Solution Methods for Integral Equations
Author : M. A. Goldberg
Publisher : Springer Science & Business Media
Page : 351 pages
File Size : 34,51 MB
Release : 2013-11-21
Category : Science
ISBN : 1475714661
Computational Methods for Integral Equations
Author : L. M. Delves
Publisher : CUP Archive
Page : 392 pages
File Size : 45,88 MB
Release : 1985
Category : Mathematics
ISBN : 9780521357968
Book Description
This textbook provides a readable account of techniques for numerical solutions.
The Fast Solution of Boundary Integral Equations
Author : Sergej Rjasanow
Publisher : Springer Science & Business Media
Page : 285 pages
File Size : 41,66 MB
Release : 2007-04-17
Category : Mathematics
ISBN : 0387340424
Book Description
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
Author : Michael A. Golberg
Publisher : Springer Science & Business Media
Page : 428 pages
File Size : 23,35 MB
Release : 2013-11-11
Category : Mathematics
ISBN : 1489925937
Book Description
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.
Handbook of Integral Equations
Author : Andrei D. Polyanin
Publisher : CRC Press
Page : 1143 pages
File Size : 14,91 MB
Release : 2008-02-12
Category : Mathematics
ISBN : 0203881052
Book Description
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
Computational Methods for Linear Integral Equations
Author : Prem Kythe
Publisher : Springer Science & Business Media
Page : 525 pages
File Size : 27,45 MB
Release : 2011-06-28
Category : Mathematics
ISBN : 1461201012
Book Description
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.
Methods in Nonlinear Integral Equations
Author : R Precup
Publisher : Springer Science & Business Media
Page : 221 pages
File Size : 25,70 MB
Release : 2013-03-09
Category : Mathematics
ISBN : 9401599866
Book Description
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
Author : Kendall E. Atkinson
Publisher : Cambridge University Press
Page : 572 pages
File Size : 14,31 MB
Release : 1997-06-28
Category : Mathematics
ISBN : 0521583918
Book Description
This book provides an extensive introduction to the numerical solution of a large class of integral equations.
Integral Equation Methods in Scattering Theory
Author : David Colton
Publisher : SIAM
Page : 286 pages
File Size : 37,63 MB
Release : 2013-11-15
Category : Mathematics
ISBN : 1611973155
Book Description
This classic book provides a rigorous treatment of the Riesz?Fredholm theory of compact operators in dual systems, followed by a derivation of the jump relations and mapping properties of scalar and vector potentials in spaces of continuous and H?lder continuous functions. These results are then used to study scattering problems for the Helmholtz and Maxwell equations. Readers will benefit from a full discussion of the mapping properties of scalar and vector potentials in spaces of continuous and H?lder continuous functions, an in-depth treatment of the use of boundary integral equations to solve scattering problems for acoustic and electromagnetic waves, and an introduction to inverse scattering theory with an emphasis on the ill-posedness and nonlinearity of the inverse scattering problem.
Linear and Nonlinear Integral Equations
Author : Abdul-Majid Wazwaz
Publisher : Springer Science & Business Media
Page : 639 pages
File Size : 48,80 MB
Release : 2011-11-24
Category : Mathematics
ISBN : 3642214495
Book Description
Linear and Nonlinear Integral Equations: Methods and Applications is a self-contained book divided into two parts. Part I offers a comprehensive and systematic treatment of linear integral equations of the first and second kinds. The text brings together newly developed methods to reinforce and complement the existing procedures for solving linear integral equations. The Volterra integral and integro-differential equations, the Fredholm integral and integro-differential equations, the Volterra-Fredholm integral equations, singular and weakly singular integral equations, and systems of these equations, are handled in this part by using many different computational schemes. Selected worked-through examples and exercises will guide readers through the text. Part II provides an extensive exposition on the nonlinear integral equations and their varied applications, presenting in an accessible manner a systematic treatment of ill-posed Fredholm problems, bifurcation points, and singular points. Selected applications are also investigated by using the powerful Padé approximants. This book is intended for scholars and researchers in the fields of physics, applied mathematics and engineering. It can also be used as a text for advanced undergraduate and graduate students in applied mathematics, science and engineering, and related fields. Dr. Abdul-Majid Wazwaz is a Professor of Mathematics at Saint Xavier University in Chicago, Illinois, USA.
