Singular Integral Equations And Discrete Vortices

Author : I. K. Lifanov
Publisher : Walter de Gruyter GmbH & Co KG
Page : 488 pages
File Size : 40,8 Mb
Release : 2018-11-05
Category : Mathematics
ISBN : 9783110926040

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Singular Integral Equations and Discrete Vortices by I. K. Lifanov Pdf

This monograph is divided into five parts and opens with elements of the theory of singular integral equation solutions in the class of absolutely integrable and non-integrable functions. The second part deals with elements of potential theory for the Helmholtz equation, especially with the reduction of Dirichlet and Neumann problems for Laplace and Helmholtz equations to singular integral equations. Part three contains methods of calculation for different one-dimensional and two-dimensional singular integrals. In this part, quadrature formulas of discrete vortex pair type in the plane case and closed vortex frame type in the spatial case for singular integrals are described for the first time. These quadrature formulas are applied to numerical solutions of singular integral equations of the 1st and 2nd kind with constant and variable coefficients, in part four of the book. Finally, discrete mathematical models of some problems in aerodynamics, electrodynamics and elasticity theory are given.

Author : S. M. Belotserkovsky,I.K. Lifanov
Publisher : CRC Press
Page : 464 pages
File Size : 47,9 Mb
Release : 1992-12-31
Category : Technology & Engineering
ISBN : 0849393078

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Method of Discrete Vortices by S. M. Belotserkovsky,I.K. Lifanov Pdf

Method of Discrete Vortices presents a mathematical substantiation and in-depth description of numerical methods for solving singular integral equations with one-dimensional and multiple Cauchy integrals. The book also presents the fundamentals of the theory of singular equations and numerical methods as applied to solving problems in such branches of mechanics as aerodynamics, elasticity, and electrodynamics.

Author : Gennadi Vainikko
Publisher : Springer
Page : 169 pages
File Size : 51,9 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540477730

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Multidimensional Weakly Singular Integral Equations by Gennadi Vainikko Pdf

The final aim of the book is to construct effective discretization methods to solve multidimensional weakly singular integral equations of the second kind on a region of Rn e.g. equations arising in the radiation transfer theory. To this end, the smoothness of the solution is examined proposing sharp estimates of the growth of the derivatives of the solution near the boundary G. The superconvergence effect of collocation methods at the collocation points is established. This is a book for graduate students and researchers in the fields of analysis, integral equations, mathematical physics and numerical methods. No special knowledge beyond standard undergraduate courses is assumed.

Author : Ricardo Estrada,Ram P. Kanwal
Publisher : Springer Science & Business Media
Page : 433 pages
File Size : 48,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461213826

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Singular Integral Equations by Ricardo Estrada,Ram P. Kanwal Pdf

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 : N. I. Muskhelishvili,J. R. M. Radok
Publisher : Courier Corporation
Page : 466 pages
File Size : 52,7 Mb
Release : 2008-01-01
Category : Science
ISBN : 9780486462424

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Singular Integral Equations by N. I. Muskhelishvili,J. R. M. Radok Pdf

This high-level treatment considers one-dimensional singular integral equations involving Cauchy principal values, covering Hölder condition, Hilbert and Riemann-Hilbert problems, Dirichlet problems, inversion formulas for arcs, more. 1992 edition.

Author : B. N. Mandal,A. Chakrabarti
Publisher : CRC Press
Page : 270 pages
File Size : 48,7 Mb
Release : 2016-04-19
Category : Mathematics
ISBN : 9781439876213

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Applied Singular Integral Equations by B. N. Mandal,A. Chakrabarti Pdf

The book is devoted to varieties of linear singular integral equations, with special emphasis on their methods of solution. It introduces the singular integral equations and their applications to researchers as well as graduate students of this fascinating and growing branch of applied mathematics.

Author : I.K. Lifanov,L.N. Poltavskii,MG.M. Vainikko
Publisher : CRC Press
Page : 416 pages
File Size : 48,6 Mb
Release : 2003-12-29
Category : Mathematics
ISBN : 9780203402160

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Hypersingular Integral Equations and Their Applications by I.K. Lifanov,L.N. Poltavskii,MG.M. Vainikko Pdf

A number of new methods for solving singular and hypersingular integral equations have emerged in recent years. This volume presents some of these new methods along with classical exact, approximate, and numerical methods. The authors explore the analysis of hypersingular integral equations based on the theory of pseudodifferential operators and co

Author : Nikolaĭ Ivanovich Muskhelishvili
Publisher : Unknown
Page : 447 pages
File Size : 50,5 Mb
Release : 1977
Category : Electronic
ISBN : OCLC:255192241

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Singular Integral Equations by Nikolaĭ Ivanovich Muskhelishvili Pdf

Author : Nikolaĭ Ivanovich Muskhelishvili
Publisher : Courier Dover Publications
Page : 468 pages
File Size : 53,5 Mb
Release : 1992
Category : Boundary value problems
ISBN : CORNELL:31924063601334

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Singular Integral Equations by Nikolaĭ Ivanovich Muskhelishvili Pdf

High-level treatment covers one-dimensional singular integral equations involving Cauchy principal values; coverage includes Holder Condition, Hilbert and Riemann-Hilbert problems, Dirichlet problem, inversion formulae for arcs, and much more. For graduate students, engineers, mathematicians, physicists, more. 1953 edition. Introduction.

Author : Nikolaj I. Muschelišvili
Publisher : Unknown
Page : 447 pages
File Size : 46,5 Mb
Release : 1960
Category : Electronic
ISBN : OCLC:917976039

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Singular Integral Equations by Nikolaj I. Muschelišvili Pdf

Author : Michael A. Golberg
Publisher : Springer Science & Business Media
Page : 428 pages
File Size : 47,7 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781489925930

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Numerical Solution of Integral Equations by Michael A. Golberg Pdf

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 : Christos H. Skiadas,Yiannis Dimotikalis
Publisher : Springer Nature
Page : 560 pages
File Size : 41,8 Mb
Release : 2022-06-13
Category : Science
ISBN : 9783030969646

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14th Chaotic Modeling and Simulation International Conference by Christos H. Skiadas,Yiannis Dimotikalis Pdf

Gathering the proceedings of the 14th CHAOS2021 International Conference, this book highlights recent developments in nonlinear, dynamical and complex systems. The conference was intended to provide an essential forum for Scientists and Engineers to exchange ideas, methods, and techniques in the field of Nonlinear Dynamics, Chaos, Fractals and their applications in General Science and the Engineering Sciences. The respective chapters address key methods, empirical data and computer techniques, as well as major theoretical advances in the applied nonlinear field. Beyond showcasing the state of the art, the book will help academic and industrial researchers alike apply chaotic theory in their studies. Chapter "On the Origin of the Universe: Chaos or Cosmos" is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com

Author : Harendra Singh,Hemen Dutta,Marcelo M. Cavalcanti
Publisher : Springer Nature
Page : 255 pages
File Size : 42,9 Mb
Release : 2021-04-16
Category : Technology & Engineering
ISBN : 9783030655099

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Topics in Integral and Integro-Differential Equations by Harendra Singh,Hemen Dutta,Marcelo M. Cavalcanti Pdf

This book includes different topics associated with integral and integro-differential equations and their relevance and significance in various scientific areas of study and research. Integral and integro-differential equations are capable of modelling many situations from science and engineering. Readers should find several useful and advanced methods for solving various types of integral and integro-differential equations in this book. The book is useful for graduate students, Ph.D. students, researchers and educators interested in mathematical modelling, applied mathematics, applied sciences, engineering, etc. Key Features • New and advanced methods for solving integral and integro-differential equations • Contains comparison of various methods for accuracy • Demonstrates the applicability of integral and integro-differential equations in other scientific areas • Examines qualitative as well as quantitative properties of solutions of various types of integral and integro-differential equations

Author : Johannes Elschner,Israel Gohberg,Bernd Silbermann
Publisher : Birkhäuser
Page : 530 pages
File Size : 53,7 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783034882767

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Problems and Methods in Mathematical Physics by Johannes Elschner,Israel Gohberg,Bernd Silbermann Pdf

This volume presents the proceedings of the 11th Conference on Problems and Methods in Mathematical Physics (11th TMP), held in Chemnitz, March 25-28, 1999. The conference was dedicated to the memory of Siegfried Prössdorf, who made important contributions to the theory and numerical analysis of operator equations and their applications in mathematical physics and mechanics. The main part of the book comprises original research papers. The topics are ranging from integral and pseudodifferential equations, boundary value problems, operator theory, boundary element and wavelet methods, approximation theory and inverse problems to various concrete problems and applications in physics and engineering, and reflect Prössdorf's broad spectrum of research activities. The volume also contains articles describing the life and mathematical achievements of Siegfried Prössdorf and includes a list of his publications. The book is addressed to a wide audience in the mathematical and engineering sciences.

Author : E.G. Ladopoulos
Publisher : Springer Science & Business Media
Page : 569 pages
File Size : 41,6 Mb
Release : 2013-03-09
Category : Technology & Engineering
ISBN : 9783662042915

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Singular Integral Equations by E.G. Ladopoulos Pdf

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.