Numerical Solution Of Integral Equations

Author : Michael A. Golberg
Publisher : Springer Science & Business Media
ISBN 13 : 1489925937
Total Pages : 428 pages
Book Rating : 4.30/5 ( download)

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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 : Kendall E. Atkinson
Publisher : Cambridge University Press
ISBN 13 : 0521583918
Total Pages : 572 pages
Book Rating : 4.16/5 ( download)

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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 : M. A. Goldberg
Publisher : Springer Science & Business Media
ISBN 13 : 1475714661
Total Pages : 351 pages
Book Rating : 4.61/5 ( download)

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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 : L. M. Delves
Publisher : CUP Archive
ISBN 13 : 9780521357968
Total Pages : 392 pages
Book Rating : 4.69/5 ( download)

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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.

Author : George C. Sih
Publisher : Springer Science & Business Media
ISBN 13 : 9789001798604
Total Pages : 578 pages
Book Rating : 4.08/5 ( download)

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Download or read book Methods of Analysis and Solutions of Crack Problems written by George C. Sih and published by Springer Science & Business Media. This book was released on 1973-01-31 with total page 578 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is weH known that the traditional failure criteria cannot adequately explain failures which occur at a nominal stress level considerably lower than the ultimate strength of the material. The current procedure for predicting the safe loads or safe useful life of a structural member has been evolved around the discipline oflinear fracture mechanics. This approach introduces the concept of a crack extension force which can be used to rank materials in some order of fracture resistance. The idea is to determine the largest crack that a material will tolerate without failure. Laboratory methods for characterizing the fracture toughness of many engineering materials are now available. While these test data are useful for providing some rough guidance in the choice of materials, it is not clear how they could be used in the design of a structure. The understanding of the relationship between laboratory tests and fracture design of structures is, to say the least, deficient. Fracture mechanics is presently at astandstill until the basic problems of scaling from laboratory models to fuH size structures and mixed mode crack propagation are resolved. The answers to these questions require some basic understanding ofthe theory and will not be found by testing more specimens. The current theory of fracture is inadequate for many reasons. First of aH it can only treat idealized problems where the applied load must be directed normal to the crack plane.

Author : Tofigh Allahviranloo
Publisher :
ISBN 13 : 9783030853518
Total Pages : 0 pages
Book Rating : 4.19/5 ( download)

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Download or read book A Course on Integral Equations with Numerical Analysis written by Tofigh Allahviranloo and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book suggests that the numerical analysis subjects' matter are the important tools of the book topic, because numerical errors and methods have important roles in solving integral equations. Therefore, all needed topics including a brief description of interpolation are explained in the book. The integral equations have many applications in the engineering, medical, and economic sciences, so the present book contains new and useful materials about interval computations including interval interpolations that are going to be used in interval integral equations. The concepts of integral equations are going to be discussed in two directions, analytical concepts, and numerical solutions which both are necessary for these kinds of dynamic systems. The differences between this book with the others are a full discussion of error topics and also using interval interpolations concepts to obtain interval integral equations. All researchers and students in the field of mathematical, computer, and also engineering sciences can benefit the subjects of the book.

Author : Prem Kythe
Publisher : Springer Science & Business Media
ISBN 13 : 1461201012
Total Pages : 525 pages
Book Rating : 4.14/5 ( download)

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Download or read book Computational Methods for Linear Integral Equations written by Prem Kythe and published by Springer Science & Business Media. This book was released on 2011-06-28 with total page 525 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents numerical methods and computational aspects for linear integral equations. Such equations occur in various areas of applied mathematics, physics, and engineering. The material covered in this book, though not exhaustive, offers useful techniques for solving a variety of problems. Historical information cover ing the nineteenth and twentieth centuries is available in fragments in Kantorovich and Krylov (1958), Anselone (1964), Mikhlin (1967), Lonseth (1977), Atkinson (1976), Baker (1978), Kondo (1991), and Brunner (1997). Integral equations are encountered in a variety of applications in many fields including continuum mechanics, potential theory, geophysics, electricity and mag netism, kinetic theory of gases, hereditary phenomena in physics and biology, renewal theory, quantum mechanics, radiation, optimization, optimal control sys tems, communication theory, mathematical economics, population genetics, queue ing theory, and medicine. Most of the boundary value problems involving differ ential equations can be converted into problems in integral equations, but there are certain problems which can be formulated only in terms of integral equations. A computational approach to the solution of integral equations is, therefore, an essential branch of scientific inquiry.

Author : Karl F. Warnick
Publisher : Artech House
ISBN 13 : 1596933348
Total Pages : 234 pages
Book Rating : 4.47/5 ( download)

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Download or read book Numerical Analysis for Electromagnetic Integral Equations written by Karl F. Warnick and published by Artech House. This book was released on 2008 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction -- Surface integral equation formulations and the method of moments -- Error analysis of the EFIE / with W.C. Chew -- Error analysis of the MFIE and CFIE / with C.P. Davis -- Geometrical singularities and the flat strip -- Resonant structures -- Error analysis for 3D problems -- Higher-order basis functions / with A.F. Peterson -- Operator spectra and iterative solution methods.

Author : R.S. Anderssen
Publisher : Springer
ISBN 13 :
Total Pages : 280 pages
Book Rating : 4.91/5 ( download)

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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 1980-03-31 with total page 280 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 : Rainer Kress
Publisher : Springer Science & Business Media
ISBN 13 : 1461495938
Total Pages : 427 pages
Book Rating : 4.32/5 ( download)

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Download or read book Linear Integral Equations written by Rainer Kress and published by Springer Science & Business Media. This book was released on 2013-12-04 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book combines theory, applications, and numerical methods, and covers each of these fields with the same weight. In order to make the book accessible to mathematicians, physicists, and engineers alike, the author has made it as self-contained as possible, requiring only a solid foundation in differential and integral calculus. The functional analysis which is necessary for an adequate treatment of the theory and the numerical solution of integral equations is developed within the book itself. Problems are included at the end of each chapter. For this third edition in order to make the introduction to the basic functional analytic tools more complete the Hahn–Banach extension theorem and the Banach open mapping theorem are now included in the text. The treatment of boundary value problems in potential theory has been extended by a more complete discussion of integral equations of the first kind in the classical Holder space setting and of both integral equations of the first and second kind in the contemporary Sobolev space setting. In the numerical solution part of the book, the author included a new collocation method for two-dimensional hypersingular boundary integral equations and a collocation method for the three-dimensional Lippmann-Schwinger equation. The final chapter of the book on inverse boundary value problems for the Laplace equation has been largely rewritten with special attention to the trilogy of decomposition, iterative and sampling methods Reviews of earlier editions: "This book is an excellent introductory text for students, scientists, and engineers who want to learn the basic theory of linear integral equations and their numerical solution." (Math. Reviews, 2000) "This is a good introductory text book on linear integral equations. It contains almost all the topics necessary for a student. The presentation of the subject matter is lucid, clear and in the proper modern framework without being too abstract." (ZbMath, 1999)