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Singular Integral Equations and Discrete Vortices

Author: I. K. Lifanov

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2018-11-05

Total Pages: 488

ISBN-13: 3110926040

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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.

Book Synopsis Singular Integral Equations and Discrete Vortices by : I. K. Lifanov

Download or read book Singular Integral Equations and Discrete Vortices written by I. K. Lifanov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-11-05 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Method of Discrete Vortices

Author: S. M. Belotserkovsky

Publisher: CRC Press

Published: 1992-12-31

Total Pages: 464

ISBN-13: 9780849393075

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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.

Book Synopsis Method of Discrete Vortices by : S. M. Belotserkovsky

Download or read book Method of Discrete Vortices written by S. M. Belotserkovsky and published by CRC Press. This book was released on 1992-12-31 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Singular Integral Equations

Author: Ricardo Estrada

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 433

ISBN-13: 1461213827

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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 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

Multidimensional Weakly Singular Integral Equations

Author: Gennadi Vainikko

Publisher: Springer

Published: 2006-11-15

Total Pages: 169

ISBN-13: 354047773X

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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.

Book Synopsis Multidimensional Weakly Singular Integral Equations by : Gennadi Vainikko

Download or read book Multidimensional Weakly Singular Integral Equations written by Gennadi Vainikko and published by Springer. This book was released on 2006-11-15 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Singular Integral Equations

Author: N. I. Muskhelishvili

Publisher: Courier Corporation

Published: 2008-01-01

Total Pages: 466

ISBN-13: 0486462420

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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.

Book Synopsis Singular Integral Equations by : N. I. Muskhelishvili

Download or read book Singular Integral Equations written by N. I. Muskhelishvili and published by Courier Corporation. This book was released on 2008-01-01 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Applied Singular Integral Equations

Author: B. N. Mandal

Publisher: CRC Press

Published: 2016-04-19

Total Pages: 274

ISBN-13: 1439876215

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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.

Book Synopsis Applied Singular Integral Equations by : B. N. Mandal

Download or read book Applied Singular Integral Equations written by B. N. Mandal and published by CRC Press. This book was released on 2016-04-19 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Hypersingular Integral Equations and Their Applications

Author: I.K. Lifanov

Publisher: CRC Press

Published: 2003-12-29

Total Pages: 416

ISBN-13: 0203402162

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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

Book Synopsis Hypersingular Integral Equations and Their Applications by : I.K. Lifanov

Download or read book Hypersingular Integral Equations and Their Applications written by I.K. Lifanov and published by CRC Press. This book was released on 2003-12-29 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Singular Integral Equations

Author: Nikolaĭ Ivanovich Muskhelishvili

Publisher:

Published: 1977

Total Pages: 447

ISBN-13:

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Book Synopsis Singular Integral Equations by : Nikolaĭ Ivanovich Muskhelishvili

Download or read book Singular Integral Equations written by Nikolaĭ Ivanovich Muskhelishvili and published by . This book was released on 1977 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Multidimensional Singular Integrals and Integral Equations

Author: S. G. Mikhlin

Publisher: Elsevier

Published: 2014-07-10

Total Pages: 273

ISBN-13: 1483164497

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Multidimensional Singular Integrals and Integral Equations presents the results of the theory of multidimensional singular integrals and of equations containing such integrals. Emphasis is on singular integrals taken over Euclidean space or in the closed manifold of Liapounov and equations containing such integrals. This volume is comprised of eight chapters and begins with an overview of some theorems on linear equations in Banach spaces, followed by a discussion on the simplest properties of multidimensional singular integrals. Subsequent chapters deal with compounding of singular integrals; properties of the symbol, with particular reference to Fourier transform of a kernel and the symbol of a singular operator; singular integrals in Lp spaces; and singular integral equations. The differentiation of integrals with a weak singularity is also considered, along with the rule for the multiplication of the symbols in the general case. The final chapter describes several applications of multidimensional singular integral equations to boundary problems in mathematical physics. This book will be of interest to mathematicians and students of mathematics.

Book Synopsis Multidimensional Singular Integrals and Integral Equations by : S. G. Mikhlin

Download or read book Multidimensional Singular Integrals and Integral Equations written by S. G. Mikhlin and published by Elsevier. This book was released on 2014-07-10 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multidimensional Singular Integrals and Integral Equations presents the results of the theory of multidimensional singular integrals and of equations containing such integrals. Emphasis is on singular integrals taken over Euclidean space or in the closed manifold of Liapounov and equations containing such integrals. This volume is comprised of eight chapters and begins with an overview of some theorems on linear equations in Banach spaces, followed by a discussion on the simplest properties of multidimensional singular integrals. Subsequent chapters deal with compounding of singular integrals; properties of the symbol, with particular reference to Fourier transform of a kernel and the symbol of a singular operator; singular integrals in Lp spaces; and singular integral equations. The differentiation of integrals with a weak singularity is also considered, along with the rule for the multiplication of the symbols in the general case. The final chapter describes several applications of multidimensional singular integral equations to boundary problems in mathematical physics. This book will be of interest to mathematicians and students of mathematics.

Singular Integral Equations

Author: Nikolaĭ Ivanovich Muskhelishvili

Publisher:

Published: 1946

Total Pages: 447

ISBN-13:

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Book Synopsis Singular Integral Equations by : Nikolaĭ Ivanovich Muskhelishvili

Download or read book Singular Integral Equations written by Nikolaĭ Ivanovich Muskhelishvili and published by . This book was released on 1946 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: