Download or read book On the Solution of Integral Equations with a Generalized Cauchy Kernal written by and published by . This book was released on 1986 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Integral Equations of First Kind written by A. V. Bitsadze and published by World Scientific. This book was released on 1995 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies classes of linear integral equations of the first kind most often met in applications. Since the general theory of integral equations of the first kind has not been formed yet, the book considers the equations whose solutions either are estimated in quadratures or can be reduced to well-investigated classes of integral equations of the second kind.In this book the theory of integral equations of the first kind is constructed by using the methods of the theory of functions both of real and complex variables. Special attention is paid to the inversion formulas of model equations most often met in physics, mechanics, astrophysics, chemical physics etc. The general theory of linear equations including the Fredholm, the Noether, the Hausdorff theorems, the Hilbert-Schmidt theorem, the Picard theorem and the application of this theory to the solution of boundary problems are given in this book. The book studies the equations of the first kind with the Schwarz Kernel, the Poisson and the Neumann kernels; the Volterra integral equations of the first kind, the Abel equations and some generalizations, one-dimensional and many-dimensional analogues of the Cauchy type integral and some of their applications.

Download or read book Integral Equations written by S. G. Mikhlin and published by Elsevier. This book was released on 2014-07-22 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integral Equations: And their Applications to Certain Problems in Mechanics, Mathematical Physics and Technology, Second Revised Edition contains an account of the general theory of Fredholm and Hilbert-Schmidt. This edition discusses methods of approximate solution of Fredholm's equation and, in particular, their application to the solution of basic problems in mathematical physics, including certain problems in hydrodynamics and the theory of elasticity. Other topics include the equations of Volterra type, determination of the first eigenvalue by Ritz's method, and systems of singular integral equations. The generalized method of Schwarz, convergence of successive approximations, stability of a rod in compression, and mixed problem of the theory of elasticity are also elaborated. This publication is recommended for mathematicians, students, and researchers concerned with singular integral equations.

Download or read book The Classical Theory of Integral Equations written by Stephen M. Zemyan and published by Springer Science & Business Media. This book was released on 2012-07-10 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Classical Theory of Integral Equations is a thorough, concise, and rigorous treatment of the essential aspects of the theory of integral equations. The book provides the background and insight necessary to facilitate a complete understanding of the fundamental results in the field. With a firm foundation for the theory in their grasp, students will be well prepared and motivated for further study. Included in the presentation are: A section entitled Tools of the Trade at the beginning of each chapter, providing necessary background information for comprehension of the results presented in that chapter; Thorough discussions of the analytical methods used to solve many types of integral equations; An introduction to the numerical methods that are commonly used to produce approximate solutions to integral equations; Over 80 illustrative examples that are explained in meticulous detail; Nearly 300 exercises specifically constructed to enhance the understanding of both routine and challenging concepts; Guides to Computation to assist the student with particularly complicated algorithmic procedures. This unique textbook offers a comprehensive and balanced treatment of material needed for a general understanding of the theory of integral equations by using only the mathematical background that a typical undergraduate senior should have. The self-contained book will serve as a valuable resource for advanced undergraduate and beginning graduate-level students as well as for independent study. Scientists and engineers who are working in the field will also find this text to be user friendly and informative.

Download or read book Integral Equations on Time Scales written by Svetlin G. Georgiev and published by Springer. This book was released on 2016-10-30 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers the reader an overview of recent developments of integral equations on time scales. It also contains elegant analytical and numerical methods. This book is primarily intended for senior undergraduate students and beginning graduate students of engineering and science courses. The students in mathematical and physical sciences will find many sections of direct relevance. The book contains nine chapters and each chapter is pedagogically organized. This book is specially designed for those who wish to understand integral equations on time scales without having extensive mathematical background.

Download or read book On the Solution of Integral Equations with Strongly Singular Kernels written by and published by . This book was released on 1986 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Approximation Methods for Solutions of Differential and Integral Equations written by V. K. Dzyadyk and published by VSP. This book was released on 1995 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the result of 20 years of investigations carried out by the author and his colleagues in order to bring closer and, to a certain extent, synthesize a number of well-known results, ideas and methods from the theory of function approximation, theory of differential and integral equations and numerical analysis. The book opens with an introduction on the theory of function approximation and is followed by a new approach to the Fredholm integral equations to the second kind. Several chapters are devoted to the construction of new methods for the effective approximation of solutions of several important integral, and ordinary and partial differential equations. In addition, new general results on the theory of linear differential equations with one regular singular point, as well as applications of the various new methods are discussed.

Download or read book THE SOLUTION OF SOME NON LINEAR INTEGRAL EQUATIONS WITH CAUCHY KERNELS written by and published by . This book was released on 1963 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Lectures on the Theory of Integral Equations written by I. G. Petrovskii and published by Courier Corporation. This book was released on 1996-09-01 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: Simple, clear exposition of the Fredholm theory for integral equations of the second kind of Fredholm type. A brief treatment of the Volterra equation is also included. An outstanding feature is a table comparing finite dimensional spaces to function spaces. ". . . An excellent presentation."—Am. Math. Monthly. Translated from second revised (1951) Russian edition. Bibliography.

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.

Download or read book Numerical Solution of Integral Equations written by Michael A. Golberg and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1979, I edited Volume 18 in this series: Solution Methods for Integral Equations: Theory and Applications. Since that time, there has been an explosive growth in all aspects of the numerical solution of integral equations. By my estimate over 2000 papers on this subject have been published in the last decade, and more than 60 books on theory and applications have appeared. In particular, as can be seen in many of the chapters in this book, integral equation techniques are playing an increas ingly important role in the solution of many scientific and engineering problems. For instance, the boundary element method discussed by Atkinson in Chapter 1 is becoming an equal partner with finite element and finite difference techniques for solving many types of partial differential equations. Obviously, in one volume it would be impossible to present a complete picture of what has taken place in this area during the past ten years. Consequently, we have chosen a number of subjects in which significant advances have been made that we feel have not been covered in depth in other books. For instance, ten years ago the theory of the numerical solution of Cauchy singular equations was in its infancy. Today, as shown by Golberg and Elliott in Chapters 5 and 6, the theory of polynomial approximations is essentially complete, although many details of practical implementation remain to be worked out.

Download or read book Singular Integral Equations written by E.G. Ladopoulos and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 569 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present book deals with the finite-part singular integral equations, the multidimensional singular integral equations and the non-linear singular integral equations, which are currently used in many fields of engineering mechanics with applied character, like elasticity, plasticity, thermoelastoplasticity, viscoelasticity, viscoplasticity, fracture mechanics, structural analysis, fluid mechanics, aerodynamics and elastodynamics. These types of singular integral equations form the latest high technology on the solution of very important problems of solid and fluid mechanics and therefore special attention should be given by the reader of the present book, who is interested for the new technology of the twentieth-one century. Chapter 1 is devoted with a historical report and an extended outline of References, for the finite-part singular integral equations, the multidimensional singular integral equations and the non-linear singular integral equations. Chapter 2 provides a finite-part singular integral representation analysis in Lp spaces and in general Hilbert spaces. In the same Chapter are investigated all possible approximation methods for the numerical evaluation of the finite-part singular integral equations, as closed form solutions for the above type of integral equations are available only in simple cases. Also, Chapter 2 provides further a generalization of the well known Sokhotski-Plemelj formulae and the Nother theorems, for the case of a finite-part singular integral equation.

Download or read book Singular Integrals and Singular Integral Equations with a Cauchy Kernel and the Method of Symmetric Pairing written by Erwin H. Bareiss and published by . This book was released on 1965 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt: The method of symmetric pairing, combined with midpoint integration, is introduced for the numerical evaluation of Hilbert transforms (and the Kramers-Kronig relations) and singular integral equations with a Cauchy kernel. The method, for use on high-speed computers, is simple, reliable, and inexpensive. Numerical examples are presented.

Download or read book The Theory of Approximate Methods and Their Applications to the Numerical Solution of Singular Integral Equations written by A.A. Ivanov and published by Springer Science & Business Media. This book was released on 1976-06-30 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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

Download or read book Integral Equations written by Wolfgang Hackbusch and published by Birkhäuser. This book was released on 2012-12-06 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of integral equations has been an active research field for many years and is based on analysis, function theory, and functional analysis. On the other hand, integral equations are of practical interest because of the «boundary integral equation method», which transforms partial differential equations on a domain into integral equations over its boundary. This book grew out of a series of lectures given by the author at the Ruhr-Universitat Bochum and the Christian-Albrecht-Universitat zu Kiel to students of mathematics. The contents of the first six chapters correspond to an intensive lecture course of four hours per week for a semester. Readers of the book require background from analysis and the foundations of numeri cal mathematics. Knowledge of functional analysis is helpful, but to begin with some basic facts about Banach and Hilbert spaces are sufficient. The theoretical part of this book is reduced to a minimum; in Chapters 2, 4, and 5 more importance is attached to the numerical treatment of the integral equations than to their theory. Important parts of functional analysis (e. g. , the Riesz-Schauder theory) are presented without proof. We expect the reader either to be already familiar with functional analysis or to become motivated by the practical examples given here to read a book about this topic. We recall that also from a historical point of view, functional analysis was initially stimulated by the investigation of integral equations.

Download or read book Generalized Analytic Functions on Riemann Surfaces written by Yuri L. Rodin and published by Springer. This book was released on 2006-11-14 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: