Ebook: Computational Methods for Linear Integral Equations
- Tags: Integral Equations, Numeric Computing, Several Complex Variables and Analytic Spaces
- Year: 2002
- Publisher: Birkhäuser Basel
- Edition: 1
- Language: English
- 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.
Content:
Front Matter....Pages i-xviii
Introduction....Pages 1-43
Eigenvalue Problems....Pages 44-89
Equations of the Second Kind....Pages 90-105
Classical Methods for FK2....Pages 106-129
Variational Methods....Pages 130-145
Iteration Methods....Pages 146-174
Singular Equations....Pages 175-212
Weakly Singular Equations....Pages 213-251
Cauchy Singular Equations....Pages 252-285
Sinc-Galerkin Methods....Pages 286-320
Equations of the First Kind....Pages 321-374
Inversion of Laplace Transforms....Pages 375-415
Back Matter....Pages 416-508
Content:
Front Matter....Pages i-xviii
Introduction....Pages 1-43
Eigenvalue Problems....Pages 44-89
Equations of the Second Kind....Pages 90-105
Classical Methods for FK2....Pages 106-129
Variational Methods....Pages 130-145
Iteration Methods....Pages 146-174
Singular Equations....Pages 175-212
Weakly Singular Equations....Pages 213-251
Cauchy Singular Equations....Pages 252-285
Sinc-Galerkin Methods....Pages 286-320
Equations of the First Kind....Pages 321-374
Inversion of Laplace Transforms....Pages 375-415
Back Matter....Pages 416-508
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