques based on optimization theory, partial differential equations (PDEs), mathematical modeling and fractional calculus that can be used to model and understand complex behavior in natural phenomena. Specific topics covered in detail include new numerical methods for nonlinear partial differential equations, global optimization, unconstrained optimization, detection of HIV- Protease, modelling with new fractional operators, analysis of biological models, and stochastic modelling.
Book Synopsis On the theory of generalized Abel integral equations on the half line by : Frank Penzel
Download or read book On the theory of generalized Abel integral equations on the half line written by Frank Penzel and published by . This book was released on 1986 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis On the theory of generalized Abel integral equations on the half-linie by : Frank Penzel
Download or read book On the theory of generalized Abel integral equations on the half-linie written by Frank Penzel and published by . This book was released on 1986 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis An Operational Method for Solving Generalized Abel Integral Equations of Second Kind by : Rudolf Gorenflo
Download or read book An Operational Method for Solving Generalized Abel Integral Equations of Second Kind written by Rudolf Gorenflo and published by . This book was released on 1995 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Abel’s Theorem in Problems and Solutions by : V.B. Alekseev
Download or read book Abel’s Theorem in Problems and Solutions written by V.B. Alekseev and published by Springer Science & Business Media. This book was released on 2007-05-08 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: Do formulas exist for the solution to algebraical equations in one variable of any degree like the formulas for quadratic equations? The main aim of this book is to give new geometrical proof of Abel's theorem, as proposed by Professor V.I. Arnold. The theorem states that for general algebraical equations of a degree higher than 4, there are no formulas representing roots of these equations in terms of coefficients with only arithmetic operations and radicals. A secondary, and more important aim of this book, is to acquaint the reader with two very important branches of modern mathematics: group theory and theory of functions of a complex variable. This book also has the added bonus of an extensive appendix devoted to the differential Galois theory, written by Professor A.G. Khovanskii. As this text has been written assuming no specialist prior knowledge and is composed of definitions, examples, problems and solutions, it is suitable for self-study or teaching students of mathematics, from high school to graduate.
Book Synopsis Abel Integral Equations by : Rudolf Gorenflo
Download or read book Abel Integral Equations written by Rudolf Gorenflo and published by . This book was released on 2014-01-15 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Systems of Generalized Abel Integral Equations with Applications to Simultaneous Dual Relations by : J. R. Walton
Download or read book Systems of Generalized Abel Integral Equations with Applications to Simultaneous Dual Relations written by J. R. Walton and published by . This book was released on 1977 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt: A method is presented for solving certain systems of generalized Abel integral equations by constructing equivalent singular integral equations and their corresponding Riemann boundary value problems. An application is then given to a class of simultaneous dual relations of a type arising in bimedia fracture problems in elasticity and viscoelasticity. The equations discussed in this paper are a generalization of those considered earlier.
Book Synopsis Systems of Generalized Abel Integral Equations by : M. Lowengrub
Download or read book Systems of Generalized Abel Integral Equations written by M. Lowengrub and published by . This book was released on 1977 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt: A method is presented for solving systems of generalized Abel integral equations by reduction to equivalent coupled Riemann-Hilbert boundary value problems. It is demonstrated how the Riemann system may be uncoupled and closed form solutions computed. An application is then given to solving certain simultaneous dual relations which arise in bimedia fracture problems in elasticity. (Author).
