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Integral equations form an important class of problems, arising frequently in engineering, and in mathematical and scientific analysis. This textbook provides an up-to-date and readable account of techniques for their numerical solution. The authors devote their attention primarily to efficient techniques using high order approximations, taking particular account of situations where singularities are present. The classes of problems which arise frequently in practice, Fredholm of the first and second kind and eigenvalue problems, are dealt with in depth. Some knowledge of numerical methods and linear algebra is assumed, but the book includes introductory sections on numerical quadrature and function space concepts. ... Read more

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Computational Methods for Integral Equations
I need th chapter 4.4 & 5.5 of this book ... Read more

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This volume, dedicated to Bernd Silbermann on his sixtieth birthday, collects research articles on Toeplitz matrices and singular integral equations written by leading area experts.

The subjects of the contributions include Banach algebraic methods, Toeplitz determinants and random matrix theory, Fredholm theory and numerical analysis for singular integral equations, and efficient algorithms for linear systems with structured matrices, and reflect Bernd Silbermann's broad spectrum of research interests. The volume also contains a biographical essay and a list of publications.

The book is addressed to a wide audience in the mathematical and engineering sciences. The articles are carefully written and are accessible to motivated readers with basic knowledge in functional analysis and operator theory. ... Read more

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This book describes the solution of electrodynamic boundary problems, which arose in the practical life of a designer. Only a few problems can be solved analytically and some of these solutions are given in the book, for example, the computation of a strip line in a rectangular or circular cylinder capacitance. Practical lines' configurations require computational work. As the authors' practice shows, the use of Green functions, leading to singular integral equations, is a powerful and pretty universal method to solve different boundary problems, including electrodynamic ones. The book 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 properties of gyrotropic media are described in the book for the reader's convenience. The geometrical shape may be practically any. The integral equations are exact and give the proper field near the edges. Actually, the use of singular integral equations reduces the experimental verification to minimum. 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. ... Read more

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This volume presents a state-of-the-art account of the theoryand applications of integral equations of convolution type, and ofcertain classes of integro-differential and non-linear integralequations. An extensive and well-motivated discussion of some openquestions and of various important directions for further research isalso presented. The book has been written so as to be self-contained,and includes a list of symbols with their definitions.
For users of convolution integral equations, the volume containsnumerous, well-classified inversion tables which correspond to thevarious convolutions and intervals of integration. It also has anextensive, up-to-date bibliography. The convolution integral equationswhich are considered arise naturally from a large variety of physicalsituations and it is felt that the types of solutions discussed willbe usefull in many diverse disciplines of applied mathematics andmathematical physical.
For researchers and graduate students in the mathematical and physicalsciences whose work involves the solution of integral equations.
... Read more

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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 and exact, approximate, and numerical methods. The authors explore the analysis of hypersingular integral equations based on the theory of pseudodifferential operators and consider one-, two- and multi-dimensional integral equations. The text also presents the discrete closed vortex frame method and some other numerical methods for solving hypersingular integral equations. The treatment includes applications to problems in areas such as aerodynamics, elasticity, diffraction, and heat and mass transfer. ... Read more

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This volume presents a valuable and comprehensive collection ofproblems and exercises, together with guidelines and worked solutions,of a wide range of the most important commonly occurring differentialand integral equations.
The book is divided into two parts. Part I, which comprises eightchapters, contains the problems and exercises, and Part II, havingeight corresponding chapters, presents the worked solutions.
The various chapters deal, respectively, with: (1) the classical typeof differential equations of first and higher order; (2) problemsrelating to existence and uniqueness theorems; (3) linear differentialequations; (4) the method of the Laplace transform; (5) integral andintegro-differential equations; (6) numerical and approximationmethods; and (7) first-order partial differential equations. The finalchapter (8) presents a miscellaneous selection of problems andexercises dealing with the deepest areas of differential, integral andpartial differential equations.
Many of the problems discussed are original, and all have been triedand tested in a teaching environment.
This volume provides an invaluable guide to the solving ofdifferential and integral equations and can be recommended to allresearchers, students and teachers, whose work involves thisfundamental aspect of mathematics. ... Read more

Product Description
This monograph is a cumulation mainly of the author's researchover a period of more than ten years and offers easily verifiableexistence criteria for differential, difference and integral equationsover the infinite interval. An important feature of this monograph isthe illustration of almost all results with examples. This book shouldturn out to be a stimulus to the further development of thetheory.Audience: This work will be of interest to mathematicians andgraduate students in the disciplines of theoretical and appliedmathematics. ... Read more