Solution Methods for Integral Equations

Solution Methods for Integral Equations
Title Solution Methods for Integral Equations PDF eBook
Author M. A. Goldberg
Publisher Springer Science & Business Media
Pages 351
Release 2013-11-21
Genre Science
ISBN 1475714661

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Computational Methods for Integral Equations

Computational Methods for Integral Equations
Title Computational Methods for Integral Equations PDF eBook
Author L. M. Delves
Publisher CUP Archive
Pages 392
Release 1985
Genre Mathematics
ISBN 9780521357968

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

The Fast Solution of Boundary Integral Equations

The Fast Solution of Boundary Integral Equations
Title The Fast Solution of Boundary Integral Equations PDF eBook
Author Sergej Rjasanow
Publisher Springer Science & Business Media
Pages 285
Release 2007-04-17
Genre Mathematics
ISBN 0387340424

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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.

Numerical Solution of Integral Equations

Numerical Solution of Integral Equations
Title Numerical Solution of Integral Equations PDF eBook
Author Michael A. Golberg
Publisher Springer Science & Business Media
Pages 428
Release 2013-11-11
Genre Mathematics
ISBN 1489925937

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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.

Methods in Nonlinear Integral Equations

Methods in Nonlinear Integral Equations
Title Methods in Nonlinear Integral Equations PDF eBook
Author R Precup
Publisher Springer Science & Business Media
Pages 221
Release 2013-03-09
Genre Mathematics
ISBN 9401599866

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Methods in Nonlinear Integral Equations presents several extremely fruitful methods for the analysis of systems and nonlinear integral equations. They include: fixed point methods (the Schauder and Leray-Schauder principles), variational methods (direct variational methods and mountain pass theorems), and iterative methods (the discrete continuation principle, upper and lower solutions techniques, Newton's method and the generalized quasilinearization method). Many important applications for several classes of integral equations and, in particular, for initial and boundary value problems, are presented to complement the theory. Special attention is paid to the existence and localization of solutions in bounded domains such as balls and order intervals. The presentation is essentially self-contained and leads the reader from classical concepts to current ideas and methods of nonlinear analysis.

The Numerical Solution of Integral Equations of the Second Kind

The Numerical Solution of Integral Equations of the Second Kind
Title The Numerical Solution of Integral Equations of the Second Kind PDF eBook
Author Kendall E. Atkinson
Publisher Cambridge University Press
Pages 572
Release 1997-06-28
Genre Mathematics
ISBN 0521583918

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

Handbook of Integral Equations

Handbook of Integral Equations
Title Handbook of Integral Equations PDF eBook
Author Andrei D. Polyanin
Publisher CRC Press
Pages 1143
Release 2008-02-12
Genre Mathematics
ISBN 0203881052

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Unparalleled in scope compared to the literature currently available, the Handbook of Integral Equations, Second Edition contains over 2,500 integral equations with solutions as well as analytical and numerical methods for solving linear and nonlinear equations. It explores Volterra, Fredholm, WienerHopf, Hammerstein, Uryson, and other equa