Computational Methods for Linear Integral Equations
Kythe, Prem, Puri, Pratap
2002, XVIII, 508 p.
A product of Birkhäuser Basel
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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.
Preface Notation Introduction Eigenvalue Problems Equations of the Second Kind Classical Methods for FK2 Variational Methods Iteration Methods Singular Equations Weakly Singular Equations Cauchy Singular Equations Sinc-Galerkin Methods Equations of the First Kind Inversion of Laplace Transforms A. Quadrature Rules B. Orthogonal Polynomials C. Whittaker's Cardinal Functions D. Singular Integrals Bibliography Subject Index