Integral Equations And Numerical Methods

Author : Michael A. Golberg
Publisher : Springer Science & Business Media
Page : 428 pages
File Size : 42,8 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 : Tofigh Allahviranloo,Armin Esfandiari
Publisher : Unknown
Page : 0 pages
File Size : 54,7 Mb
Release : 2022
Category : Electronic
ISBN : 3030853519

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A Course on Integral Equations with Numerical Analysis by Tofigh Allahviranloo,Armin Esfandiari Pdf

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 : Kendall E. Atkinson
Publisher : Cambridge University Press
Page : 572 pages
File Size : 45,9 Mb
Release : 1997-06-28
Category : Mathematics
ISBN : 9780521583916

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The Numerical Solution of Integral Equations of the Second Kind by Kendall E. Atkinson Pdf

This book provides an extensive introduction to the numerical solution of a large class of integral equations.

Author : Karl F. Warnick
Publisher : Artech House
Page : 234 pages
File Size : 55,9 Mb
Release : 2008
Category : Mathematics
ISBN : 9781596933347

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Numerical Analysis for Electromagnetic Integral Equations by Karl F. Warnick Pdf

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 : London Mathematical Society
Publisher : Unknown
Page : 520 pages
File Size : 55,9 Mb
Release : 1982
Category : Mathematics
ISBN : UCAL:B4360098

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Treatment of Integral Equations by Numerical Methods by London Mathematical Society Pdf

Author : L. M. Delves,J. L. Mohamed
Publisher : CUP Archive
Page : 392 pages
File Size : 43,5 Mb
Release : 1985
Category : Mathematics
ISBN : 0521357969

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Computational Methods for Integral Equations by L. M. Delves,J. L. Mohamed Pdf

This textbook provides a readable account of techniques for numerical solutions.

Author : Wolfgang Hackbusch
Publisher : Birkhäuser
Page : 377 pages
File Size : 48,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034892155

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Integral Equations by Wolfgang Hackbusch Pdf

The theory of integral equations has been an active research field for many years and is based on analysis, function theory, and functional analysis. On the other hand, integral equations are of practical interest because of the «boundary integral equation method», which transforms partial differential equations on a domain into integral equations over its boundary. This book grew out of a series of lectures given by the author at the Ruhr-Universitat Bochum and the Christian-Albrecht-Universitat zu Kiel to students of mathematics. The contents of the first six chapters correspond to an intensive lecture course of four hours per week for a semester. Readers of the book require background from analysis and the foundations of numeri cal mathematics. Knowledge of functional analysis is helpful, but to begin with some basic facts about Banach and Hilbert spaces are sufficient. The theoretical part of this book is reduced to a minimum; in Chapters 2, 4, and 5 more importance is attached to the numerical treatment of the integral equations than to their theory. Important parts of functional analysis (e. g. , the Riesz-Schauder theory) are presented without proof. We expect the reader either to be already familiar with functional analysis or to become motivated by the practical examples given here to read a book about this topic. We recall that also from a historical point of view, functional analysis was initially stimulated by the investigation of integral equations.

Author : M. A. Goldberg
Publisher : Springer Science & Business Media
Page : 350 pages
File Size : 47,8 Mb
Release : 2013-11-21
Category : Science
ISBN : 9781475714661

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Solution Methods for Integral Equations by M. A. Goldberg Pdf

Author : Tofigh Allahviranloo,Armin Esfandiari
Publisher : Springer Nature
Page : 222 pages
File Size : 52,5 Mb
Release : 2021-10-30
Category : Technology & Engineering
ISBN : 9783030853501

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A Course on Integral Equations with Numerical Analysis by Tofigh Allahviranloo,Armin Esfandiari Pdf

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,Pratap Puri
Publisher : Springer Science & Business Media
Page : 525 pages
File Size : 47,9 Mb
Release : 2011-06-28
Category : Mathematics
ISBN : 9781461201014

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Computational Methods for Linear Integral Equations by Prem Kythe,Pratap Puri Pdf

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 : Peter Linz
Publisher : SIAM
Page : 240 pages
File Size : 54,8 Mb
Release : 1985-01-01
Category : Mathematics
ISBN : 1611970857

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Analytical and Numerical Methods for Volterra Equations by Peter Linz Pdf

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.

Author : Christopher T. H. Baker
Publisher : Oxford University Press, USA
Page : 1056 pages
File Size : 48,6 Mb
Release : 1977
Category : Business & Economics
ISBN : UCSD:31822011360195

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The Numerical Treatment of Integral Equations by Christopher T. H. Baker Pdf

Author : Svetlin G. Georgiev
Publisher : Springer
Page : 402 pages
File Size : 46,5 Mb
Release : 2016-10-30
Category : Mathematics
ISBN : 9789462392281

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Integral Equations on Time Scales by Svetlin G. Georgiev Pdf

This book offers the reader an overview of recent developments of integral equations on time scales. It also contains elegant analytical and numerical methods. This book is primarily intended for senior undergraduate students and beginning graduate students of engineering and science courses. The students in mathematical and physical sciences will find many sections of direct relevance. The book contains nine chapters and each chapter is pedagogically organized. This book is specially designed for those who wish to understand integral equations on time scales without having extensive mathematical background.

Author : Sergej Rjasanow,Olaf Steinbach
Publisher : Springer Science & Business Media
Page : 285 pages
File Size : 46,7 Mb
Release : 2007-04-17
Category : Mathematics
ISBN : 9780387340425

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The Fast Solution of Boundary Integral Equations by Sergej Rjasanow,Olaf Steinbach Pdf

This book provides a detailed description of fast boundary element methods, all based on rigorous mathematical analysis. In particular, the authors use a symmetric formulation of boundary integral equations as well as discussing Galerkin discretisation. All the necessary related stability and error estimates are derived. The authors therefore describe the Adaptive Cross Approximation Algorithm, starting from the basic ideas and proceeding to their practical realization. Numerous examples representing standard problems are given.

Author : Peter Junghanns,Giuseppe Mastroianni,Incoronata Notarangelo
Publisher : Springer Nature
Page : 662 pages
File Size : 55,9 Mb
Release : 2021-08-10
Category : Mathematics
ISBN : 9783030774974

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Weighted Polynomial Approximation and Numerical Methods for Integral Equations by Peter Junghanns,Giuseppe Mastroianni,Incoronata Notarangelo Pdf

The book presents a combination of two topics: one coming from the theory of approximation of functions and integrals by interpolation and quadrature, respectively, and the other from the numerical analysis of operator equations, in particular, of integral and related equations. The text focusses on interpolation and quadrature processes for functions defined on bounded and unbounded intervals and having certain singularities at the endpoints of the interval, as well as on numerical methods for Fredholm integral equations of first and second kind with smooth and weakly singular kernel functions, linear and nonlinear Cauchy singular integral equations, and hypersingular integral equations. The book includes both classic and very recent results and will appeal to graduate students and researchers who want to learn about the approximation of functions and the numerical solution of operator equations, in particular integral equations.