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Author : Kuo-Tong Thau
Publisher :
ISBN 13 :
Total Pages : 324 pages
Book Rating : 4.:/5 (231 download)
Download or read book A Numerical Solution of Abel's Integral Equation in Terms of Fresnel Integrals written by Kuo-Tong Thau and published by . This book was released on 1990 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Rudolf Gorenflo
Publisher : Springer
ISBN 13 : 3540469494
Total Pages : 225 pages
Book Rating : 4.5/5 (44 download)
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.
Author : Michael A. Golberg
Publisher : Springer Science & Business Media
ISBN 13 : 1489925937
Total Pages : 428 pages
Book Rating : 4.4/5 (899 download)
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.
Author : Maxime Bôcher
Publisher :
ISBN 13 :
Total Pages : 88 pages
Book Rating : 4.F/5 ( download)
Download or read book An Introduction to the Study of Integral Equations written by Maxime Bôcher and published by . This book was released on 1914 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Kendall E. Atkinson
Publisher : Cambridge University Press
ISBN 13 : 0521583918
Total Pages : 572 pages
Book Rating : 4.5/5 (215 download)
Download or read book The Numerical Solution of Integral Equations of the Second Kind written by Kendall E. Atkinson and published by Cambridge University Press. This book was released on 1997-06-28 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an extensive introduction to the numerical solution of a large class of integral equations.
Author : Bo Einarsson
Publisher :
ISBN 13 :
Total Pages : 52 pages
Book Rating : 4.E/5 ( download)
Download or read book Numerical Solution of Abel's Integral Equation with Spline Functions (Numerisk Lösning Av Abels Integralekvation Med Ri-funktioner) written by Bo Einarsson and published by . This book was released on 1971 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Rudolf Gorenflo
Publisher :
ISBN 13 : 9783662201886
Total Pages : 232 pages
Book Rating : 4.2/5 (18 download)
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:
Author : Stanisław Lewanowicz
Publisher :
ISBN 13 :
Total Pages : 11 pages
Book Rating : 4.:/5 (82 download)
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:
Author : M. A. Goldberg
Publisher : Springer Science & Business Media
ISBN 13 : 1475714661
Total Pages : 351 pages
Book Rating : 4.4/5 (757 download)
Download or read book Solution Methods for Integral Equations written by M. A. Goldberg and published by Springer Science & Business Media. This book was released on 2013-11-21 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Michael P. Benson
Publisher :
ISBN 13 :
Total Pages : 416 pages
Book Rating : 4.:/5 (89 download)
Download or read book Errors in Numerical Quadrature for Certain Singular Integrands, and the Numerical Solution of Abel Integral Equations written by Michael P. Benson and published by . This book was released on 1973 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : R.S. Anderssen
Publisher : Springer
ISBN 13 : 9789400991323
Total Pages : 270 pages
Book Rating : 4.9/5 (913 download)
Download or read book The application and numerical solution of integral equations written by R.S. Anderssen and published by Springer. This book was released on 2011-11-15 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: This publication reports the proceedings of a one-day seminar on The Application and Numerical Solution of Integral Equations held at the Australian National University on Wednesday, November 29, 1978. It was organized by the Computing Research Group, Australian National University and the Division of Mathematics and Statistics, CSIRO. Due to unforeseen circumstances, Dr M.L. Dow was unable to participate. At short notice, Professor D. Elliott reviewed Cauchy singular integral equations, but a paper on same is not included in these proceedings. The interested reader is referred to the recent translation of V.V. Ivanov, The Theory of Approximate Methods and their Application to the Numerical Solution of Singular Integral Equations, Noordhoff International Publishers, Leyden, 1976. An attempt was made to structure the program to the extent that the emphasis was on the numerical solution of integral equations for which known applications exist along with explanations of how and why integral equation formalisms arise. In addition, the programme reflected the broad classification of most integral equations as either singular or non singular, as either Fredholm or Volterra and as either first or second kind.
Author : Robert S. Anderssen
Publisher :
ISBN 13 :
Total Pages : 56 pages
Book Rating : 4.:/5 (227 download)
Download or read book Application and Numerical Solution of Abel-Type Integral Equations written by Robert S. Anderssen and published by . This book was released on 1977 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper reviews the numerous applications in which the solution of equations like the Abel-type integral equation for discrete observational data (d sub i) is the basic step, compares, with respect to given discrete observational data (d sub i), the use of pseudo-analytic methods and the direct evaluation of its inversion formulas as a basis for solving this equation, proposes a specific algorithm based on these conclusions, and examines the consequences of the fact that, for the equation, linear functionals defined on its solution u(x) can be redefined as linear functionals on the data s(y). The justification for the latter is that, in applications involving separable first kind Abel-type integral equations, inferences are usually based on (linear) functionals defined on u(x), not on u(x) itself. This point is illustrated with an example from metallurgy.
Author : Ricardo Estrada
Publisher : Springer Science & Business Media
ISBN 13 : 1461213827
Total Pages : 433 pages
Book Rating : 4.4/5 (612 download)
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
Author : R. S. Anderssen
Publisher :
ISBN 13 :
Total Pages : 42 pages
Book Rating : 4.:/5 (897 download)
Download or read book Application and Numerical Solution of Abel-type Integral Equations written by R. S. Anderssen and published by . This book was released on 1982 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Andrei D. Polyanin
Publisher : CRC Press
ISBN 13 : 9780849328763
Total Pages : 816 pages
Book Rating : 4.3/5 (287 download)
Download or read book Handbook of Integral Equations written by Andrei D. Polyanin and published by CRC Press. This book was released on 1998-03-31 with total page 816 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integral equations are encountered in various fields of science and in numerous applications, including elasticity, plasticity, heat and mass transfer, oscillation theory, fluid dynamics, filtration theory, electrostatics, electrodynamics, biomechanics, game theory, control, queuing theory, electrical engineering, economics, and medicine. Exact (closed-form) solutions of integral equations play an important role in the proper understanding of qualitative features of many phenomena and processes in various areas of natural science. Equations of physics, chemistry, and biology contain functions or parameters obtained from experiments - hence, they are not strictly fixed. Therefore, it is expedient to choose the structure of these functions for more easily analyzing and solving the equation. As a possible selection criterion, one may adopt the requirement that the model integral equation admit a solution in a closed form. Exact solutions can be used to verify the consistency and estimate errors of various numerical, asymptotic, and approximate methods. The first part of Handbook of Integral Equations: Contains more than 2,100 integral equations and their solutions Includes many new exact solutions to linear and nonlinear equations Addresses equations of general form, which depend on arbitrary functions Other equations contain one or more free parameters (the book actually deals with families of integral equations); the reader has the option to fix these parameters. The second part of the book - chapters 7 through 14 - presents exact, approximate analytical, and numerical methods for solving linear and nonlinear integral equations. Apart from the classical methods, the text also describes some new methods. When selecting the material, the authors emphasize practical aspects of the matter, specifically for methods that allow an effective "constructing" of the solution. Each section provides examples of applicatio
Author : Douglas William Nychka
Publisher :
ISBN 13 :
Total Pages : 534 pages
Book Rating : 4.:/5 (89 download)
Download or read book The Solution of Abel-type Integral Equations with an Application in Stereology written by Douglas William Nychka and published by . This book was released on 1983 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher :
ISBN 13 :
Total Pages : 730 pages
Book Rating : 4.F/5 ( download)
Download or read book Dissertation Abstracts International written by and published by . This book was released on 1990 with total page 730 pages. Available in PDF, EPUB and Kindle. Book excerpt:
