Download or read book An Analysis of Some Direct Methods for the Numerical Solution of Singular Integral Equations written by Ezio Venturino and published by . This book was released on 1984 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Numerical Solution of Singular Integral Equations Arising in Mixed Boundary Value Problems of Elasticity written by R. P. Srivastav and published by . This book was released on 1983 with total page 6 pages. Available in PDF, EPUB and Kindle. Book excerpt: The central theme of this project was the development and analysis of direct methods, based on collocation for the solution of singular integral equations with a principal value integral. These equations arise in such diverse fields as linear elastic fracture mechanics, neutron transport, long water waves, image reconstruction and radiative transfer. In the classical approach, the singular integral equation is regularized to yield a Fredholm integral equation of the second kind. The numerical implementation of the regularization is usually quite cumbersome. While direct methods proposed by Erdogan. Erdogan and Gupta, and Theocaris and Ioakimidis have been used in Fracture Mechanics, their convergence and stability has received scant attention. The work at Stony Brook has made important strides in both directions. The author analyzed the behavior of approximate solutions enhancing our understanding of the convergence and stability of the methods based on Gaussian quadrature. He has also proposed methods which can be employed in the situations where the Gaussian quadrature-collocation schemes fail. (Author).
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 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.
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:
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.
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.
Download or read book A direct Method for the Study of Singular Integral Equations written by Fred Marion Wright and published by . This book was released on 1949 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book Direct Methods for the Approximate Solution of Singular Integral Equations written by Erica Jen and published by . This book was released on 1981 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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
Download or read book Singular Integral Equations Methods for the Analysis of Microwave Structures written by Liudmila Nickelson and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-11-05 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes the solution of electrodynamic boundary problems, which arose in the practical life of a designer. It presents the results of computations of microstrip lines on magnetized (longitudinally and transversally) ferrite and semiconductor substrates taking into account all the geometric sizes. The book will be useful for students, engineers, designers and researchers. It contains a lot of computed results, which are verified experimentally and can be used immediately.
Download or read book Modern Mathematical Methods and High Performance Computing in Science and Technology written by Vinai K. Singh and published by Springer. This book was released on 2016-08-06 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book discusses important results in modern mathematical models and high performance computing, such as applied operations research, simulation of operations, statistical modeling and applications, invisibility regions and regular meta-materials, unmanned vehicles, modern radar techniques/SAR imaging, satellite remote sensing, coding, and robotic systems. Furthermore, it is valuable as a reference work and as a basis for further study and research. All contributing authors are respected academicians, scientists and researchers from around the globe. All the papers were presented at the international conference on Modern Mathematical Methods and High Performance Computing in Science & Technology (M3HPCST 2015), held at Raj Kumar Goel Institute of Technology, Ghaziabad, India, from 27–29 December 2015, and peer-reviewed by international experts. The conference provided an exceptional platform for leading researchers, academicians, developers, engineers and technocrats from a broad range of disciplines to meet and discuss state-of-the-art mathematical methods and high performance computing in science & technology solutions. This has brought new prospects for collaboration across disciplines and ideas that facilitate novel breakthroughs.
Download or read book Analytical and Numerical Methods for Volterra Equations written by Peter Linz and published by SIAM. This book was released on 1985-01-01 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents an aspect of activity in integral equations methods for the solution of Volterra equations for those who need to solve real-world problems. Since there are few known analytical methods leading to closed-form solutions, the emphasis is on numerical techniques. The major points of the analytical methods used to study the properties of the solution are presented in the first part of the book. These techniques are important for gaining insight into the qualitative behavior of the solutions and for designing effective numerical methods. The second part of the book is devoted entirely to numerical methods. The author has chosen the simplest possible setting for the discussion, the space of real functions of real variables. The text is supplemented by examples and exercises.
Download or read book Computational Methods for Integral Equations written by L. M. Delves and published by CUP Archive. This book was released on 1985 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides a readable account of techniques for numerical solutions.
