Integral Equations With Difference Kernels On Finite Intervals Ii
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Integral Equations With Difference Kernels On Finite Intervals
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Author : Lev A. Sakhnovich
language : en
Publisher: Springer Science & Business Media
Release Date : 1995-01-26
Integral Equations With Difference Kernels On Finite Intervals written by Lev A. Sakhnovich and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-01-26 with Mathematics categories.
Optimal synthesis, light scattering, and diffraction on a ribbon are just some of the applied problems for which integral equations with difference kernels are employed. The same equations are also met in important mathematical problems such as inverse spectral problems, nonlinear integral equations, and factorization of operators. On the basis of the operator identity method, the theory of integral operators with difference kernels is developed here, and the connection with many applied and theoretical problems is studied. A number of important examples are analyzed.
Integral Equations With Difference Kernels On Finite Intervals Ii
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Author : A. Leonard
language : en
Publisher:
Release Date : 1964
Integral Equations With Difference Kernels On Finite Intervals Ii written by A. Leonard and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1964 with Finite differences categories.
In this memorandum the authors present a technique for the solution of certain integral equations, on a finite interval of the real line, that arise in the theories of neutron transport, radiative transfer, and linearized gas dynamics. The kernels in the equations studied are functions of the difference of the arguments and involve an exponential factor. By the methods of singular integral equations, the result for the resolvent kernel is obtained in the form of simple quadratures and rapidly convergent Fredholmequations. (Author).
Integral Equations With Difference Kernels On Finite Intervals
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Author : Lev A Sakhnovich
language : en
Publisher:
Release Date : 1995-01-26
Integral Equations With Difference Kernels On Finite Intervals written by Lev A Sakhnovich and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-01-26 with categories.
Handbook Of Integral Equations
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Author : Andrei D. Polyanin
language : en
Publisher: CRC Press
Release Date : 2008-02-12
Handbook Of Integral Equations written by Andrei D. Polyanin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-02-12 with Mathematics categories.
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
Integral Equations With Difference Kernels On Finite Intervals
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Author : Lev A. Sakhnovich
language : en
Publisher: Birkhäuser
Release Date : 2015-05-05
Integral Equations With Difference Kernels On Finite Intervals written by Lev A. Sakhnovich and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-05 with Mathematics categories.
This book focuses on solving integral equations with difference kernels on finite intervals. The corresponding problem on the semiaxis was previously solved by N. Wiener–E. Hopf and by M.G. Krein. The problem on finite intervals, though significantly more difficult, may be solved using our method of operator identities. This method is also actively employed in inverse spectral problems, operator factorization and nonlinear integral equations. Applications of the obtained results to optimal synthesis, light scattering, diffraction, and hydrodynamics problems are discussed in this book, which also describes how the theory of operators with difference kernels is applied to stable processes and used to solve the famous M. Kac problems on stable processes. In this second edition these results are extensively generalized and include the case of all Levy processes. We present the convolution expression for the well-known Ito formula of the generator operator, a convolution expression that has proven to be fruitful. Furthermore we have added a new chapter on triangular representation, which is closely connected with previous results and includes a new important class of operators with non-trivial invariant subspaces. Numerous formulations and proofs have now been improved, and the bibliography has been updated to reflect more recent additions to the body of literature.
Computational Methods For Linear Integral Equations
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Author : Prem Kythe
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-28
Computational Methods For Linear Integral Equations written by Prem Kythe and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-28 with Mathematics categories.
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.
Technical Abstract Bulletin
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Author : Defense Documentation Center (U.S.)
language : en
Publisher:
Release Date : 1964
Technical Abstract Bulletin written by Defense Documentation Center (U.S.) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1964 with Military art and science categories.
Scientific And Technical Aerospace Reports
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Author :
language : en
Publisher:
Release Date : 1970
Scientific And Technical Aerospace Reports written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Aeronautics categories.
Inverse Problems And Nonlinear Evolution Equations
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Author : Alexander L. Sakhnovich
language : en
Publisher: Walter de Gruyter
Release Date : 2013-07-31
Inverse Problems And Nonlinear Evolution Equations written by Alexander L. Sakhnovich and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-31 with Mathematics categories.
This book is based on the method of operator identities and related theory of S-nodes, both developed by Lev Sakhnovich. The notion of the transfer matrix function generated by the S-node plays an essential role. The authors present fundamental solutions of various important systems of differential equations using the transfer matrix function, that is, either directly in the form of the transfer matrix function or via the representation in this form of the corresponding Darboux matrix, when Bäcklund–Darboux transformations and explicit solutions are considered. The transfer matrix function representation of the fundamental solution yields solution of an inverse problem, namely, the problem to recover system from its Weyl function. Weyl theories of selfadjoint and skew-selfadjoint Dirac systems, related canonical systems, discrete Dirac systems, system auxiliary to the N-wave equation and a system rationally depending on the spectral parameter are obtained in this way. The results on direct and inverse problems are applied in turn to the study of the initial-boundary value problems for integrable (nonlinear) wave equations via inverse spectral transformation method. Evolution of the Weyl function and solution of the initial-boundary value problem in a semi-strip are derived for many important nonlinear equations. Some uniqueness and global existence results are also proved in detail using evolution formulas. The reading of the book requires only some basic knowledge of linear algebra, calculus and operator theory from the standard university courses.
Iutam Symposium On Diffraction And Scattering In Fluid Mechanics And Elasticity
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Author : I. David Abrahams
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Iutam Symposium On Diffraction And Scattering In Fluid Mechanics And Elasticity written by I. David Abrahams and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Science categories.
These Conference Proceedings are intended to summarise the latest developments in diffraction and scattering theory as reported at the IU TAM Symposium on Diffraction and Scattering in Fluid Mechanics and Elasticity held in Manchester, England on 16-20 July 2000. This in formal meeting was organised to discuss mathematical advances, both from the theoretical and more applied points of view. However, its pri mary goal was to bring together groups of researchers working in dis parate application areas, but who nevertheless share common models, phenomenological features arising in such problems, and common math ematical tools. To this end, we were delighted to have four Plenary Speakers, Professors Allan Pierce, Ed Kerschen, Roger Grimshaw and John Willis FRS, who are undisputed leaders in the four thematic ar eas of our meeting (these are respectively acoustics, aeroacoustics, water or other free surface waves, elasticity). These Proceedings should offer an excellent vehicle for continuing the dialogue between these groups of researchers. The participants were invited because of their expertise and recent contributions to this field. Collectively, there were around 90 contrib utors to the Symposium from some 13 countries located all around the world. These included 45 speakers, 35 co-authors and about 10 other delegates. Individuals came from many of the major international cen tres of excellence in the field of scattering theory.